pca is a python package to perform Principal Component Analysis and to examine the variance in-depth. The core of PCA is build on sklearn to find maximum compatibility when combining with other packages. But this package can do a lot more. Besides the regular Principal Components, it also integrates SparsePCA, TruncatedSVD, and provides the information that can be extracted from the components.
pca
Functionalities of PCA are:
diff --git a/docs/pages/html/Additional_Information.html b/docs/pages/html/Additional_Information.html index 345bf1f..9c7d6df 100644 --- a/docs/pages/html/Additional_Information.html +++ b/docs/pages/html/Additional_Information.html @@ -1,20 +1,22 @@ + + - + - + Additional Information — pca pca documentation - - - - + + + + - - - + + + + + @@ -33,9 +35,6 @@ pca - - 2.0.1 - @@ -134,7 +133,7 @@ -Additional Information +Additional Information PCA_lecture -<html class="writer-html5" lang="en" > +<html class="writer-html5" lang="en" data-content_root="./"> <head> - <meta charset="utf-8" /><meta name="generator" content="Docutils 0.18.1: http://docutils.sourceforge.net/" /> + <meta charset="utf-8" /><meta name="viewport" content="width=device-width, initial-scale=1" /> <meta name="viewport" content="width=device-width, initial-scale=1.0" /> <title>Algorithm — pca pca documentation</title> - <link rel="stylesheet" href="_static/pygments.css" type="text/css" /> - <link rel="stylesheet" href="_static/css/theme.css" type="text/css" /> - <link rel="stylesheet" href="_static/css/custom.css" type="text/css" /> - <!--[if lt IE 9]> - <script src="_static/js/html5shiv.min.js"></script> - <![endif]--> + <link rel="stylesheet" type="text/css" href="_static/pygments.css?v=fa44fd50" /> + <link rel="stylesheet" type="text/css" href="_static/css/theme.css?v=e59714d7" /> + <link rel="stylesheet" type="text/css" href="_static/css/custom.css?v=e0179649" /> + - <script data-url_root="./" id="documentation_options" src="_static/documentation_options.js"></script> - <script src="_static/doctools.js"></script> - <script src="_static/sphinx_highlight.js"></script> + <script src="_static/jquery.js?v=5d32c60e"></script> + <script src="_static/_sphinx_javascript_frameworks_compat.js?v=2cd50e6c"></script> + <script src="_static/documentation_options.js?v=5d2b88f6"></script> + <script src="_static/doctools.js?v=9bcbadda"></script> + <script src="_static/sphinx_highlight.js?v=dc90522c"></script> <script src="_static/js/theme.js"></script> <link rel="index" title="Index" href="genindex.html" /> <link rel="search" title="Search" href="search.html" /> @@ -33,9 +35,6 @@ <a href="index.html" class="icon icon-home"> pca </a> - <div class="version"> - 2.0.1 - </div> <div role="search"> <form id="rtd-search-form" class="wy-form" action="search.html" method="get"> <input type="text" name="q" placeholder="Search docs" aria-label="Search docs" /> @@ -134,14 +133,14 @@ <div itemprop="articleBody"> <section id="algorithm"> -<h1>Algorithm<a class="headerlink" href="#algorithm" title="Permalink to this heading"></a></h1> +<h1>Algorithm<a class="headerlink" href="#algorithm" title="Link to this heading"></a></h1> <p>Principal Component Analysis, or PCA, is a dimensionality-reduction method that is often used to reduce the dimensionality of large data sets.</p> <p>Reducing the number of variables of a data set naturally comes at the expense of accuracy, but the trick in dimensionality reduction is to trade a little accuracy for <em>simplicity</em>. Because smaller data sets are easier to explore and visualize, it becomes easier and faster to analyze your data.</p> <p>The idea of PCA is simple — <strong>reduce the number of variables</strong> of a data set, while <strong>preserving</strong> as much <strong>information</strong> as possible.</p> <p>The <code class="docutils literal notranslate"><span class="pre">pca</span></code> library contains various functionalities to carefully examine the data, which can help for better understanding and removal of redundant information.</p> </section> <section id="standardization"> -<h1>Standardization<a class="headerlink" href="#standardization" title="Permalink to this heading"></a></h1> +<h1>Standardization<a class="headerlink" href="#standardization" title="Link to this heading"></a></h1> <p>Feature scaling through standardization (or Z-score normalization) is an important preprocessing step for many machine learning algorithms. Standardization involves rescaling the features such that they have the properties of a standard normal distribution with a mean of zero and a standard deviation of one. The standardization step depends on the type of variables, the distribution of the data, and also your aim. In general, the standardizing step is to range the continuous initial variables so that each one of them contributes <em>equally</em> to the analysis.</p> <p>It is utterly important to carefully standardize your data because PCA works under the assumption that the data is <em>normal distributed</em>, and is very <em>sensitive</em> to the variance of the variables. Or in other words, large differences between the ranges of variables will dominate over those with small ranges. Let me explain this by example; a variable that ranges between 0 and 100 will dominate over a variable that ranges between 0 and 1. Transforming the data to comparable scales can prevent this issue.</p> <p>The most straightforward manner for standardization is by computing the <em>Z-scores</em> or <em>Standardized scores</em>. @@ -178,7 +177,7 @@ <h1>Standardization<a class="headerlink" href="#standardization" title="Permalin </div> <p>An example of the differences of feature reduction using PCA with and without standardization.</p> <table class="docutils align-center" id="id1"> -<caption><span class="caption-text">Without standardization (left) and with standardization (right)</span><a class="headerlink" href="#id1" title="Permalink to this table"></a></caption> +<caption><span class="caption-text">Without standardization (left) and with standardization (right)</span><a class="headerlink" href="#id1" title="Link to this table"></a></caption> <tbody> <tr class="row-odd"><td><p><img alt="figA3" src="_images/wine_no_standardization.png" /></p></td> <td><p><img alt="figA4" src="_images/wine_yes_standardization.png" /></p></td> @@ -187,7 +186,7 @@ <h1>Standardization<a class="headerlink" href="#standardization" title="Permalin </table> </section> <section id="explained-variance"> -<h1>Explained Variance<a class="headerlink" href="#explained-variance" title="Permalink to this heading"></a></h1> +<h1>Explained Variance<a class="headerlink" href="#explained-variance" title="Link to this heading"></a></h1> <p>Before jumping into the <strong>explained variance</strong>, we first need to understand what principal components are.</p> <p><strong>Principal components</strong> are new (latent) <strong>variables</strong> that are constructed as <strong>linear combinations</strong> or <strong>mixtures</strong> of the initial variables. These combinations are in such a way that the new variables (i.e., principal components) are uncorrelated and most of the information within the initial variables is squeezed or compressed into the first components. <strong>Explained variance</strong> refers to the variance explained by each of the principal components (eigenvectors). By organizing information Principal</p> @@ -206,20 +205,25 @@ <h1>Explained Variance<a class="headerlink" href="#explained-variance" title="Pe </pre></div> </div> <p>In this example we have 13 variables in the <strong>wine</strong> dataset, and thus 13 dimensions. PCA will optimize to store maximum variance in the first PC, then in the second and so on, until having something like shown in the plot below. This plot provides insights in the amount of <em>information</em> or <em>explained variance</em> in the data. We can clearly see that the 1st PC contains almost 36% of explained variance in total. With the top 10 PCs we cover 97.9% of all variance.</p> -<a class="reference internal image-reference" href="_images/wine_explained_variance.png"><img alt="_images/wine_explained_variance.png" class="align-center" src="_images/wine_explained_variance.png" style="width: 600px;" /></a> +<a class="reference internal image-reference" href="_images/wine_explained_variance.png"><img alt="_images/wine_explained_variance.png" class="align-center" src="_images/wine_explained_variance.png" style="width: 600px;" /> +</a> <p>There are as many principal components as there are variables in the data. The <strong>explained variance plot</strong> can therefore never have more then 13 PCs in this case. Principal components are constructed in such a manner that the first principal component accounts for the largest possible variance in the data set.</p> </section> <section id="loadings"> -<h1>Loadings<a class="headerlink" href="#loadings" title="Permalink to this heading"></a></h1> +<h1>Loadings<a class="headerlink" href="#loadings" title="Link to this heading"></a></h1> <p>It is important to realize that principal components are less interpretable and don’t have any real meaning since they are constructed as <strong>linear combinations</strong> of the initial variables. But we can analyze the <strong>loadings</strong> which describe the importance of the independent variables. The first principal component (Y1) is given by a linear combination of the variables X1, X2, …, Xp, and is calculated such that it accounts for the greatest possible variance in the data.</p> -<a class="reference internal image-reference" href="_images/PCAequation1.png"><img alt="_images/PCAequation1.png" src="_images/PCAequation1.png" style="width: 300px;" /></a> +<a class="reference internal image-reference" href="_images/PCAequation1.png"><img alt="_images/PCAequation1.png" src="_images/PCAequation1.png" style="width: 300px;" /> +</a> <p>Of course, one could make the variance of Y1 as large as possible by choosing large values for the weights a11, a12, … a1p. To prevent this, the sum of squares of the weights is constrained to be 1.</p> -<a class="reference internal image-reference" href="_images/PCAequation3.png"><img alt="_images/PCAequation3.png" src="_images/PCAequation3.png" style="width: 300px;" /></a> +<a class="reference internal image-reference" href="_images/PCAequation3.png"><img alt="_images/PCAequation3.png" src="_images/PCAequation3.png" style="width: 300px;" /> +</a> <p>For example, let’s assume that the scatter plot of our data set is as shown below. Can we guess the first principal component? Yes, it’s approximately the line that matches the purple marks because it goes through the origin and it’s the line in which the projection of the points (red dots) is the most spread out. Or mathematically speaking, it’s the line that maximizes the variance which is the average of the squared distances from the projected points (red dots) to the origin.</p> -<a class="reference internal image-reference" href="_images/PCA_rotation.gif"><img alt="_images/PCA_rotation.gif" class="align-center" src="_images/PCA_rotation.gif" style="width: 900px;" /></a> +<a class="reference internal image-reference" href="_images/PCA_rotation.gif"><img alt="_images/PCA_rotation.gif" class="align-center" src="_images/PCA_rotation.gif" style="width: 900px;" /> +</a> <p>The second principal component is calculated in the same way, with the conditions that it is uncorrelated with (i.e., perpendicular to) the first principal component and that it accounts for the next highest variance.</p> -<a class="reference internal image-reference" href="_images/PCAequation4.png"><img alt="_images/PCAequation4.png" src="_images/PCAequation4.png" style="width: 300px;" /></a> +<a class="reference internal image-reference" href="_images/PCAequation4.png"><img alt="_images/PCAequation4.png" src="_images/PCAequation4.png" style="width: 300px;" /> +</a> <p>This continues until a total of <strong>p</strong> principal components have been calculated, that is, the number of principal components is the same as the original number of variables. At this point, the total variance on all of the principal components will equal the total variance among all of the variables. In this way, all of the information contained in the original data is preserved; no information is lost: PCA is just a rotation of the data.</p> <p>The elements of an eigenvector, that is, the values within a particular row of matrix, are the weights <strong>aij</strong>. These values are called the <strong>loadings</strong>, and they describe how much each variable contributes to a particular principal component.</p> <blockquote> @@ -249,10 +253,11 @@ <h1>Loadings<a class="headerlink" href="#loadings" title="Permalink to this head </pre></div> </div> <p>First of all, we see a nice seperation of the 3 wine classes (red, orange and gray samples). In the middle of the plot we see various arrows. Each of the arrows describes its story in the Principal Components. The angle of the arrow describes the contribution of the variable that is seen in the particular PC. The length describes the strength of the loading.</p> -<a class="reference internal image-reference" href="_images/wine_biplot.png"><img alt="_images/wine_biplot.png" class="align-center" src="_images/wine_biplot.png" style="width: 600px;" /></a> +<a class="reference internal image-reference" href="_images/wine_biplot.png"><img alt="_images/wine_biplot.png" class="align-center" src="_images/wine_biplot.png" style="width: 600px;" /> +</a> </section> <section id="examination-of-the-loadings"> -<h1>Examination of the loadings<a class="headerlink" href="#examination-of-the-loadings" title="Permalink to this heading"></a></h1> +<h1>Examination of the loadings<a class="headerlink" href="#examination-of-the-loadings" title="Link to this heading"></a></h1> <p>Let’s examine the <strong>loadings</strong> (arrows) a bit more to understand what is going on in the distribution of the samples given the variables. The variable <strong>flavanoids</strong> has a positive loading and explaines mostly the variance in the first PC1 (it is almost a horizontal line). If we would color the samples in the scatter plot based on <strong>flavanoids</strong> values, we expect to see a distinction between samples that are respectively left and right side of the scatter plot.</p> <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="c1"># Grap the values for flavanoids</span> <span class="n">X_feat</span> <span class="o">=</span> <span class="n">X</span><span class="p">[:,</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">col_labels</span><span class="p">)</span><span class="o">==</span><span class="s1">'flavanoids'</span><span class="p">]</span> @@ -268,7 +273,7 @@ <h1>Examination of the loadings<a class="headerlink" href="#examination-of-the-l </pre></div> </div> <table class="docutils align-center" id="id2"> -<caption><span class="caption-text">Color on flavanoids</span><a class="headerlink" href="#id2" title="Permalink to this table"></a></caption> +<caption><span class="caption-text">Color on flavanoids</span><a class="headerlink" href="#id2" title="Link to this table"></a></caption> <tbody> <tr class="row-odd"><td><p><img alt="figA1" src="_images/wine_flavanoids.png" /></p></td> <td><p><img alt="figA2" src="_images/wine_flavanoids3d.png" /></p></td> @@ -290,7 +295,7 @@ <h1>Examination of the loadings<a class="headerlink" href="#examination-of-the-l </pre></div> </div> <table class="docutils align-center" id="id3"> -<caption><span class="caption-text">Color on alcohol</span><a class="headerlink" href="#id3" title="Permalink to this table"></a></caption> +<caption><span class="caption-text">Color on alcohol</span><a class="headerlink" href="#id3" title="Link to this table"></a></caption> <tbody> <tr class="row-odd"><td><p><img alt="figA8" src="_images/wine_alcohol.png" /></p></td> <td><p><img alt="figA9" src="_images/wine_alcohol3d.png" /></p></td> @@ -299,7 +304,7 @@ <h1>Examination of the loadings<a class="headerlink" href="#examination-of-the-l </table> </section> <section id="best-performing-features"> -<h1>Best Performing Features<a class="headerlink" href="#best-performing-features" title="Permalink to this heading"></a></h1> +<h1>Best Performing Features<a class="headerlink" href="#best-performing-features" title="Link to this heading"></a></h1> <p>Extracting the best performing features is based on the loadings of the Principal Components, which are readily computed. The information is stored in the object itself. We can extract it as following:</p> <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="c1"># Print the top features.</span> diff --git a/docs/pages/html/Coding quality.html b/docs/pages/html/Coding quality.html index 516ac4b..006b9ef 100644 --- a/docs/pages/html/Coding quality.html +++ b/docs/pages/html/Coding quality.html @@ -1,20 +1,22 @@ + + <!DOCTYPE html> -<html class="writer-html5" lang="en" > +<html class="writer-html5" lang="en" data-content_root="./"> <head> - <meta charset="utf-8" /><meta name="generator" content="Docutils 0.18.1: http://docutils.sourceforge.net/" /> + <meta charset="utf-8" /><meta name="viewport" content="width=device-width, initial-scale=1" /> <meta name="viewport" content="width=device-width, initial-scale=1.0" /> <title>Coding quality — pca pca documentation</title> - <link rel="stylesheet" href="_static/pygments.css" type="text/css" /> - <link rel="stylesheet" href="_static/css/theme.css" type="text/css" /> - <link rel="stylesheet" href="_static/css/custom.css" type="text/css" /> - <!--[if lt IE 9]> - <script src="_static/js/html5shiv.min.js"></script> - <![endif]--> + <link rel="stylesheet" type="text/css" href="_static/pygments.css?v=fa44fd50" /> + <link rel="stylesheet" type="text/css" href="_static/css/theme.css?v=e59714d7" /> + <link rel="stylesheet" type="text/css" href="_static/css/custom.css?v=e0179649" /> + - <script data-url_root="./" id="documentation_options" src="_static/documentation_options.js"></script> - <script src="_static/doctools.js"></script> - <script src="_static/sphinx_highlight.js"></script> + <script src="_static/jquery.js?v=5d32c60e"></script> + <script src="_static/_sphinx_javascript_frameworks_compat.js?v=2cd50e6c"></script> + <script src="_static/documentation_options.js?v=5d2b88f6"></script> + <script src="_static/doctools.js?v=9bcbadda"></script> + <script src="_static/sphinx_highlight.js?v=dc90522c"></script> <script src="_static/js/theme.js"></script> <link rel="index" title="Index" href="genindex.html" /> <link rel="search" title="Search" href="search.html" /> @@ -33,9 +35,6 @@ <a href="index.html" class="icon icon-home"> pca </a> - <div class="version"> - 2.0.1 - </div> <div role="search"> <form id="rtd-search-form" class="wy-form" action="search.html" method="get"> <input type="text" name="q" placeholder="Search docs" aria-label="Search docs" /> @@ -140,50 +139,50 @@ <div itemprop="articleBody"> <section id="coding-quality"> -<h1>Coding quality<a class="headerlink" href="#coding-quality" title="Permalink to this heading"></a></h1> +<h1>Coding quality<a class="headerlink" href="#coding-quality" title="Link to this heading"></a></h1> <p>I value software quality. Higher quality software has fewer defects, better security, and better performance, which leads to happier users who can work more effectively. Code reviews are an effective method for improving software quality. McConnell (2004) suggests that unit testing finds approximately 25% of defects, function testing 35%, integration testing 45%, and code review 55-60%. While this means that none of these methods are good enough on their own and that they should be combined, clearly code review is an essential tool here.</p> <p>This library is therefore developed with several techniques, such as coding styling, low complexity, docstrings, reviews, and unit tests. Such conventions are helpfull to improve the quality, make the code cleaner and more understandable but alos to trace future bugs, and spot syntax errors.</p> <section id="library"> -<h2>Library<a class="headerlink" href="#library" title="Permalink to this heading"></a></h2> +<h2>Library<a class="headerlink" href="#library" title="Link to this heading"></a></h2> <p>The file structure of the generated package looks like:</p> <div class="highlight-bash notranslate"><div class="highlight"><pre><span></span>path/to/pca/ -├── .editorconfig -├── .gitignore -├── .pre-commit-config.yml -├── .prospector.yml -├── CHANGELOG.rst -├── docs -│ ├── conf.py -│ ├── index.rst -│ └── ... -├── LICENSE -├── MANIFEST.in -├── NOTICE -├── pca -│ ├── __init__.py -│ ├── __version__.py -│ └── pca.py -├── README.md -├── requirements.txt -├── setup.cfg -├── setup.py -└── tests - ├── __init__.py - └── test_pca.py +├──<span class="w"> </span>.editorconfig +├──<span class="w"> </span>.gitignore +├──<span class="w"> </span>.pre-commit-config.yml +├──<span class="w"> </span>.prospector.yml +├──<span class="w"> </span>CHANGELOG.rst +├──<span class="w"> </span>docs +│<span class="w"> </span>├──<span class="w"> </span>conf.py +│<span class="w"> </span>├──<span class="w"> </span>index.rst +│<span class="w"> </span>└──<span class="w"> </span>... +├──<span class="w"> </span>LICENSE +├──<span class="w"> </span>MANIFEST.in +├──<span class="w"> </span>NOTICE +├──<span class="w"> </span>pca +│<span class="w"> </span>├──<span class="w"> </span>__init__.py +│<span class="w"> </span>├──<span class="w"> </span>__version__.py +│<span class="w"> </span>└──<span class="w"> </span>pca.py +├──<span class="w"> </span>README.md +├──<span class="w"> </span>requirements.txt +├──<span class="w"> </span>setup.cfg +├──<span class="w"> </span>setup.py +└──<span class="w"> </span>tests +<span class="w"> </span>├──<span class="w"> </span>__init__.py +<span class="w"> </span>└──<span class="w"> </span>test_pca.py </pre></div> </div> </section> <section id="style"> -<h2>Style<a class="headerlink" href="#style" title="Permalink to this heading"></a></h2> +<h2>Style<a class="headerlink" href="#style" title="Link to this heading"></a></h2> <p>This library is compliant with the PEP-8 standards. PEP stands for Python Enhancement Proposal and sets a baseline for the readability of Python code. Each public function contains a docstring that is based on numpy standards.</p> </section> <section id="complexity"> -<h2>Complexity<a class="headerlink" href="#complexity" title="Permalink to this heading"></a></h2> +<h2>Complexity<a class="headerlink" href="#complexity" title="Link to this heading"></a></h2> <p>This library has been developed by using measures that help decreasing technical debt. Developing software with low(er) technical dept may take extra development time, but has many advantages:</p> <ul class="simple"> @@ -194,7 +193,7 @@ <h2>Complexity<a class="headerlink" href="#complexity" title="Permalink to this </ul> </section> <section id="unit-tests"> -<h2>Unit tests<a class="headerlink" href="#unit-tests" title="Permalink to this heading"></a></h2> +<h2>Unit tests<a class="headerlink" href="#unit-tests" title="Link to this heading"></a></h2> <p>The use of unit tests is essential to garantee a consistent output of developed functions. The following tests are secured using <code class="xref py py-func docutils literal notranslate"><span class="pre">tests.test_pca()</span></code>:</p> <ul class="simple"> diff --git a/docs/pages/html/Documentation.html b/docs/pages/html/Documentation.html index 933e4d6..6ea5da0 100644 --- a/docs/pages/html/Documentation.html +++ b/docs/pages/html/Documentation.html @@ -1,20 +1,22 @@ + + <!DOCTYPE html> -<html class="writer-html5" lang="en" > +<html class="writer-html5" lang="en" data-content_root="./"> <head> - <meta charset="utf-8" /><meta name="generator" content="Docutils 0.18.1: http://docutils.sourceforge.net/" /> + <meta charset="utf-8" /><meta name="viewport" content="width=device-width, initial-scale=1" /> <meta name="viewport" content="width=device-width, initial-scale=1.0" /> <title>Sponsor — pca pca documentation</title> - <link rel="stylesheet" href="_static/pygments.css" type="text/css" /> - <link rel="stylesheet" href="_static/css/theme.css" type="text/css" /> - <link rel="stylesheet" href="_static/css/custom.css" type="text/css" /> - <!--[if lt IE 9]> - <script src="_static/js/html5shiv.min.js"></script> - <![endif]--> + <link rel="stylesheet" type="text/css" href="_static/pygments.css?v=fa44fd50" /> + <link rel="stylesheet" type="text/css" href="_static/css/theme.css?v=e59714d7" /> + <link rel="stylesheet" type="text/css" href="_static/css/custom.css?v=e0179649" /> + - <script data-url_root="./" id="documentation_options" src="_static/documentation_options.js"></script> - <script src="_static/doctools.js"></script> - <script src="_static/sphinx_highlight.js"></script> + <script src="_static/jquery.js?v=5d32c60e"></script> + <script src="_static/_sphinx_javascript_frameworks_compat.js?v=2cd50e6c"></script> + <script src="_static/documentation_options.js?v=5d2b88f6"></script> + <script src="_static/doctools.js?v=9bcbadda"></script> + <script src="_static/sphinx_highlight.js?v=dc90522c"></script> <script src="_static/js/theme.js"></script> <link rel="index" title="Index" href="genindex.html" /> <link rel="search" title="Search" href="search.html" /> @@ -33,9 +35,6 @@ <a href="index.html" class="icon icon-home"> pca </a> - <div class="version"> - 2.0.1 - </div> <div role="search"> <form id="rtd-search-form" class="wy-form" action="search.html" method="get"> <input type="text" name="q" placeholder="Search docs" aria-label="Search docs" /> @@ -134,7 +133,7 @@ <div itemprop="articleBody"> <section id="sponsor"> -<h1>Sponsor<a class="headerlink" href="#sponsor" title="Permalink to this heading"></a></h1> +<h1>Sponsor<a class="headerlink" href="#sponsor" title="Link to this heading"></a></h1> <div class="admonition tip"> <p class="admonition-title">Tip</p> <p>You can support this project in various ways ❤️</p> @@ -142,36 +141,38 @@ <h1>Sponsor<a class="headerlink" href="#sponsor" title="Permalink to this headin <li><p>Become a <a class="reference external" href="https://github.com/sponsors/erdogant?o=esb/">Sponsor</a>!</p></li> <li><p><a class="reference external" href="https://www.buymeacoffee.com/erdogant">Buy</a> me a coffee! I ❤️ coffee :)</p></li> <li><p><a class="reference external" href="https://erdogant.github.io/donate/?currency=USD&amount=1000">Donate</a> in Bitcoin.</p></li> -<li><p>Follow me on medium! Go to my <a class="reference external" href="https://erdogant.medium.com/">medium profile</a> and press <em>follow</em>.</p></li> +<li><p>Follow me on Medium! Go to my <a class="reference external" href="https://erdogant.medium.com/">medium profile</a> and press <em>follow</em>.</p></li> +<li><p>Subscribe to me on Substack! Go to my <a class="reference external" href="https://erdogant.substack.com/">profile</a> where you can <em>subscribe</em>.</p></li> <li><p><strong>Star</strong> this repo at the github page.</p></li> +<li><p>You can also buy a digital educational product over <a class="reference external" href="https://erdogant.gumroad.com/">here</a>.</p></li> <li><p>Other contributions can be in the form of feature requests, idea discussions, reporting bugs, opening pull requests.</p></li> </ul> <p>Cheers Mate.</p> </div> <iframe src="https://github.com/sponsors/erdogant/button" title="Sponsor erdogant" height="35" width="116" style="border: 0;"> -Blog +Blog Note Read more details and the usage in the Medium Blog: What are PCA loadings and Biplots? -Github +Github Note Source code of pca can be found at Github -Colab Notebook +Colab Notebook Note Experiment with pca library using the Colab notebook. -Citing +Citing Note Bibtex can be found at the right side at the github page. diff --git a/docs/pages/html/Examples.html b/docs/pages/html/Examples.html index 01adbfa..9e80ac7 100644 --- a/docs/pages/html/Examples.html +++ b/docs/pages/html/Examples.html @@ -1,20 +1,22 @@ + + - + - + Quickstart — pca pca documentation - - - - + + + + - - - + + + + + @@ -33,9 +35,6 @@ pca - - 2.0.1 - @@ -144,7 +143,7 @@ -Quickstart +Quickstart A quick example how perform feature reduction using pca. import numpy as np from sklearn.datasets import load_iris @@ -187,7 +186,7 @@ Quickstart -Compute explained variance +Compute explained variance After the fit_transform, the cumulative expained variance is stored together with the explained variance per PC. # Cumulative explained variance print(model.results['explained_var']) @@ -201,10 +200,11 @@ Compute explained variancefig, ax = model.plot() - + + -PCs that cover 95% of the explained variance +PCs that cover 95% of the explained variance The number of PCs can be reduced by setting the n_components parameter. Note that the number of components can never be larger than the number of variables in your dataset. By setting n_components larger than 1, a feature reduction will be performed to exactly that number of components. By setting n_components smaller than 1, it describes the percentage of explained variance that needs to be covered at least. Or in other words, by setting n_components=0.95, the number of components are extracted that cover at least 95% of the explained variance. # Reduce the data towards 3 PCs model = pca(n_components=3) @@ -215,7 +215,7 @@ PCs that cover 95% of the explained variance -Scatter plot +Scatter plot # 2D plot fig, ax = model.scatter() @@ -224,7 +224,7 @@ Scatter plot -Color on alcohol +Color on alcohol @@ -233,7 +233,7 @@ Scatter plot -Biplot +Biplot # 2D plot fig, ax = model.biplot(n_feat=4, PC=[0,1]) @@ -241,11 +241,12 @@ Biplotfig, ax = model.biplot3d(n_feat=2, PC=[0,1,2]) - + + -Demonstration of feature importance +Demonstration of feature importance This example is created to showcase the working of extracting features that are most important in a PCA reduction. We will create random variables with increasingly more variance. The first feature (f1) will have most of the variance, followed by feature 2 (f2) etc. # Print the top features. @@ -294,14 +295,15 @@ Demonstration of feature importance -Explained variance plot +Explained variance plot model.plot() - + + -Biplot +Biplot Make the biplot. It can be nicely seen that the first feature with most variance (f1), is almost horizontal in the plot, whereas the second most variance (f2) is almost vertical. This is expected because most of the variance is in f1, followed by f2 etc. Biplot in 3d. Here we see the nice addition of the expected f3 in the plot in the z-direction. # 2d plot ax = model.biplot(n_feat=10, legend=False) @@ -311,7 +313,7 @@ Biplot -Color on alcohol +Color on alcohol @@ -321,10 +323,10 @@ Biplot -Analyzing Discrete datasets +Analyzing Discrete datasets Analyzing datasets that have continuous and catagorical values can be challanging. To demonstrate how to do this, I will use the Titanic dataset. We need to pip install df2onehot first. -pip install df2onehot +pip install df2onehot import pca @@ -383,7 +385,7 @@ Analyzing Discrete datasets -Map unseen datapoints into fitted space +Map unseen datapoints into fitted space After fitting variables into the new principal component space, we can map new unseen samples into this space too. However, there is also normalization step which can be tricky because you now need standardize the values of the unseen samples first based on the previously performed standardization. This step is also integrated in the pca library by simply setting the parameter normalize=True. # Load libraries import matplotlib.pyplot as plt @@ -422,10 +424,11 @@ Map unseen datapoints into fitted spaceax.scatter(PCnew.iloc[:, 0], PCnew.iloc[:, 1], marker='x', s=200) - + + -Normalizing out PCs +Normalizing out PCs Normalize your data using the principal components. As an example, suppose there is (technical) variation in the fist component and you want that out. This function transforms the data using the components that you want, e.g., starting from the 2nd PC, up to the OC that contains at least 95% of the explained variance. print(X.shape) (178, 13) @@ -443,7 +446,7 @@ Normalizing out PCs -Colors in plots +Colors in plots The default colors that are used in the plots depend on how much information is provided at start. There are many parameters to change the colors in the plots. Here I will demonstrate some of the possibilities. First, we will load the data and import the libraries. @@ -476,7 +479,7 @@ Colors in plots -Left: Default plot using the provided classlabels. Right: Color on custom cmap. +Left: Default plot using the provided classlabels. Right: Color on custom cmap. @@ -498,7 +501,7 @@ Colors in plots -Left: Mark some points on y and use cmap. Right: Specify the colors manually. +Left: Mark some points on y and use cmap. Right: Specify the colors manually. @@ -514,7 +517,7 @@ Colors in plots -Left: Remove scatterpoints from plot. Right: Gradient with the used cmap. +Left: Remove scatterpoints from plot. Right: Gradient with the used cmap. @@ -539,7 +542,7 @@ Colors in plots -Fig as input to make iterative changes. +Fig as input to make iterative changes. diff --git a/docs/pages/html/Installation.html b/docs/pages/html/Installation.html index d2fd9ff..8a0f6d2 100644 --- a/docs/pages/html/Installation.html +++ b/docs/pages/html/Installation.html @@ -1,20 +1,22 @@ + + - + - + Installation — pca pca documentation - - - - + + + + - - - + + + + + @@ -33,9 +35,6 @@ pca - - 2.0.1 - @@ -138,9 +137,9 @@ -Installation +Installation -Create environment +Create environment If desired, install pca from an isolated Python environment using conda: conda create -n env_pca python=3.8 conda activate env_pca @@ -148,26 +147,26 @@ Create environment -Pip install -# Install from Pypi: +Pip install +# Install from Pypi: pip install pca -# Install directly from github +# Install directly from github pip install git+https://github.com/erdogant/pca -Uninstalling +Uninstalling Remove the environment with installation: -# List all the active environments. pca should be listed. +# List all the active environments. pca should be listed. conda env list -# Remove the pca environment +# Remove the pca environment conda env remove --name pca -# List all the active environments. pca should be absent. +# List all the active environments. pca should be absent. conda env list diff --git a/docs/pages/html/Outlier detection.html b/docs/pages/html/Outlier detection.html index 37bc204..fe764f4 100644 --- a/docs/pages/html/Outlier detection.html +++ b/docs/pages/html/Outlier detection.html @@ -1,20 +1,22 @@ + + - + - + Hotelling T2 — pca pca documentation - - - - + + + + - - - + + + + + @@ -33,9 +35,6 @@ pca - - 2.0.1 - @@ -134,7 +133,7 @@ -Hotelling T2 +Hotelling T2 To detect outliers across the multidimensional space of PCA, the hotellings T2 test is implemented. It works by computing the chi-square tests across the top n_components: default is PC1 to PC5. The reason for not using more PC’s is that it is expected that the highest variance (and thus the outliers) will be seen in the first few components. Going deeper into PC space may therefore not be required. Nevertheless, the depth is optional. The hotellings T2 test outputs a P-value matrix (samples x PCs), which are are subsequently combined using fishers method. This allows to determine outliers with its ranking (strongest to weak). The alpha parameter determines the detection of outliers (default: 0.05). @@ -192,7 +191,7 @@ Hotelling T2 -SPE/Dmodx +SPE/Dmodx Outlier can be detected using SPE/DmodX (distance to model) based on the mean and covariance of the first 2 dimensions of X. On the model plane (SPE ≈ 0). Note that the SPE or Hotelling’s T2 are complementary to each other. model.biplot(legend=True, SPE=True, HT2=True) @@ -204,7 +203,7 @@ SPE/Dmodx -Detected outliers +Detected outliers @@ -213,7 +212,7 @@ SPE/Dmodx -Selection of the Outliers +Selection of the Outliers Selecting the outliers can be usefull to remove them from the dataset or for deeper investigation. # Select the outliers Xoutliers = X[results['outliers']['y_bool'],:] @@ -224,7 +223,7 @@ Selection of the Outliers -Detect new unseen outliers +Detect new unseen outliers After fitting a model on the data, you may want to use the model in a later stage to detect outliers on unseen data. Detection of outliers is performed in the transform function and does not require any additional action. An example is shown in the code block below. # Import libraries @@ -252,7 +251,7 @@ Detect new unseen outliers -Detected outliers +Detected outliers @@ -288,7 +287,7 @@ Detect new unseen outliers -Detected outliers +Detected outliers @@ -296,7 +295,7 @@ Detect new unseen outliers -Detection of outliers without PCA +Detection of outliers without PCA If desired, the outliers can also be detected directly using the hotelling T2 and/or SPE/DmodX functionality. For demonstration purposes I use the PCs from the results but any other dataset would also work. import pca diff --git a/docs/pages/html/Plots.html b/docs/pages/html/Plots.html index c1677b6..f054370 100644 --- a/docs/pages/html/Plots.html +++ b/docs/pages/html/Plots.html @@ -1,20 +1,22 @@ + + - + - + Load dataset — pca pca documentation - - - - + + + + - - - + + + + + @@ -33,9 +35,6 @@ pca - - 2.0.1 - @@ -134,7 +133,7 @@ -Load dataset +Load dataset Let’s load the wine dataset to demonstrate the plots. # Load library from sklearn.datasets import load_wine @@ -166,7 +165,7 @@ Load dataset -Scatter plot +Scatter plot # Make scatterplot model.scatter() @@ -187,7 +186,7 @@ Scatter plot -Scatterplots +Scatterplots @@ -204,16 +203,40 @@ Scatter plot -Biplot +Biplot +The biplot draws the loadings (arrows) together with the samples (scatterplot). +The loadings can be colored red and blue which indicates the strength of the particular feature in the PC. +For each principal component (PC), the feature is determined with the largest absolute loading. This indicates which feature contributes the most to each PC and can occur in multiple PCs. +The highest loading values for the features are colored red in the biplot and described as “best” in the output dataframe. +The features that were not seen with highest loadings for any PC are considered weaker features, and are colored blue the biplot. In the output dataframe these features are described as “weak”. # Make biplot model.biplot() # Here again, many other options can be turned on and off model.biplot(SPE=True, HT2=True, legend=1) + +# Show the top features +results['topfeat'] + +# PC feature loading type +# 0 PC1 flavanoids 0.422934 best +# 1 PC2 color_intensity 0.529996 best +# 2 PC3 ash 0.626224 best +# 3 PC4 malic_acid 0.536890 best +# 4 PC5 magnesium 0.727049 best +# 5 PC6 malic_acid 0.536814 best +# 6 PC7 nonflavanoid_phenols 0.595447 best +# 7 PC8 hue 0.436624 best +# 8 PC9 proline 0.575786 best +# 9 PC10 od280/od315_of_diluted_wines 0.523706 best +# 10 PC9 alcohol -0.508619 weak +# 11 PC3 alcalinity_of_ash 0.612080 weak +# 12 PC8 total_phenols -0.405934 weak +# 13 PC6 proanthocyanins -0.533795 weak -Biplots +Biplots @@ -223,28 +246,30 @@ Biplot -Biplot (only arrows) +Biplot (only arrows) # Make plot with parameters: set cmap to None and label and legend to False. Only directions will be plotted. model.biplot(cmap=None, legend=False) - + + -Explained variance plot +Explained variance plot model.plot() - + + -Alpha Transparency +Alpha Transparency fig, ax = model.scatter(alpha=1) -Markers +Markers import numpy as np from sklearn.datasets import make_friedman1 from pca import pca @@ -272,7 +297,7 @@ Markers -Biplots with markers +Biplots with markers @@ -280,7 +305,7 @@ Markers -Control color/marker/size per sample +Control color/marker/size per sample import numpy as np import matplotlib.pyplot as plt import matplotlib.colors as mcolors @@ -329,7 +354,7 @@ Control color/marker/size per sample -Biplot with customized properties per sample. +Biplot with customized properties per sample. @@ -337,15 +362,16 @@ Control color/marker/size per sample -3D plots +3D plots All plots can also be created in 3D by setting the d3=True parameter. model.biplot3d() - + + -Toggle visible status +Toggle visible status The visible status for can be turned on and off. # Make plot but not visible. fig, ax = model.biplot(visible=False) diff --git a/docs/pages/html/_sources/Plots.rst.txt b/docs/pages/html/_sources/Plots.rst.txt index 33319b2..38cd2db 100644 --- a/docs/pages/html/_sources/Plots.rst.txt +++ b/docs/pages/html/_sources/Plots.rst.txt @@ -83,6 +83,14 @@ Scatter plot Biplot ############### +The biplot draws the loadings (arrows) together with the samples (scatterplot). +The loadings can be colored red and blue which indicates the strength of the particular feature in the PC. + +For each principal component (PC), the feature is determined with the largest absolute loading. This indicates which feature contributes the most to each PC and can occur in multiple PCs. +The highest loading values for the features are colored red in the biplot and described as "best" in the output dataframe. +The features that were not seen with highest loadings for any PC are considered weaker features, and are colored blue the biplot. In the output dataframe these features are described as "weak". + + .. code:: python # Make biplot @@ -91,6 +99,24 @@ Biplot # Here again, many other options can be turned on and off model.biplot(SPE=True, HT2=True, legend=1) + # Show the top features + results['topfeat'] + + # PC feature loading type + # 0 PC1 flavanoids 0.422934 best + # 1 PC2 color_intensity 0.529996 best + # 2 PC3 ash 0.626224 best + # 3 PC4 malic_acid 0.536890 best + # 4 PC5 magnesium 0.727049 best + # 5 PC6 malic_acid 0.536814 best + # 6 PC7 nonflavanoid_phenols 0.595447 best + # 7 PC8 hue 0.436624 best + # 8 PC9 proline 0.575786 best + # 9 PC10 od280/od315_of_diluted_wines 0.523706 best + # 10 PC9 alcohol -0.508619 weak + # 11 PC3 alcalinity_of_ash 0.612080 weak + # 12 PC8 total_phenols -0.405934 weak + # 13 PC6 proanthocyanins -0.533795 weak .. |figP5| image:: ../figs/wine_biplot.png .. |figP6| image:: ../figs/wine_biplot_with_outliers.png diff --git a/docs/pages/html/_sources/sponsor.rst.txt b/docs/pages/html/_sources/sponsor.rst.txt index a46c410..f006896 100644 --- a/docs/pages/html/_sources/sponsor.rst.txt +++ b/docs/pages/html/_sources/sponsor.rst.txt @@ -4,8 +4,10 @@ * Become a `Sponsor `_! * `Buy `_ me a coffee! I ❤️ coffee :) * `Donate `_ in Bitcoin. - * Follow me on medium! Go to my `medium profile `_ and press *follow*. + * Follow me on Medium! Go to my `medium profile `_ and press *follow*. + * Subscribe to me on Substack! Go to my `profile `_ where you can *subscribe*. * **Star** this repo at the github page. + * You can also buy a digital educational product over `here `_. * Other contributions can be in the form of feature requests, idea discussions, reporting bugs, opening pull requests. Cheers Mate. diff --git a/docs/pages/html/_static/_sphinx_javascript_frameworks_compat.js b/docs/pages/html/_static/_sphinx_javascript_frameworks_compat.js new file mode 100644 index 0000000..8141580 --- /dev/null +++ b/docs/pages/html/_static/_sphinx_javascript_frameworks_compat.js @@ -0,0 +1,123 @@ +/* Compatability shim for jQuery and underscores.js. + * + * Copyright Sphinx contributors + * Released under the two clause BSD licence + */ + +/** + * small helper function to urldecode strings + * + * See https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/decodeURIComponent#Decoding_query_parameters_from_a_URL + */ +jQuery.urldecode = function(x) { + if (!x) { + return x + } + return decodeURIComponent(x.replace(/\+/g, ' ')); +}; + +/** + * small helper function to urlencode strings + */ +jQuery.urlencode = encodeURIComponent; + +/** + * This function returns the parsed url parameters of the + * current request. Multiple values per key are supported, + * it will always return arrays of strings for the value parts. + */ +jQuery.getQueryParameters = function(s) { + if (typeof s === 'undefined') + s = document.location.search; + var parts = s.substr(s.indexOf('?') + 1).split('&'); + var result = {}; + for (var i = 0; i < parts.length; i++) { + var tmp = parts[i].split('=', 2); + var key = jQuery.urldecode(tmp[0]); + var value = jQuery.urldecode(tmp[1]); + if (key in result) + result[key].push(value); + else + result[key] = [value]; + } + return result; +}; + +/** + * highlight a given string on a jquery object by wrapping it in + * span elements with the given class name. + */ +jQuery.fn.highlightText = function(text, className) { + function highlight(node, addItems) { + if (node.nodeType === 3) { + var val = node.nodeValue; + var pos = val.toLowerCase().indexOf(text); + if (pos >= 0 && + !jQuery(node.parentNode).hasClass(className) && + !jQuery(node.parentNode).hasClass("nohighlight")) { + var span; + var isInSVG = jQuery(node).closest("body, svg, foreignObject").is("svg"); + if (isInSVG) { + span = document.createElementNS("http://www.w3.org/2000/svg", "tspan"); + } else { + span = document.createElement("span"); + span.className = className; + } + span.appendChild(document.createTextNode(val.substr(pos, text.length))); + node.parentNode.insertBefore(span, node.parentNode.insertBefore( + document.createTextNode(val.substr(pos + text.length)), + node.nextSibling)); + node.nodeValue = val.substr(0, pos); + if (isInSVG) { + var rect = document.createElementNS("http://www.w3.org/2000/svg", "rect"); + var bbox = node.parentElement.getBBox(); + rect.x.baseVal.value = bbox.x; + rect.y.baseVal.value = bbox.y; + rect.width.baseVal.value = bbox.width; + rect.height.baseVal.value = bbox.height; + rect.setAttribute('class', className); + addItems.push({ + "parent": node.parentNode, + "target": rect}); + } + } + } + else if (!jQuery(node).is("button, select, textarea")) { + jQuery.each(node.childNodes, function() { + highlight(this, addItems); + }); + } + } + var addItems = []; + var result = this.each(function() { + highlight(this, addItems); + }); + for (var i = 0; i < addItems.length; ++i) { + jQuery(addItems[i].parent).before(addItems[i].target); + } + return result; +}; + +/* + * backward compatibility for jQuery.browser + * This will be supported until firefox bug is fixed. + */ +if (!jQuery.browser) { + jQuery.uaMatch = function(ua) { + ua = ua.toLowerCase(); + + var match = /(chrome)[ \/]([\w.]+)/.exec(ua) || + /(webkit)[ \/]([\w.]+)/.exec(ua) || + /(opera)(?:.*version|)[ \/]([\w.]+)/.exec(ua) || + /(msie) ([\w.]+)/.exec(ua) || + ua.indexOf("compatible") < 0 && /(mozilla)(?:.*? rv:([\w.]+)|)/.exec(ua) || + []; + + return { + browser: match[ 1 ] || "", + version: match[ 2 ] || "0" + }; + }; + jQuery.browser = {}; + jQuery.browser[jQuery.uaMatch(navigator.userAgent).browser] = true; +} diff --git a/docs/pages/html/_static/basic.css b/docs/pages/html/_static/basic.css index 7577acb..7ebbd6d 100644 --- a/docs/pages/html/_static/basic.css +++ b/docs/pages/html/_static/basic.css @@ -1,12 +1,5 @@ /* - * basic.css - * ~~~~~~~~~ - * * Sphinx stylesheet -- basic theme. - * - * :copyright: Copyright 2007-2023 by the Sphinx team, see AUTHORS. - * :license: BSD, see LICENSE for details. - * */ /* -- main layout ----------------------------------------------------------- */ @@ -115,15 +108,11 @@ img { /* -- search page ----------------------------------------------------------- */ ul.search { - margin: 10px 0 0 20px; - padding: 0; + margin-top: 10px; } ul.search li { - padding: 5px 0 5px 20px; - background-image: url(file.png); - background-repeat: no-repeat; - background-position: 0 7px; + padding: 5px 0; } ul.search li a { @@ -237,6 +226,10 @@ a.headerlink { visibility: hidden; } +a:visited { + color: #551A8B; +} + h1:hover > a.headerlink, h2:hover > a.headerlink, h3:hover > a.headerlink, @@ -670,6 +663,16 @@ dd { 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{ + const config = event.detail.data(); + + const flyout = ` + + + Read the Docs + v: ${config.versions.current.slug} + + + + + ${renderLanguages(config)} + ${renderVersions(config)} + ${renderDownloads(config)} + + On Read the Docs + + Project Home + + + Builds + + + Downloads + + + + Search + + + + + + + + + Hosted by Read the Docs + + + + `; + + // Inject the generated flyout into the body HTML element. + document.body.insertAdjacentHTML("beforeend", flyout); + + // Trigger the Read the Docs Addons Search modal when clicking on the "Search docs" input from inside the flyout. + document + .querySelector("#flyout-search-form") + .addEventListener("focusin", () => { + const event = new CustomEvent("readthedocs-search-show"); + document.dispatchEvent(event); + }); + }) +} + +if (themeLanguageSelector || themeVersionSelector) { + function onSelectorSwitch(event) { + const option = event.target.selectedIndex; + const item = event.target.options[option]; + window.location.href = item.dataset.url; + } + + document.addEventListener("readthedocs-addons-data-ready", function (event) { + const config = event.detail.data(); + + const versionSwitch = document.querySelector( + "div.switch-menus > div.version-switch", + ); + if (themeVersionSelector) { + let versions = config.versions.active; + if (config.versions.current.hidden || config.versions.current.type === "external") { + versions.unshift(config.versions.current); + } + const versionSelect = ` + + ${versions + .map( + (version) => ` + + ${version.slug} + `, + ) + .join("\n")} + + `; + + versionSwitch.innerHTML = versionSelect; + versionSwitch.firstElementChild.addEventListener("change", onSelectorSwitch); + } + + const languageSwitch = document.querySelector( + "div.switch-menus > div.language-switch", + ); + + if (themeLanguageSelector) { + if (config.projects.translations.length) { + // Add the current language to the options on the selector + let languages = config.projects.translations.concat( + config.projects.current, + ); + languages = languages.sort((a, b) => + a.language.name.localeCompare(b.language.name), + ); + + const languageSelect = ` + + ${languages + .map( + (language) => ` + + ${language.language.name} + `, + ) + .join("\n")} + + `; + + languageSwitch.innerHTML = languageSelect; + languageSwitch.firstElementChild.addEventListener("change", onSelectorSwitch); + } + else { + languageSwitch.remove(); + } + } + }); +} + +document.addEventListener("readthedocs-addons-data-ready", function (event) { + // Trigger the Read the Docs Addons Search modal when clicking on "Search docs" input from the topnav. + document + .querySelector("[role='search'] input") + .addEventListener("focusin", () => { + const event = new CustomEvent("readthedocs-search-show"); + document.dispatchEvent(event); + }); +}); \ No newline at end of file diff --git a/docs/pages/html/_static/language_data.js b/docs/pages/html/_static/language_data.js index 250f566..c7fe6c6 100644 --- a/docs/pages/html/_static/language_data.js +++ b/docs/pages/html/_static/language_data.js @@ -1,19 +1,12 @@ /* - * language_data.js - * ~~~~~~~~~~~~~~~~ - * * This script contains the language-specific data used by searchtools.js, * namely the list of stopwords, stemmer, scorer and splitter. - * - * :copyright: Copyright 2007-2023 by the Sphinx team, see AUTHORS. - * :license: BSD, see LICENSE for details. - * */ var stopwords = ["a", "and", "are", "as", "at", "be", "but", "by", "for", "if", "in", "into", "is", "it", "near", "no", "not", "of", "on", "or", "such", "that", "the", "their", "then", "there", "these", "they", "this", "to", "was", "will", "with"]; -/* Non-minified version is copied as a separate JS file, is available */ +/* Non-minified version is copied as a separate JS file, if available */ /** * Porter Stemmer diff --git a/docs/pages/html/_static/notebooks/pca_examples.html b/docs/pages/html/_static/notebooks/pca_examples.html index c9a75dc..7bb55a3 100644 --- a/docs/pages/html/_static/notebooks/pca_examples.html +++ b/docs/pages/html/_static/notebooks/pca_examples.html @@ -1,13 +1,9 @@ - - - + + + pca_examples - - - - - - - - - - - - - - + + + - - - - + void Promise.all([...diagrams].map(renderOneMarmaid)); + }); + + + + + + + - + pca A Python Package for Principal Component Analysis. The core of PCA is build on sklearn functionality to find maximum compatibility when combining with other packages. But this package can do a lot more. Besides the regular pca, it can also perform SparsePCA, and TruncatedSVD. Depending on your input data, the best approach will be choosen. Other functionalities are: @@ -15124,38 +7531,30 @@ github pca - - - + + -In [1]: +In [1]: - -!pip install pca + +!pip install pca - - - + - - - - - - - + + Requirement already satisfied: pca in /usr/local/lib/python3.7/dist-packages (1.7.2) Requirement already satisfied: matplotlib in /usr/local/lib/python3.7/dist-packages (from pca) (3.2.2) Requirement already satisfied: wget in /usr/local/lib/python3.7/dist-packages (from pca) (3.2) @@ -15180,179 +7579,149 @@ - - - - - + + - + Lets check the version - - - + + -In [2]: +In [2]: - -import pca + +import pca print(pca.__version__) - - - + - - - - - - - + + 1.7.2 - - - - - + + - + Import the pca library - - - + + -In [3]: +In [3]: - -from pca import pca + +from pca import pca import numpy as np import pandas as pd - - - - - + + + - + Here we will create a random dataset. - - - + + -In [4]: +In [4]: - -# Dataset + +# Dataset from sklearn.datasets import load_iris X = pd.DataFrame(data=load_iris().data, columns=load_iris().feature_names, index=load_iris().target) - - - - - + + + - + Initialize using specified parameters. The parameters here are the default parameters. - - - + + -In [5]: +In [5]: - -# Initialize + +# Initialize model = pca(n_components=3, normalize=True) - - - - - + + + -In [6]: +In [6]: - -# Fit transform + +# Fit transform out = model.fit_transform(X) - - - + - - - - - - - + + [pca] >Processing dataframe.. [pca] >Normalizing input data per feature (zero mean and unit variance).. [pca] >The PCA reduction is performed on the [4] columns of the input dataframe. @@ -15364,171 +7733,119 @@ - - - - - + + -In [7]: +In [7]: - -# Make plot with only the directions (no scatter) + +# Make plot with only the directions (no scatter) fig, ax = model.biplot(textlabel=True, legend=False, figsize=(10, 6)) - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 with loadings. - - - - - - - - + + + - - - - - - + + -In [8]: +In [8]: - -# Make plot with only the directions (no scatter) + +# Make plot with only the directions (no scatter) fig, ax = model.biplot(cmap=None, textlabel=False, legend=False, figsize=(10, 6)) - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 with loadings. - - - - - - - - + + + - - - - - - + + -In [9]: +In [9]: - -from pca import pca + +from pca import pca # Load example data from sklearn.datasets import load_iris X = pd.DataFrame(data=load_iris().data, columns=load_iris().feature_names, index=load_iris().target) - - - - - + + + -In [10]: +In [10]: - -# Initialize + +# Initialize model = pca(n_components=3) # Fit using PCA results = model.fit_transform(X) - - - + - - - - - - - + + [pca] >Processing dataframe.. [pca] >The PCA reduction is performed on the [4] columns of the input dataframe. [pca] >Fit using PCA. @@ -15539,20 +7856,17 @@ - - - - - + + -In [11]: +In [11]: - -# Make plots + +# Make plots # Scree plot fig, ax = model.plot(figsize=(10, 6)) @@ -15563,190 +7877,117 @@ # Biplot fig, ax = model.biplot(figsize=(10, 6)) - - - + - - - - - - - - - - + + + - - - - - - - - - + + + - - - - - - + + [pca] >Plot PC1 vs PC2 with loadings. - - - - - - - + + <Figure size 432x288 with 0 Axes> - - - - - - - - - + + + - - - - - - + + -In [17]: +In [17]: - -# Coloring on density to focus on the core samples. + +# Coloring on density to focus on the core samples. # Biplot -fig, ax = model.biplot(figsize=(10, 6), gradient='#ffffff') +fig, ax = model.biplot(figsize=(10, 6), gradient='#ffffff') - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 with loadings. - - - - - - - - + + + - - - - - - + + -In [18]: +In [18]: - -# Outliers are stored in results: -results['outliers'] + +# Outliers are stored in results: +results['outliers'] # Outliers based on T2 -print('--------T2------------') -print(results['outliers'].loc[results['outliers']['y_bool'], :]) +print('--------T2------------') +print(results['outliers'].loc[results['outliers']['y_bool'], :]) # Outliers based on SPE -print('--------SPE------------') -print(results['outliers'].loc[results['outliers']['y_bool_spe'], :]) +print('--------SPE------------') +print(results['outliers'].loc[results['outliers']['y_bool_spe'], :]) - - - + - - - - - - - + + --------T2------------ y_proba y_score y_bool y_bool_spe y_score_spe 2 0.040551 13.160880 True True 3.679935 @@ -15771,270 +8012,168 @@ - - - - - + + -In [20]: +In [20]: - -# Outlier detection + +# Outlier detection fig, ax = model.biplot(SPE=True, HT2=True, figsize=(10, 6)) - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 with loadings. - - - - - - - - + + + - - - - - - + + -In [21]: +In [21]: - -# 3D plots + +# 3D plots fig, ax = model.scatter3d(figsize=(10, 6)) fig, ax = model.biplot3d(figsize=(10, 6)) fig, ax = model.biplot3d(SPE=True, HT2=True, figsize=(10, 6)) - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 vs PC3 with loadings. - - - - - - - - + + + - - - - - - - - - + + + - - - - - - + + [pca] >Plot PC1 vs PC2 vs PC3 with loadings. - - - - - - - - + + + - - - - - - + + -In [22]: +In [22]: - -fig, ax = model.biplot3d(SPE=True, HT2=True, visible=False, figsize=(10, 6)) + +fig, ax = model.biplot3d(SPE=True, HT2=True, visible=False, figsize=(10, 6)) # Set the figure again to True and show the figure. fig.set_visible(True) fig - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 vs PC3 with loadings. - - Out[22]: - - - - - - +Out[22]: + + - - - - - - - - - + + + - - - - - - + + -In [23]: +In [23]: - -# Normalize out PCs + +
PCA_lecture
-<html class="writer-html5" lang="en" > +<html class="writer-html5" lang="en" data-content_root="./"> <head> - <meta charset="utf-8" /><meta name="generator" content="Docutils 0.18.1: http://docutils.sourceforge.net/" /> + <meta charset="utf-8" /><meta name="viewport" content="width=device-width, initial-scale=1" /> <meta name="viewport" content="width=device-width, initial-scale=1.0" /> <title>Algorithm — pca pca documentation</title> - <link rel="stylesheet" href="_static/pygments.css" type="text/css" /> - <link rel="stylesheet" href="_static/css/theme.css" type="text/css" /> - <link rel="stylesheet" href="_static/css/custom.css" type="text/css" /> - <!--[if lt IE 9]> - <script src="_static/js/html5shiv.min.js"></script> - <![endif]--> + <link rel="stylesheet" type="text/css" href="_static/pygments.css?v=fa44fd50" /> + <link rel="stylesheet" type="text/css" href="_static/css/theme.css?v=e59714d7" /> + <link rel="stylesheet" type="text/css" href="_static/css/custom.css?v=e0179649" /> + - <script data-url_root="./" id="documentation_options" src="_static/documentation_options.js"></script> - <script src="_static/doctools.js"></script> - <script src="_static/sphinx_highlight.js"></script> + <script src="_static/jquery.js?v=5d32c60e"></script> + <script src="_static/_sphinx_javascript_frameworks_compat.js?v=2cd50e6c"></script> + <script src="_static/documentation_options.js?v=5d2b88f6"></script> + <script src="_static/doctools.js?v=9bcbadda"></script> + <script src="_static/sphinx_highlight.js?v=dc90522c"></script> <script src="_static/js/theme.js"></script> <link rel="index" title="Index" href="genindex.html" /> <link rel="search" title="Search" href="search.html" /> @@ -33,9 +35,6 @@ <a href="index.html" class="icon icon-home"> pca </a> - <div class="version"> - 2.0.1 - </div> <div role="search"> <form id="rtd-search-form" class="wy-form" action="search.html" method="get"> <input type="text" name="q" placeholder="Search docs" aria-label="Search docs" /> @@ -134,14 +133,14 @@ <div itemprop="articleBody"> <section id="algorithm"> -<h1>Algorithm<a class="headerlink" href="#algorithm" title="Permalink to this heading"></a></h1> +<h1>Algorithm<a class="headerlink" href="#algorithm" title="Link to this heading"></a></h1> <p>Principal Component Analysis, or PCA, is a dimensionality-reduction method that is often used to reduce the dimensionality of large data sets.</p> <p>Reducing the number of variables of a data set naturally comes at the expense of accuracy, but the trick in dimensionality reduction is to trade a little accuracy for <em>simplicity</em>. Because smaller data sets are easier to explore and visualize, it becomes easier and faster to analyze your data.</p> <p>The idea of PCA is simple — <strong>reduce the number of variables</strong> of a data set, while <strong>preserving</strong> as much <strong>information</strong> as possible.</p> <p>The <code class="docutils literal notranslate"><span class="pre">pca</span></code> library contains various functionalities to carefully examine the data, which can help for better understanding and removal of redundant information.</p> </section> <section id="standardization"> -<h1>Standardization<a class="headerlink" href="#standardization" title="Permalink to this heading"></a></h1> +<h1>Standardization<a class="headerlink" href="#standardization" title="Link to this heading"></a></h1> <p>Feature scaling through standardization (or Z-score normalization) is an important preprocessing step for many machine learning algorithms. Standardization involves rescaling the features such that they have the properties of a standard normal distribution with a mean of zero and a standard deviation of one. The standardization step depends on the type of variables, the distribution of the data, and also your aim. In general, the standardizing step is to range the continuous initial variables so that each one of them contributes <em>equally</em> to the analysis.</p> <p>It is utterly important to carefully standardize your data because PCA works under the assumption that the data is <em>normal distributed</em>, and is very <em>sensitive</em> to the variance of the variables. Or in other words, large differences between the ranges of variables will dominate over those with small ranges. Let me explain this by example; a variable that ranges between 0 and 100 will dominate over a variable that ranges between 0 and 1. Transforming the data to comparable scales can prevent this issue.</p> <p>The most straightforward manner for standardization is by computing the <em>Z-scores</em> or <em>Standardized scores</em>. @@ -178,7 +177,7 @@ <h1>Standardization<a class="headerlink" href="#standardization" title="Permalin </div> <p>An example of the differences of feature reduction using PCA with and without standardization.</p> <table class="docutils align-center" id="id1"> -<caption><span class="caption-text">Without standardization (left) and with standardization (right)</span><a class="headerlink" href="#id1" title="Permalink to this table"></a></caption> +<caption><span class="caption-text">Without standardization (left) and with standardization (right)</span><a class="headerlink" href="#id1" title="Link to this table"></a></caption> <tbody> <tr class="row-odd"><td><p><img alt="figA3" src="_images/wine_no_standardization.png" /></p></td> <td><p><img alt="figA4" src="_images/wine_yes_standardization.png" /></p></td> @@ -187,7 +186,7 @@ <h1>Standardization<a class="headerlink" href="#standardization" title="Permalin </table> </section> <section id="explained-variance"> -<h1>Explained Variance<a class="headerlink" href="#explained-variance" title="Permalink to this heading"></a></h1> +<h1>Explained Variance<a class="headerlink" href="#explained-variance" title="Link to this heading"></a></h1> <p>Before jumping into the <strong>explained variance</strong>, we first need to understand what principal components are.</p> <p><strong>Principal components</strong> are new (latent) <strong>variables</strong> that are constructed as <strong>linear combinations</strong> or <strong>mixtures</strong> of the initial variables. These combinations are in such a way that the new variables (i.e., principal components) are uncorrelated and most of the information within the initial variables is squeezed or compressed into the first components. <strong>Explained variance</strong> refers to the variance explained by each of the principal components (eigenvectors). By organizing information Principal</p> @@ -206,20 +205,25 @@ <h1>Explained Variance<a class="headerlink" href="#explained-variance" title="Pe </pre></div> </div> <p>In this example we have 13 variables in the <strong>wine</strong> dataset, and thus 13 dimensions. PCA will optimize to store maximum variance in the first PC, then in the second and so on, until having something like shown in the plot below. This plot provides insights in the amount of <em>information</em> or <em>explained variance</em> in the data. We can clearly see that the 1st PC contains almost 36% of explained variance in total. With the top 10 PCs we cover 97.9% of all variance.</p> -<a class="reference internal image-reference" href="_images/wine_explained_variance.png"><img alt="_images/wine_explained_variance.png" class="align-center" src="_images/wine_explained_variance.png" style="width: 600px;" /></a> +<a class="reference internal image-reference" href="_images/wine_explained_variance.png"><img alt="_images/wine_explained_variance.png" class="align-center" src="_images/wine_explained_variance.png" style="width: 600px;" /> +</a> <p>There are as many principal components as there are variables in the data. The <strong>explained variance plot</strong> can therefore never have more then 13 PCs in this case. Principal components are constructed in such a manner that the first principal component accounts for the largest possible variance in the data set.</p> </section> <section id="loadings"> -<h1>Loadings<a class="headerlink" href="#loadings" title="Permalink to this heading"></a></h1> +<h1>Loadings<a class="headerlink" href="#loadings" title="Link to this heading"></a></h1> <p>It is important to realize that principal components are less interpretable and don’t have any real meaning since they are constructed as <strong>linear combinations</strong> of the initial variables. But we can analyze the <strong>loadings</strong> which describe the importance of the independent variables. The first principal component (Y1) is given by a linear combination of the variables X1, X2, …, Xp, and is calculated such that it accounts for the greatest possible variance in the data.</p> -<a class="reference internal image-reference" href="_images/PCAequation1.png"><img alt="_images/PCAequation1.png" src="_images/PCAequation1.png" style="width: 300px;" /></a> +<a class="reference internal image-reference" href="_images/PCAequation1.png"><img alt="_images/PCAequation1.png" src="_images/PCAequation1.png" style="width: 300px;" /> +</a> <p>Of course, one could make the variance of Y1 as large as possible by choosing large values for the weights a11, a12, … a1p. To prevent this, the sum of squares of the weights is constrained to be 1.</p> -<a class="reference internal image-reference" href="_images/PCAequation3.png"><img alt="_images/PCAequation3.png" src="_images/PCAequation3.png" style="width: 300px;" /></a> +<a class="reference internal image-reference" href="_images/PCAequation3.png"><img alt="_images/PCAequation3.png" src="_images/PCAequation3.png" style="width: 300px;" /> +</a> <p>For example, let’s assume that the scatter plot of our data set is as shown below. Can we guess the first principal component? Yes, it’s approximately the line that matches the purple marks because it goes through the origin and it’s the line in which the projection of the points (red dots) is the most spread out. Or mathematically speaking, it’s the line that maximizes the variance which is the average of the squared distances from the projected points (red dots) to the origin.</p> -<a class="reference internal image-reference" href="_images/PCA_rotation.gif"><img alt="_images/PCA_rotation.gif" class="align-center" src="_images/PCA_rotation.gif" style="width: 900px;" /></a> +<a class="reference internal image-reference" href="_images/PCA_rotation.gif"><img alt="_images/PCA_rotation.gif" class="align-center" src="_images/PCA_rotation.gif" style="width: 900px;" /> +</a> <p>The second principal component is calculated in the same way, with the conditions that it is uncorrelated with (i.e., perpendicular to) the first principal component and that it accounts for the next highest variance.</p> -<a class="reference internal image-reference" href="_images/PCAequation4.png"><img alt="_images/PCAequation4.png" src="_images/PCAequation4.png" style="width: 300px;" /></a> +<a class="reference internal image-reference" href="_images/PCAequation4.png"><img alt="_images/PCAequation4.png" src="_images/PCAequation4.png" style="width: 300px;" /> +</a> <p>This continues until a total of <strong>p</strong> principal components have been calculated, that is, the number of principal components is the same as the original number of variables. At this point, the total variance on all of the principal components will equal the total variance among all of the variables. In this way, all of the information contained in the original data is preserved; no information is lost: PCA is just a rotation of the data.</p> <p>The elements of an eigenvector, that is, the values within a particular row of matrix, are the weights <strong>aij</strong>. These values are called the <strong>loadings</strong>, and they describe how much each variable contributes to a particular principal component.</p> <blockquote> @@ -249,10 +253,11 @@ <h1>Loadings<a class="headerlink" href="#loadings" title="Permalink to this head </pre></div> </div> <p>First of all, we see a nice seperation of the 3 wine classes (red, orange and gray samples). In the middle of the plot we see various arrows. Each of the arrows describes its story in the Principal Components. The angle of the arrow describes the contribution of the variable that is seen in the particular PC. The length describes the strength of the loading.</p> -<a class="reference internal image-reference" href="_images/wine_biplot.png"><img alt="_images/wine_biplot.png" class="align-center" src="_images/wine_biplot.png" style="width: 600px;" /></a> +<a class="reference internal image-reference" href="_images/wine_biplot.png"><img alt="_images/wine_biplot.png" class="align-center" src="_images/wine_biplot.png" style="width: 600px;" /> +</a> </section> <section id="examination-of-the-loadings"> -<h1>Examination of the loadings<a class="headerlink" href="#examination-of-the-loadings" title="Permalink to this heading"></a></h1> +<h1>Examination of the loadings<a class="headerlink" href="#examination-of-the-loadings" title="Link to this heading"></a></h1> <p>Let’s examine the <strong>loadings</strong> (arrows) a bit more to understand what is going on in the distribution of the samples given the variables. The variable <strong>flavanoids</strong> has a positive loading and explaines mostly the variance in the first PC1 (it is almost a horizontal line). If we would color the samples in the scatter plot based on <strong>flavanoids</strong> values, we expect to see a distinction between samples that are respectively left and right side of the scatter plot.</p> <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="c1"># Grap the values for flavanoids</span> <span class="n">X_feat</span> <span class="o">=</span> <span class="n">X</span><span class="p">[:,</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">col_labels</span><span class="p">)</span><span class="o">==</span><span class="s1">'flavanoids'</span><span class="p">]</span> @@ -268,7 +273,7 @@ <h1>Examination of the loadings<a class="headerlink" href="#examination-of-the-l </pre></div> </div> <table class="docutils align-center" id="id2"> -<caption><span class="caption-text">Color on flavanoids</span><a class="headerlink" href="#id2" title="Permalink to this table"></a></caption> +<caption><span class="caption-text">Color on flavanoids</span><a class="headerlink" href="#id2" title="Link to this table"></a></caption> <tbody> <tr class="row-odd"><td><p><img alt="figA1" src="_images/wine_flavanoids.png" /></p></td> <td><p><img alt="figA2" src="_images/wine_flavanoids3d.png" /></p></td> @@ -290,7 +295,7 @@ <h1>Examination of the loadings<a class="headerlink" href="#examination-of-the-l </pre></div> </div> <table class="docutils align-center" id="id3"> -<caption><span class="caption-text">Color on alcohol</span><a class="headerlink" href="#id3" title="Permalink to this table"></a></caption> +<caption><span class="caption-text">Color on alcohol</span><a class="headerlink" href="#id3" title="Link to this table"></a></caption> <tbody> <tr class="row-odd"><td><p><img alt="figA8" src="_images/wine_alcohol.png" /></p></td> <td><p><img alt="figA9" src="_images/wine_alcohol3d.png" /></p></td> @@ -299,7 +304,7 @@ <h1>Examination of the loadings<a class="headerlink" href="#examination-of-the-l </table> </section> <section id="best-performing-features"> -<h1>Best Performing Features<a class="headerlink" href="#best-performing-features" title="Permalink to this heading"></a></h1> +<h1>Best Performing Features<a class="headerlink" href="#best-performing-features" title="Link to this heading"></a></h1> <p>Extracting the best performing features is based on the loadings of the Principal Components, which are readily computed. The information is stored in the object itself. We can extract it as following:</p> <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="c1"># Print the top features.</span> diff --git a/docs/pages/html/Coding quality.html b/docs/pages/html/Coding quality.html index 516ac4b..006b9ef 100644 --- a/docs/pages/html/Coding quality.html +++ b/docs/pages/html/Coding quality.html @@ -1,20 +1,22 @@ + + <!DOCTYPE html> -<html class="writer-html5" lang="en" > +<html class="writer-html5" lang="en" data-content_root="./"> <head> - <meta charset="utf-8" /><meta name="generator" content="Docutils 0.18.1: http://docutils.sourceforge.net/" /> + <meta charset="utf-8" /><meta name="viewport" content="width=device-width, initial-scale=1" /> <meta name="viewport" content="width=device-width, initial-scale=1.0" /> <title>Coding quality — pca pca documentation</title> - <link rel="stylesheet" href="_static/pygments.css" type="text/css" /> - <link rel="stylesheet" href="_static/css/theme.css" type="text/css" /> - <link rel="stylesheet" href="_static/css/custom.css" type="text/css" /> - <!--[if lt IE 9]> - <script src="_static/js/html5shiv.min.js"></script> - <![endif]--> + <link rel="stylesheet" type="text/css" href="_static/pygments.css?v=fa44fd50" /> + <link rel="stylesheet" type="text/css" href="_static/css/theme.css?v=e59714d7" /> + <link rel="stylesheet" type="text/css" href="_static/css/custom.css?v=e0179649" /> + - <script data-url_root="./" id="documentation_options" src="_static/documentation_options.js"></script> - <script src="_static/doctools.js"></script> - <script src="_static/sphinx_highlight.js"></script> + <script src="_static/jquery.js?v=5d32c60e"></script> + <script src="_static/_sphinx_javascript_frameworks_compat.js?v=2cd50e6c"></script> + <script src="_static/documentation_options.js?v=5d2b88f6"></script> + <script src="_static/doctools.js?v=9bcbadda"></script> + <script src="_static/sphinx_highlight.js?v=dc90522c"></script> <script src="_static/js/theme.js"></script> <link rel="index" title="Index" href="genindex.html" /> <link rel="search" title="Search" href="search.html" /> @@ -33,9 +35,6 @@ <a href="index.html" class="icon icon-home"> pca </a> - <div class="version"> - 2.0.1 - </div> <div role="search"> <form id="rtd-search-form" class="wy-form" action="search.html" method="get"> <input type="text" name="q" placeholder="Search docs" aria-label="Search docs" /> @@ -140,50 +139,50 @@ <div itemprop="articleBody"> <section id="coding-quality"> -<h1>Coding quality<a class="headerlink" href="#coding-quality" title="Permalink to this heading"></a></h1> +<h1>Coding quality<a class="headerlink" href="#coding-quality" title="Link to this heading"></a></h1> <p>I value software quality. Higher quality software has fewer defects, better security, and better performance, which leads to happier users who can work more effectively. Code reviews are an effective method for improving software quality. McConnell (2004) suggests that unit testing finds approximately 25% of defects, function testing 35%, integration testing 45%, and code review 55-60%. While this means that none of these methods are good enough on their own and that they should be combined, clearly code review is an essential tool here.</p> <p>This library is therefore developed with several techniques, such as coding styling, low complexity, docstrings, reviews, and unit tests. Such conventions are helpfull to improve the quality, make the code cleaner and more understandable but alos to trace future bugs, and spot syntax errors.</p> <section id="library"> -<h2>Library<a class="headerlink" href="#library" title="Permalink to this heading"></a></h2> +<h2>Library<a class="headerlink" href="#library" title="Link to this heading"></a></h2> <p>The file structure of the generated package looks like:</p> <div class="highlight-bash notranslate"><div class="highlight"><pre><span></span>path/to/pca/ -├── .editorconfig -├── .gitignore -├── .pre-commit-config.yml -├── .prospector.yml -├── CHANGELOG.rst -├── docs -│ ├── conf.py -│ ├── index.rst -│ └── ... -├── LICENSE -├── MANIFEST.in -├── NOTICE -├── pca -│ ├── __init__.py -│ ├── __version__.py -│ └── pca.py -├── README.md -├── requirements.txt -├── setup.cfg -├── setup.py -└── tests - ├── __init__.py - └── test_pca.py +├──<span class="w"> </span>.editorconfig +├──<span class="w"> </span>.gitignore +├──<span class="w"> </span>.pre-commit-config.yml +├──<span class="w"> </span>.prospector.yml +├──<span class="w"> </span>CHANGELOG.rst +├──<span class="w"> </span>docs +│<span class="w"> </span>├──<span class="w"> </span>conf.py +│<span class="w"> </span>├──<span class="w"> </span>index.rst +│<span class="w"> </span>└──<span class="w"> </span>... +├──<span class="w"> </span>LICENSE +├──<span class="w"> </span>MANIFEST.in +├──<span class="w"> </span>NOTICE +├──<span class="w"> </span>pca +│<span class="w"> </span>├──<span class="w"> </span>__init__.py +│<span class="w"> </span>├──<span class="w"> </span>__version__.py +│<span class="w"> </span>└──<span class="w"> </span>pca.py +├──<span class="w"> </span>README.md +├──<span class="w"> </span>requirements.txt +├──<span class="w"> </span>setup.cfg +├──<span class="w"> </span>setup.py +└──<span class="w"> </span>tests +<span class="w"> </span>├──<span class="w"> </span>__init__.py +<span class="w"> </span>└──<span class="w"> </span>test_pca.py </pre></div> </div> </section> <section id="style"> -<h2>Style<a class="headerlink" href="#style" title="Permalink to this heading"></a></h2> +<h2>Style<a class="headerlink" href="#style" title="Link to this heading"></a></h2> <p>This library is compliant with the PEP-8 standards. PEP stands for Python Enhancement Proposal and sets a baseline for the readability of Python code. Each public function contains a docstring that is based on numpy standards.</p> </section> <section id="complexity"> -<h2>Complexity<a class="headerlink" href="#complexity" title="Permalink to this heading"></a></h2> +<h2>Complexity<a class="headerlink" href="#complexity" title="Link to this heading"></a></h2> <p>This library has been developed by using measures that help decreasing technical debt. Developing software with low(er) technical dept may take extra development time, but has many advantages:</p> <ul class="simple"> @@ -194,7 +193,7 @@ <h2>Complexity<a class="headerlink" href="#complexity" title="Permalink to this </ul> </section> <section id="unit-tests"> -<h2>Unit tests<a class="headerlink" href="#unit-tests" title="Permalink to this heading"></a></h2> +<h2>Unit tests<a class="headerlink" href="#unit-tests" title="Link to this heading"></a></h2> <p>The use of unit tests is essential to garantee a consistent output of developed functions. The following tests are secured using <code class="xref py py-func docutils literal notranslate"><span class="pre">tests.test_pca()</span></code>:</p> <ul class="simple"> diff --git a/docs/pages/html/Documentation.html b/docs/pages/html/Documentation.html index 933e4d6..6ea5da0 100644 --- a/docs/pages/html/Documentation.html +++ b/docs/pages/html/Documentation.html @@ -1,20 +1,22 @@ + + <!DOCTYPE html> -<html class="writer-html5" lang="en" > +<html class="writer-html5" lang="en" data-content_root="./"> <head> - <meta charset="utf-8" /><meta name="generator" content="Docutils 0.18.1: http://docutils.sourceforge.net/" /> + <meta charset="utf-8" /><meta name="viewport" content="width=device-width, initial-scale=1" /> <meta name="viewport" content="width=device-width, initial-scale=1.0" /> <title>Sponsor — pca pca documentation</title> - <link rel="stylesheet" href="_static/pygments.css" type="text/css" /> - <link rel="stylesheet" href="_static/css/theme.css" type="text/css" /> - <link rel="stylesheet" href="_static/css/custom.css" type="text/css" /> - <!--[if lt IE 9]> - <script src="_static/js/html5shiv.min.js"></script> - <![endif]--> + <link rel="stylesheet" type="text/css" href="_static/pygments.css?v=fa44fd50" /> + <link rel="stylesheet" type="text/css" href="_static/css/theme.css?v=e59714d7" /> + <link rel="stylesheet" type="text/css" href="_static/css/custom.css?v=e0179649" /> + - <script data-url_root="./" id="documentation_options" src="_static/documentation_options.js"></script> - <script src="_static/doctools.js"></script> - <script src="_static/sphinx_highlight.js"></script> + <script src="_static/jquery.js?v=5d32c60e"></script> + <script src="_static/_sphinx_javascript_frameworks_compat.js?v=2cd50e6c"></script> + <script src="_static/documentation_options.js?v=5d2b88f6"></script> + <script src="_static/doctools.js?v=9bcbadda"></script> + <script src="_static/sphinx_highlight.js?v=dc90522c"></script> <script src="_static/js/theme.js"></script> <link rel="index" title="Index" href="genindex.html" /> <link rel="search" title="Search" href="search.html" /> @@ -33,9 +35,6 @@ <a href="index.html" class="icon icon-home"> pca </a> - <div class="version"> - 2.0.1 - </div> <div role="search"> <form id="rtd-search-form" class="wy-form" action="search.html" method="get"> <input type="text" name="q" placeholder="Search docs" aria-label="Search docs" /> @@ -134,7 +133,7 @@ <div itemprop="articleBody"> <section id="sponsor"> -<h1>Sponsor<a class="headerlink" href="#sponsor" title="Permalink to this heading"></a></h1> +<h1>Sponsor<a class="headerlink" href="#sponsor" title="Link to this heading"></a></h1> <div class="admonition tip"> <p class="admonition-title">Tip</p> <p>You can support this project in various ways ❤️</p> @@ -142,36 +141,38 @@ <h1>Sponsor<a class="headerlink" href="#sponsor" title="Permalink to this headin <li><p>Become a <a class="reference external" href="https://github.com/sponsors/erdogant?o=esb/">Sponsor</a>!</p></li> <li><p><a class="reference external" href="https://www.buymeacoffee.com/erdogant">Buy</a> me a coffee! I ❤️ coffee :)</p></li> <li><p><a class="reference external" href="https://erdogant.github.io/donate/?currency=USD&amount=1000">Donate</a> in Bitcoin.</p></li> -<li><p>Follow me on medium! Go to my <a class="reference external" href="https://erdogant.medium.com/">medium profile</a> and press <em>follow</em>.</p></li> +<li><p>Follow me on Medium! Go to my <a class="reference external" href="https://erdogant.medium.com/">medium profile</a> and press <em>follow</em>.</p></li> +<li><p>Subscribe to me on Substack! Go to my <a class="reference external" href="https://erdogant.substack.com/">profile</a> where you can <em>subscribe</em>.</p></li> <li><p><strong>Star</strong> this repo at the github page.</p></li> +<li><p>You can also buy a digital educational product over <a class="reference external" href="https://erdogant.gumroad.com/">here</a>.</p></li> <li><p>Other contributions can be in the form of feature requests, idea discussions, reporting bugs, opening pull requests.</p></li> </ul> <p>Cheers Mate.</p> </div> <iframe src="https://github.com/sponsors/erdogant/button" title="Sponsor erdogant" height="35" width="116" style="border: 0;">
Note
Read more details and the usage in the Medium Blog: What are PCA loadings and Biplots?
Source code of pca can be found at Github
Experiment with pca library using the Colab notebook.
Bibtex can be found at the right side at the github page.
A quick example how perform feature reduction using pca.
import numpy as np from sklearn.datasets import load_iris @@ -187,7 +186,7 @@ Quickstart -Compute explained variance +Compute explained variance After the fit_transform, the cumulative expained variance is stored together with the explained variance per PC. # Cumulative explained variance print(model.results['explained_var']) @@ -201,10 +200,11 @@ Compute explained variancefig, ax = model.plot() - + + -PCs that cover 95% of the explained variance +PCs that cover 95% of the explained variance The number of PCs can be reduced by setting the n_components parameter. Note that the number of components can never be larger than the number of variables in your dataset. By setting n_components larger than 1, a feature reduction will be performed to exactly that number of components. By setting n_components smaller than 1, it describes the percentage of explained variance that needs to be covered at least. Or in other words, by setting n_components=0.95, the number of components are extracted that cover at least 95% of the explained variance. # Reduce the data towards 3 PCs model = pca(n_components=3) @@ -215,7 +215,7 @@ PCs that cover 95% of the explained variance -Scatter plot +Scatter plot # 2D plot fig, ax = model.scatter() @@ -224,7 +224,7 @@ Scatter plot -Color on alcohol +Color on alcohol @@ -233,7 +233,7 @@ Scatter plot -Biplot +Biplot # 2D plot fig, ax = model.biplot(n_feat=4, PC=[0,1]) @@ -241,11 +241,12 @@ Biplotfig, ax = model.biplot3d(n_feat=2, PC=[0,1,2]) - + + -Demonstration of feature importance +Demonstration of feature importance This example is created to showcase the working of extracting features that are most important in a PCA reduction. We will create random variables with increasingly more variance. The first feature (f1) will have most of the variance, followed by feature 2 (f2) etc. # Print the top features. @@ -294,14 +295,15 @@ Demonstration of feature importance -Explained variance plot +Explained variance plot model.plot() - + + -Biplot +Biplot Make the biplot. It can be nicely seen that the first feature with most variance (f1), is almost horizontal in the plot, whereas the second most variance (f2) is almost vertical. This is expected because most of the variance is in f1, followed by f2 etc. Biplot in 3d. Here we see the nice addition of the expected f3 in the plot in the z-direction. # 2d plot ax = model.biplot(n_feat=10, legend=False) @@ -311,7 +313,7 @@ Biplot -Color on alcohol +Color on alcohol @@ -321,10 +323,10 @@ Biplot -Analyzing Discrete datasets +Analyzing Discrete datasets Analyzing datasets that have continuous and catagorical values can be challanging. To demonstrate how to do this, I will use the Titanic dataset. We need to pip install df2onehot first. -pip install df2onehot +pip install df2onehot import pca @@ -383,7 +385,7 @@ Analyzing Discrete datasets -Map unseen datapoints into fitted space +Map unseen datapoints into fitted space After fitting variables into the new principal component space, we can map new unseen samples into this space too. However, there is also normalization step which can be tricky because you now need standardize the values of the unseen samples first based on the previously performed standardization. This step is also integrated in the pca library by simply setting the parameter normalize=True. # Load libraries import matplotlib.pyplot as plt @@ -422,10 +424,11 @@ Map unseen datapoints into fitted spaceax.scatter(PCnew.iloc[:, 0], PCnew.iloc[:, 1], marker='x', s=200) - + + -Normalizing out PCs +Normalizing out PCs Normalize your data using the principal components. As an example, suppose there is (technical) variation in the fist component and you want that out. This function transforms the data using the components that you want, e.g., starting from the 2nd PC, up to the OC that contains at least 95% of the explained variance. print(X.shape) (178, 13) @@ -443,7 +446,7 @@ Normalizing out PCs -Colors in plots +Colors in plots The default colors that are used in the plots depend on how much information is provided at start. There are many parameters to change the colors in the plots. Here I will demonstrate some of the possibilities. First, we will load the data and import the libraries. @@ -476,7 +479,7 @@ Colors in plots -Left: Default plot using the provided classlabels. Right: Color on custom cmap. +Left: Default plot using the provided classlabels. Right: Color on custom cmap. @@ -498,7 +501,7 @@ Colors in plots -Left: Mark some points on y and use cmap. Right: Specify the colors manually. +Left: Mark some points on y and use cmap. Right: Specify the colors manually. @@ -514,7 +517,7 @@ Colors in plots -Left: Remove scatterpoints from plot. Right: Gradient with the used cmap. +Left: Remove scatterpoints from plot. Right: Gradient with the used cmap. @@ -539,7 +542,7 @@ Colors in plots -Fig as input to make iterative changes. +Fig as input to make iterative changes. diff --git a/docs/pages/html/Installation.html b/docs/pages/html/Installation.html index d2fd9ff..8a0f6d2 100644 --- a/docs/pages/html/Installation.html +++ b/docs/pages/html/Installation.html @@ -1,20 +1,22 @@ + + - + - + Installation — pca pca documentation - - - - + + + + - - - + + + + + @@ -33,9 +35,6 @@ pca - - 2.0.1 - @@ -138,9 +137,9 @@ -Installation +Installation -Create environment +Create environment If desired, install pca from an isolated Python environment using conda: conda create -n env_pca python=3.8 conda activate env_pca @@ -148,26 +147,26 @@ Create environment -Pip install -# Install from Pypi: +Pip install +# Install from Pypi: pip install pca -# Install directly from github +# Install directly from github pip install git+https://github.com/erdogant/pca -Uninstalling +Uninstalling Remove the environment with installation: -# List all the active environments. pca should be listed. +# List all the active environments. pca should be listed. conda env list -# Remove the pca environment +# Remove the pca environment conda env remove --name pca -# List all the active environments. pca should be absent. +# List all the active environments. pca should be absent. conda env list diff --git a/docs/pages/html/Outlier detection.html b/docs/pages/html/Outlier detection.html index 37bc204..fe764f4 100644 --- a/docs/pages/html/Outlier detection.html +++ b/docs/pages/html/Outlier detection.html @@ -1,20 +1,22 @@ + + - + - + Hotelling T2 — pca pca documentation - - - - + + + + - - - + + + + + @@ -33,9 +35,6 @@ pca - - 2.0.1 - @@ -134,7 +133,7 @@ -Hotelling T2 +Hotelling T2 To detect outliers across the multidimensional space of PCA, the hotellings T2 test is implemented. It works by computing the chi-square tests across the top n_components: default is PC1 to PC5. The reason for not using more PC’s is that it is expected that the highest variance (and thus the outliers) will be seen in the first few components. Going deeper into PC space may therefore not be required. Nevertheless, the depth is optional. The hotellings T2 test outputs a P-value matrix (samples x PCs), which are are subsequently combined using fishers method. This allows to determine outliers with its ranking (strongest to weak). The alpha parameter determines the detection of outliers (default: 0.05). @@ -192,7 +191,7 @@ Hotelling T2 -SPE/Dmodx +SPE/Dmodx Outlier can be detected using SPE/DmodX (distance to model) based on the mean and covariance of the first 2 dimensions of X. On the model plane (SPE ≈ 0). Note that the SPE or Hotelling’s T2 are complementary to each other. model.biplot(legend=True, SPE=True, HT2=True) @@ -204,7 +203,7 @@ SPE/Dmodx -Detected outliers +Detected outliers @@ -213,7 +212,7 @@ SPE/Dmodx -Selection of the Outliers +Selection of the Outliers Selecting the outliers can be usefull to remove them from the dataset or for deeper investigation. # Select the outliers Xoutliers = X[results['outliers']['y_bool'],:] @@ -224,7 +223,7 @@ Selection of the Outliers -Detect new unseen outliers +Detect new unseen outliers After fitting a model on the data, you may want to use the model in a later stage to detect outliers on unseen data. Detection of outliers is performed in the transform function and does not require any additional action. An example is shown in the code block below. # Import libraries @@ -252,7 +251,7 @@ Detect new unseen outliers -Detected outliers +Detected outliers @@ -288,7 +287,7 @@ Detect new unseen outliers -Detected outliers +Detected outliers @@ -296,7 +295,7 @@ Detect new unseen outliers -Detection of outliers without PCA +Detection of outliers without PCA If desired, the outliers can also be detected directly using the hotelling T2 and/or SPE/DmodX functionality. For demonstration purposes I use the PCs from the results but any other dataset would also work. import pca diff --git a/docs/pages/html/Plots.html b/docs/pages/html/Plots.html index c1677b6..f054370 100644 --- a/docs/pages/html/Plots.html +++ b/docs/pages/html/Plots.html @@ -1,20 +1,22 @@ + + - + - + Load dataset — pca pca documentation - - - - + + + + - - - + + + + + @@ -33,9 +35,6 @@ pca - - 2.0.1 - @@ -134,7 +133,7 @@ -Load dataset +Load dataset Let’s load the wine dataset to demonstrate the plots. # Load library from sklearn.datasets import load_wine @@ -166,7 +165,7 @@ Load dataset -Scatter plot +Scatter plot # Make scatterplot model.scatter() @@ -187,7 +186,7 @@ Scatter plot -Scatterplots +Scatterplots @@ -204,16 +203,40 @@ Scatter plot -Biplot +Biplot +The biplot draws the loadings (arrows) together with the samples (scatterplot). +The loadings can be colored red and blue which indicates the strength of the particular feature in the PC. +For each principal component (PC), the feature is determined with the largest absolute loading. This indicates which feature contributes the most to each PC and can occur in multiple PCs. +The highest loading values for the features are colored red in the biplot and described as “best” in the output dataframe. +The features that were not seen with highest loadings for any PC are considered weaker features, and are colored blue the biplot. In the output dataframe these features are described as “weak”. # Make biplot model.biplot() # Here again, many other options can be turned on and off model.biplot(SPE=True, HT2=True, legend=1) + +# Show the top features +results['topfeat'] + +# PC feature loading type +# 0 PC1 flavanoids 0.422934 best +# 1 PC2 color_intensity 0.529996 best +# 2 PC3 ash 0.626224 best +# 3 PC4 malic_acid 0.536890 best +# 4 PC5 magnesium 0.727049 best +# 5 PC6 malic_acid 0.536814 best +# 6 PC7 nonflavanoid_phenols 0.595447 best +# 7 PC8 hue 0.436624 best +# 8 PC9 proline 0.575786 best +# 9 PC10 od280/od315_of_diluted_wines 0.523706 best +# 10 PC9 alcohol -0.508619 weak +# 11 PC3 alcalinity_of_ash 0.612080 weak +# 12 PC8 total_phenols -0.405934 weak +# 13 PC6 proanthocyanins -0.533795 weak -Biplots +Biplots @@ -223,28 +246,30 @@ Biplot -Biplot (only arrows) +Biplot (only arrows) # Make plot with parameters: set cmap to None and label and legend to False. Only directions will be plotted. model.biplot(cmap=None, legend=False) - + + -Explained variance plot +Explained variance plot model.plot() - + + -Alpha Transparency +Alpha Transparency fig, ax = model.scatter(alpha=1) -Markers +Markers import numpy as np from sklearn.datasets import make_friedman1 from pca import pca @@ -272,7 +297,7 @@ Markers -Biplots with markers +Biplots with markers @@ -280,7 +305,7 @@ Markers -Control color/marker/size per sample +Control color/marker/size per sample import numpy as np import matplotlib.pyplot as plt import matplotlib.colors as mcolors @@ -329,7 +354,7 @@ Control color/marker/size per sample -Biplot with customized properties per sample. +Biplot with customized properties per sample. @@ -337,15 +362,16 @@ Control color/marker/size per sample -3D plots +3D plots All plots can also be created in 3D by setting the d3=True parameter. model.biplot3d() - + + -Toggle visible status +Toggle visible status The visible status for can be turned on and off. # Make plot but not visible. fig, ax = model.biplot(visible=False) diff --git a/docs/pages/html/_sources/Plots.rst.txt b/docs/pages/html/_sources/Plots.rst.txt index 33319b2..38cd2db 100644 --- a/docs/pages/html/_sources/Plots.rst.txt +++ b/docs/pages/html/_sources/Plots.rst.txt @@ -83,6 +83,14 @@ Scatter plot Biplot ############### +The biplot draws the loadings (arrows) together with the samples (scatterplot). +The loadings can be colored red and blue which indicates the strength of the particular feature in the PC. + +For each principal component (PC), the feature is determined with the largest absolute loading. This indicates which feature contributes the most to each PC and can occur in multiple PCs. +The highest loading values for the features are colored red in the biplot and described as "best" in the output dataframe. +The features that were not seen with highest loadings for any PC are considered weaker features, and are colored blue the biplot. In the output dataframe these features are described as "weak". + + .. code:: python # Make biplot @@ -91,6 +99,24 @@ Biplot # Here again, many other options can be turned on and off model.biplot(SPE=True, HT2=True, legend=1) + # Show the top features + results['topfeat'] + + # PC feature loading type + # 0 PC1 flavanoids 0.422934 best + # 1 PC2 color_intensity 0.529996 best + # 2 PC3 ash 0.626224 best + # 3 PC4 malic_acid 0.536890 best + # 4 PC5 magnesium 0.727049 best + # 5 PC6 malic_acid 0.536814 best + # 6 PC7 nonflavanoid_phenols 0.595447 best + # 7 PC8 hue 0.436624 best + # 8 PC9 proline 0.575786 best + # 9 PC10 od280/od315_of_diluted_wines 0.523706 best + # 10 PC9 alcohol -0.508619 weak + # 11 PC3 alcalinity_of_ash 0.612080 weak + # 12 PC8 total_phenols -0.405934 weak + # 13 PC6 proanthocyanins -0.533795 weak .. |figP5| image:: ../figs/wine_biplot.png .. |figP6| image:: ../figs/wine_biplot_with_outliers.png diff --git a/docs/pages/html/_sources/sponsor.rst.txt b/docs/pages/html/_sources/sponsor.rst.txt index a46c410..f006896 100644 --- a/docs/pages/html/_sources/sponsor.rst.txt +++ b/docs/pages/html/_sources/sponsor.rst.txt @@ -4,8 +4,10 @@ * Become a `Sponsor `_! * `Buy `_ me a coffee! I ❤️ coffee :) * `Donate `_ in Bitcoin. - * Follow me on medium! Go to my `medium profile `_ and press *follow*. + * Follow me on Medium! Go to my `medium profile `_ and press *follow*. + * Subscribe to me on Substack! Go to my `profile `_ where you can *subscribe*. * **Star** this repo at the github page. + * You can also buy a digital educational product over `here `_. * Other contributions can be in the form of feature requests, idea discussions, reporting bugs, opening pull requests. Cheers Mate. diff --git a/docs/pages/html/_static/_sphinx_javascript_frameworks_compat.js b/docs/pages/html/_static/_sphinx_javascript_frameworks_compat.js new file mode 100644 index 0000000..8141580 --- /dev/null +++ b/docs/pages/html/_static/_sphinx_javascript_frameworks_compat.js @@ -0,0 +1,123 @@ +/* Compatability shim for jQuery and underscores.js. + * + * Copyright Sphinx contributors + * Released under the two clause BSD licence + */ + +/** + * small helper function to urldecode strings + * + * See https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/decodeURIComponent#Decoding_query_parameters_from_a_URL + */ +jQuery.urldecode = function(x) { + if (!x) { + return x + } + return decodeURIComponent(x.replace(/\+/g, ' ')); +}; + +/** + * small helper function to urlencode strings + */ +jQuery.urlencode = encodeURIComponent; + +/** + * This function returns the parsed url parameters of the + * current request. 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span; + var isInSVG = jQuery(node).closest("body, svg, foreignObject").is("svg"); + if (isInSVG) { + span = document.createElementNS("http://www.w3.org/2000/svg", "tspan"); + } else { + span = document.createElement("span"); + span.className = className; + } + span.appendChild(document.createTextNode(val.substr(pos, text.length))); + node.parentNode.insertBefore(span, node.parentNode.insertBefore( + document.createTextNode(val.substr(pos + text.length)), + node.nextSibling)); + node.nodeValue = val.substr(0, pos); + if (isInSVG) { + var rect = document.createElementNS("http://www.w3.org/2000/svg", "rect"); + var bbox = node.parentElement.getBBox(); + rect.x.baseVal.value = bbox.x; + rect.y.baseVal.value = bbox.y; + rect.width.baseVal.value = bbox.width; + rect.height.baseVal.value = bbox.height; + rect.setAttribute('class', className); + addItems.push({ + "parent": node.parentNode, + "target": rect}); + } + } + } + else if (!jQuery(node).is("button, select, textarea")) { + jQuery.each(node.childNodes, function() { + highlight(this, addItems); + }); + } + } + var addItems = []; + var result = this.each(function() { + highlight(this, addItems); + }); + for (var i = 0; i < addItems.length; ++i) { + jQuery(addItems[i].parent).before(addItems[i].target); + } + return result; +}; + +/* + * backward compatibility for jQuery.browser + * This will be supported until firefox bug is fixed. + */ +if (!jQuery.browser) { + jQuery.uaMatch = function(ua) { + ua = ua.toLowerCase(); + + var match = /(chrome)[ \/]([\w.]+)/.exec(ua) || + /(webkit)[ \/]([\w.]+)/.exec(ua) || + /(opera)(?:.*version|)[ \/]([\w.]+)/.exec(ua) || + /(msie) ([\w.]+)/.exec(ua) || + ua.indexOf("compatible") < 0 && /(mozilla)(?:.*? rv:([\w.]+)|)/.exec(ua) || + []; + + return { + browser: match[ 1 ] || "", + version: match[ 2 ] || "0" + }; + }; + jQuery.browser = {}; + jQuery.browser[jQuery.uaMatch(navigator.userAgent).browser] = true; +} diff --git a/docs/pages/html/_static/basic.css b/docs/pages/html/_static/basic.css index 7577acb..7ebbd6d 100644 --- a/docs/pages/html/_static/basic.css +++ b/docs/pages/html/_static/basic.css @@ -1,12 +1,5 @@ /* - * basic.css - * ~~~~~~~~~ - * * Sphinx stylesheet -- basic theme. - * - * :copyright: Copyright 2007-2023 by the Sphinx team, see AUTHORS. - * :license: BSD, see LICENSE for details. - * */ /* -- main layout ----------------------------------------------------------- */ @@ -115,15 +108,11 @@ img { /* -- search page ----------------------------------------------------------- */ ul.search { - margin: 10px 0 0 20px; - padding: 0; + margin-top: 10px; } ul.search li { - padding: 5px 0 5px 20px; - background-image: url(file.png); - background-repeat: no-repeat; - background-position: 0 7px; + padding: 5px 0; } ul.search li a { @@ -237,6 +226,10 @@ a.headerlink { visibility: hidden; } +a:visited { + color: #551A8B; +} + h1:hover > a.headerlink, h2:hover > a.headerlink, h3:hover > a.headerlink, @@ -670,6 +663,16 @@ dd { margin-left: 30px; } +.sig dd { + margin-top: 0px; + margin-bottom: 0px; +} + +.sig dl { + margin-top: 0px; + margin-bottom: 0px; +} + dl > dd:last-child, dl > dd:last-child > :last-child { margin-bottom: 0; @@ -738,6 +741,14 @@ abbr, acronym { cursor: help; } +.translated { + background-color: rgba(207, 255, 207, 0.2) +} + +.untranslated { + background-color: rgba(255, 207, 207, 0.2) +} + /* -- code displays --------------------------------------------------------- */ pre { diff --git a/docs/pages/html/_static/css/badge_only.css b/docs/pages/html/_static/css/badge_only.css index c718cee..88ba55b 100644 --- a/docs/pages/html/_static/css/badge_only.css +++ b/docs/pages/html/_static/css/badge_only.css @@ -1 +1 @@ -.clearfix{*zoom:1}.clearfix:after,.clearfix:before{display:table;content:""}.clearfix:after{clear:both}@font-face{font-family:FontAwesome;font-style:normal;font-weight:400;src:url(fonts/fontawesome-webfont.eot?674f50d287a8c48dc19ba404d20fe713?#iefix) 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{ + const config = event.detail.data(); + + const flyout = ` + + + Read the Docs + v: ${config.versions.current.slug} + + + + + ${renderLanguages(config)} + ${renderVersions(config)} + ${renderDownloads(config)} + + On Read the Docs + + Project Home + + + Builds + + + Downloads + + + + Search + + + + + + + + + Hosted by Read the Docs + + + + `; + + // Inject the generated flyout into the body HTML element. + document.body.insertAdjacentHTML("beforeend", flyout); + + // Trigger the Read the Docs Addons Search modal when clicking on the "Search docs" input from inside the flyout. + document + .querySelector("#flyout-search-form") + .addEventListener("focusin", () => { + const event = new CustomEvent("readthedocs-search-show"); + document.dispatchEvent(event); + }); + }) +} + +if (themeLanguageSelector || themeVersionSelector) { + function onSelectorSwitch(event) { + const option = event.target.selectedIndex; + const item = event.target.options[option]; + window.location.href = 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config.projects.current, + ); + languages = languages.sort((a, b) => + a.language.name.localeCompare(b.language.name), + ); + + const languageSelect = ` + + ${languages + .map( + (language) => ` + + ${language.language.name} + `, + ) + .join("\n")} + + `; + + languageSwitch.innerHTML = languageSelect; + languageSwitch.firstElementChild.addEventListener("change", onSelectorSwitch); + } + else { + languageSwitch.remove(); + } + } + }); +} + +document.addEventListener("readthedocs-addons-data-ready", function (event) { + // Trigger the Read the Docs Addons Search modal when clicking on "Search docs" input from the topnav. + document + .querySelector("[role='search'] input") + .addEventListener("focusin", () => { + const event = new CustomEvent("readthedocs-search-show"); + document.dispatchEvent(event); + }); +}); \ No newline at end of file diff --git a/docs/pages/html/_static/language_data.js b/docs/pages/html/_static/language_data.js index 250f566..c7fe6c6 100644 --- a/docs/pages/html/_static/language_data.js +++ b/docs/pages/html/_static/language_data.js @@ -1,19 +1,12 @@ /* - * language_data.js - * ~~~~~~~~~~~~~~~~ - * * This script contains the language-specific data used by searchtools.js, * namely the list of stopwords, stemmer, scorer and splitter. - * - * :copyright: Copyright 2007-2023 by the Sphinx team, see AUTHORS. - * :license: BSD, see LICENSE for details. - * */ var stopwords = ["a", "and", "are", "as", "at", "be", "but", "by", "for", "if", "in", "into", "is", "it", "near", "no", "not", "of", "on", "or", "such", "that", "the", "their", "then", "there", "these", "they", "this", "to", "was", "will", "with"]; -/* Non-minified version is copied as a separate JS file, is available */ +/* Non-minified version is copied as a separate JS file, if available */ /** * Porter Stemmer diff --git a/docs/pages/html/_static/notebooks/pca_examples.html b/docs/pages/html/_static/notebooks/pca_examples.html index c9a75dc..7bb55a3 100644 --- a/docs/pages/html/_static/notebooks/pca_examples.html +++ b/docs/pages/html/_static/notebooks/pca_examples.html @@ -1,13 +1,9 @@ - - - + + + pca_examples - - - - - - - - - - - - - - + + + - - - - + void Promise.all([...diagrams].map(renderOneMarmaid)); + }); + + + + + + + - + pca A Python Package for Principal Component Analysis. The core of PCA is build on sklearn functionality to find maximum compatibility when combining with other packages. But this package can do a lot more. Besides the regular pca, it can also perform SparsePCA, and TruncatedSVD. Depending on your input data, the best approach will be choosen. Other functionalities are: @@ -15124,38 +7531,30 @@ github pca - - - + + -In [1]: +In [1]: - -!pip install pca + +!pip install pca - - - + - - - - - - - + + Requirement already satisfied: pca in /usr/local/lib/python3.7/dist-packages (1.7.2) Requirement already satisfied: matplotlib in /usr/local/lib/python3.7/dist-packages (from pca) (3.2.2) Requirement already satisfied: wget in /usr/local/lib/python3.7/dist-packages (from pca) (3.2) @@ -15180,179 +7579,149 @@ - - - - - + + - + Lets check the version - - - + + -In [2]: +In [2]: - -import pca + +import pca print(pca.__version__) - - - + - - - - - - - + + 1.7.2 - - - - - + + - + Import the pca library - - - + + -In [3]: +In [3]: - -from pca import pca + +from pca import pca import numpy as np import pandas as pd - - - - - + + + - + Here we will create a random dataset. - - - + + -In [4]: +In [4]: - -# Dataset + +# Dataset from sklearn.datasets import load_iris X = pd.DataFrame(data=load_iris().data, columns=load_iris().feature_names, index=load_iris().target) - - - - - + + + - + Initialize using specified parameters. The parameters here are the default parameters. - - - + + -In [5]: +In [5]: - -# Initialize + +# Initialize model = pca(n_components=3, normalize=True) - - - - - + + + -In [6]: +In [6]: - -# Fit transform + +# Fit transform out = model.fit_transform(X) - - - + - - - - - - - + + [pca] >Processing dataframe.. [pca] >Normalizing input data per feature (zero mean and unit variance).. [pca] >The PCA reduction is performed on the [4] columns of the input dataframe. @@ -15364,171 +7733,119 @@ - - - - - + + -In [7]: +In [7]: - -# Make plot with only the directions (no scatter) + +# Make plot with only the directions (no scatter) fig, ax = model.biplot(textlabel=True, legend=False, figsize=(10, 6)) - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 with loadings. - - - - - - - - + + + - - - - - - + + -In [8]: +In [8]: - -# Make plot with only the directions (no scatter) + +# Make plot with only the directions (no scatter) fig, ax = model.biplot(cmap=None, textlabel=False, legend=False, figsize=(10, 6)) - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 with loadings. - - - - - - - - + + + - - - - - - + + -In [9]: +In [9]: - -from pca import pca + +from pca import pca # Load example data from sklearn.datasets import load_iris X = pd.DataFrame(data=load_iris().data, columns=load_iris().feature_names, index=load_iris().target) - - - - - + + + -In [10]: +In [10]: - -# Initialize + +# Initialize model = pca(n_components=3) # Fit using PCA results = model.fit_transform(X) - - - + - - - - - - - + + [pca] >Processing dataframe.. [pca] >The PCA reduction is performed on the [4] columns of the input dataframe. [pca] >Fit using PCA. @@ -15539,20 +7856,17 @@ - - - - - + + -In [11]: +In [11]: - -# Make plots + +# Make plots # Scree plot fig, ax = model.plot(figsize=(10, 6)) @@ -15563,190 +7877,117 @@ # Biplot fig, ax = model.biplot(figsize=(10, 6)) - - - + - - - - - - - - - - + + + - - - - - - - - - + + + - - - - - - + + [pca] >Plot PC1 vs PC2 with loadings. - - - - - - - + + <Figure size 432x288 with 0 Axes> - - - - - - - - - + + + - - - - - - + + -In [17]: +In [17]: - -# Coloring on density to focus on the core samples. + +# Coloring on density to focus on the core samples. # Biplot -fig, ax = model.biplot(figsize=(10, 6), gradient='#ffffff') +fig, ax = model.biplot(figsize=(10, 6), gradient='#ffffff') - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 with loadings. - - - - - - - - + + + - - - - - - + + -In [18]: +In [18]: - -# Outliers are stored in results: -results['outliers'] + +# Outliers are stored in results: +results['outliers'] # Outliers based on T2 -print('--------T2------------') -print(results['outliers'].loc[results['outliers']['y_bool'], :]) +print('--------T2------------') +print(results['outliers'].loc[results['outliers']['y_bool'], :]) # Outliers based on SPE -print('--------SPE------------') -print(results['outliers'].loc[results['outliers']['y_bool_spe'], :]) +print('--------SPE------------') +print(results['outliers'].loc[results['outliers']['y_bool_spe'], :]) - - - + - - - - - - - + + --------T2------------ y_proba y_score y_bool y_bool_spe y_score_spe 2 0.040551 13.160880 True True 3.679935 @@ -15771,270 +8012,168 @@ - - - - - + + -In [20]: +In [20]: - -# Outlier detection + +# Outlier detection fig, ax = model.biplot(SPE=True, HT2=True, figsize=(10, 6)) - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 with loadings. - - - - - - - - + + + - - - - - - + + -In [21]: +In [21]: - -# 3D plots + +# 3D plots fig, ax = model.scatter3d(figsize=(10, 6)) fig, ax = model.biplot3d(figsize=(10, 6)) fig, ax = model.biplot3d(SPE=True, HT2=True, figsize=(10, 6)) - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 vs PC3 with loadings. - - - - - - - - + + + - - - - - - - - - + + + - - - - - - + + [pca] >Plot PC1 vs PC2 vs PC3 with loadings. - - - - - - - - + + + - - - - - - + + -In [22]: +In [22]: - -fig, ax = model.biplot3d(SPE=True, HT2=True, visible=False, figsize=(10, 6)) + +fig, ax = model.biplot3d(SPE=True, HT2=True, visible=False, figsize=(10, 6)) # Set the figure again to True and show the figure. fig.set_visible(True) fig - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 vs PC3 with loadings. - - Out[22]: - - - - - - +Out[22]: + + - - - - - - - - - + + + - - - - - - + + -In [23]: +In [23]: - -# Normalize out PCs + +
After the fit_transform, the cumulative expained variance is stored together with the explained variance per PC.
fit_transform
# Cumulative explained variance print(model.results['explained_var']) @@ -201,10 +200,11 @@ Compute explained variancefig, ax = model.plot()
The number of PCs can be reduced by setting the n_components parameter. Note that the number of components can never be larger than the number of variables in your dataset. By setting n_components larger than 1, a feature reduction will be performed to exactly that number of components. By setting n_components smaller than 1, it describes the percentage of explained variance that needs to be covered at least. Or in other words, by setting n_components=0.95, the number of components are extracted that cover at least 95% of the explained variance.
n_components
n_components=0.95
# Reduce the data towards 3 PCs model = pca(n_components=3) @@ -215,7 +215,7 @@ PCs that cover 95% of the explained variance -Scatter plot +Scatter plot # 2D plot fig, ax = model.scatter() @@ -224,7 +224,7 @@ Scatter plot -Color on alcohol +Color on alcohol @@ -233,7 +233,7 @@ Scatter plot -Biplot +Biplot # 2D plot fig, ax = model.biplot(n_feat=4, PC=[0,1]) @@ -241,11 +241,12 @@ Biplotfig, ax = model.biplot3d(n_feat=2, PC=[0,1,2]) - + + -Demonstration of feature importance +Demonstration of feature importance This example is created to showcase the working of extracting features that are most important in a PCA reduction. We will create random variables with increasingly more variance. The first feature (f1) will have most of the variance, followed by feature 2 (f2) etc. # Print the top features. @@ -294,14 +295,15 @@ Demonstration of feature importance -Explained variance plot +Explained variance plot model.plot() - + + -Biplot +Biplot Make the biplot. It can be nicely seen that the first feature with most variance (f1), is almost horizontal in the plot, whereas the second most variance (f2) is almost vertical. This is expected because most of the variance is in f1, followed by f2 etc. Biplot in 3d. Here we see the nice addition of the expected f3 in the plot in the z-direction. # 2d plot ax = model.biplot(n_feat=10, legend=False) @@ -311,7 +313,7 @@ Biplot -Color on alcohol +Color on alcohol @@ -321,10 +323,10 @@ Biplot -Analyzing Discrete datasets +Analyzing Discrete datasets Analyzing datasets that have continuous and catagorical values can be challanging. To demonstrate how to do this, I will use the Titanic dataset. We need to pip install df2onehot first. -pip install df2onehot +pip install df2onehot import pca @@ -383,7 +385,7 @@ Analyzing Discrete datasets -Map unseen datapoints into fitted space +Map unseen datapoints into fitted space After fitting variables into the new principal component space, we can map new unseen samples into this space too. However, there is also normalization step which can be tricky because you now need standardize the values of the unseen samples first based on the previously performed standardization. This step is also integrated in the pca library by simply setting the parameter normalize=True. # Load libraries import matplotlib.pyplot as plt @@ -422,10 +424,11 @@ Map unseen datapoints into fitted spaceax.scatter(PCnew.iloc[:, 0], PCnew.iloc[:, 1], marker='x', s=200) - + + -Normalizing out PCs +Normalizing out PCs Normalize your data using the principal components. As an example, suppose there is (technical) variation in the fist component and you want that out. This function transforms the data using the components that you want, e.g., starting from the 2nd PC, up to the OC that contains at least 95% of the explained variance. print(X.shape) (178, 13) @@ -443,7 +446,7 @@ Normalizing out PCs -Colors in plots +Colors in plots The default colors that are used in the plots depend on how much information is provided at start. There are many parameters to change the colors in the plots. Here I will demonstrate some of the possibilities. First, we will load the data and import the libraries. @@ -476,7 +479,7 @@ Colors in plots -Left: Default plot using the provided classlabels. Right: Color on custom cmap. +Left: Default plot using the provided classlabels. Right: Color on custom cmap. @@ -498,7 +501,7 @@ Colors in plots -Left: Mark some points on y and use cmap. Right: Specify the colors manually. +Left: Mark some points on y and use cmap. Right: Specify the colors manually. @@ -514,7 +517,7 @@ Colors in plots -Left: Remove scatterpoints from plot. Right: Gradient with the used cmap. +Left: Remove scatterpoints from plot. Right: Gradient with the used cmap. @@ -539,7 +542,7 @@ Colors in plots -Fig as input to make iterative changes. +Fig as input to make iterative changes. diff --git a/docs/pages/html/Installation.html b/docs/pages/html/Installation.html index d2fd9ff..8a0f6d2 100644 --- a/docs/pages/html/Installation.html +++ b/docs/pages/html/Installation.html @@ -1,20 +1,22 @@ + + - + - + Installation — pca pca documentation - - - - + + + + - - - + + + + + @@ -33,9 +35,6 @@ pca - - 2.0.1 - @@ -138,9 +137,9 @@ -Installation +Installation -Create environment +Create environment If desired, install pca from an isolated Python environment using conda: conda create -n env_pca python=3.8 conda activate env_pca @@ -148,26 +147,26 @@ Create environment -Pip install -# Install from Pypi: +Pip install +# Install from Pypi: pip install pca -# Install directly from github +# Install directly from github pip install git+https://github.com/erdogant/pca -Uninstalling +Uninstalling Remove the environment with installation: -# List all the active environments. pca should be listed. +# List all the active environments. pca should be listed. conda env list -# Remove the pca environment +# Remove the pca environment conda env remove --name pca -# List all the active environments. pca should be absent. +# List all the active environments. pca should be absent. conda env list diff --git a/docs/pages/html/Outlier detection.html b/docs/pages/html/Outlier detection.html index 37bc204..fe764f4 100644 --- a/docs/pages/html/Outlier detection.html +++ b/docs/pages/html/Outlier detection.html @@ -1,20 +1,22 @@ + + - + - + Hotelling T2 — pca pca documentation - - - - + + + + - - - + + + + + @@ -33,9 +35,6 @@ pca - - 2.0.1 - @@ -134,7 +133,7 @@ -Hotelling T2 +Hotelling T2 To detect outliers across the multidimensional space of PCA, the hotellings T2 test is implemented. It works by computing the chi-square tests across the top n_components: default is PC1 to PC5. The reason for not using more PC’s is that it is expected that the highest variance (and thus the outliers) will be seen in the first few components. Going deeper into PC space may therefore not be required. Nevertheless, the depth is optional. The hotellings T2 test outputs a P-value matrix (samples x PCs), which are are subsequently combined using fishers method. This allows to determine outliers with its ranking (strongest to weak). The alpha parameter determines the detection of outliers (default: 0.05). @@ -192,7 +191,7 @@ Hotelling T2 -SPE/Dmodx +SPE/Dmodx Outlier can be detected using SPE/DmodX (distance to model) based on the mean and covariance of the first 2 dimensions of X. On the model plane (SPE ≈ 0). Note that the SPE or Hotelling’s T2 are complementary to each other. model.biplot(legend=True, SPE=True, HT2=True) @@ -204,7 +203,7 @@ SPE/Dmodx -Detected outliers +Detected outliers @@ -213,7 +212,7 @@ SPE/Dmodx -Selection of the Outliers +Selection of the Outliers Selecting the outliers can be usefull to remove them from the dataset or for deeper investigation. # Select the outliers Xoutliers = X[results['outliers']['y_bool'],:] @@ -224,7 +223,7 @@ Selection of the Outliers -Detect new unseen outliers +Detect new unseen outliers After fitting a model on the data, you may want to use the model in a later stage to detect outliers on unseen data. Detection of outliers is performed in the transform function and does not require any additional action. An example is shown in the code block below. # Import libraries @@ -252,7 +251,7 @@ Detect new unseen outliers -Detected outliers +Detected outliers @@ -288,7 +287,7 @@ Detect new unseen outliers -Detected outliers +Detected outliers @@ -296,7 +295,7 @@ Detect new unseen outliers -Detection of outliers without PCA +Detection of outliers without PCA If desired, the outliers can also be detected directly using the hotelling T2 and/or SPE/DmodX functionality. For demonstration purposes I use the PCs from the results but any other dataset would also work. import pca diff --git a/docs/pages/html/Plots.html b/docs/pages/html/Plots.html index c1677b6..f054370 100644 --- a/docs/pages/html/Plots.html +++ b/docs/pages/html/Plots.html @@ -1,20 +1,22 @@ + + - + - + Load dataset — pca pca documentation - - - - + + + + - - - + + + + + @@ -33,9 +35,6 @@ pca - - 2.0.1 - @@ -134,7 +133,7 @@ -Load dataset +Load dataset Let’s load the wine dataset to demonstrate the plots. # Load library from sklearn.datasets import load_wine @@ -166,7 +165,7 @@ Load dataset -Scatter plot +Scatter plot # Make scatterplot model.scatter() @@ -187,7 +186,7 @@ Scatter plot -Scatterplots +Scatterplots @@ -204,16 +203,40 @@ Scatter plot -Biplot +Biplot +The biplot draws the loadings (arrows) together with the samples (scatterplot). +The loadings can be colored red and blue which indicates the strength of the particular feature in the PC. +For each principal component (PC), the feature is determined with the largest absolute loading. This indicates which feature contributes the most to each PC and can occur in multiple PCs. +The highest loading values for the features are colored red in the biplot and described as “best” in the output dataframe. +The features that were not seen with highest loadings for any PC are considered weaker features, and are colored blue the biplot. In the output dataframe these features are described as “weak”. # Make biplot model.biplot() # Here again, many other options can be turned on and off model.biplot(SPE=True, HT2=True, legend=1) + +# Show the top features +results['topfeat'] + +# PC feature loading type +# 0 PC1 flavanoids 0.422934 best +# 1 PC2 color_intensity 0.529996 best +# 2 PC3 ash 0.626224 best +# 3 PC4 malic_acid 0.536890 best +# 4 PC5 magnesium 0.727049 best +# 5 PC6 malic_acid 0.536814 best +# 6 PC7 nonflavanoid_phenols 0.595447 best +# 7 PC8 hue 0.436624 best +# 8 PC9 proline 0.575786 best +# 9 PC10 od280/od315_of_diluted_wines 0.523706 best +# 10 PC9 alcohol -0.508619 weak +# 11 PC3 alcalinity_of_ash 0.612080 weak +# 12 PC8 total_phenols -0.405934 weak +# 13 PC6 proanthocyanins -0.533795 weak -Biplots +Biplots @@ -223,28 +246,30 @@ Biplot -Biplot (only arrows) +Biplot (only arrows) # Make plot with parameters: set cmap to None and label and legend to False. Only directions will be plotted. model.biplot(cmap=None, legend=False) - + + -Explained variance plot +Explained variance plot model.plot() - + + -Alpha Transparency +Alpha Transparency fig, ax = model.scatter(alpha=1) -Markers +Markers import numpy as np from sklearn.datasets import make_friedman1 from pca import pca @@ -272,7 +297,7 @@ Markers -Biplots with markers +Biplots with markers @@ -280,7 +305,7 @@ Markers -Control color/marker/size per sample +Control color/marker/size per sample import numpy as np import matplotlib.pyplot as plt import matplotlib.colors as mcolors @@ -329,7 +354,7 @@ Control color/marker/size per sample -Biplot with customized properties per sample. +Biplot with customized properties per sample. @@ -337,15 +362,16 @@ Control color/marker/size per sample -3D plots +3D plots All plots can also be created in 3D by setting the d3=True parameter. model.biplot3d() - + + -Toggle visible status +Toggle visible status The visible status for can be turned on and off. # Make plot but not visible. fig, ax = model.biplot(visible=False) diff --git a/docs/pages/html/_sources/Plots.rst.txt b/docs/pages/html/_sources/Plots.rst.txt index 33319b2..38cd2db 100644 --- a/docs/pages/html/_sources/Plots.rst.txt +++ b/docs/pages/html/_sources/Plots.rst.txt @@ -83,6 +83,14 @@ Scatter plot Biplot ############### +The biplot draws the loadings (arrows) together with the samples (scatterplot). +The loadings can be colored red and blue which indicates the strength of the particular feature in the PC. + +For each principal component (PC), the feature is determined with the largest absolute loading. This indicates which feature contributes the most to each PC and can occur in multiple PCs. +The highest loading values for the features are colored red in the biplot and described as "best" in the output dataframe. +The features that were not seen with highest loadings for any PC are considered weaker features, and are colored blue the biplot. In the output dataframe these features are described as "weak". + + .. code:: python # Make biplot @@ -91,6 +99,24 @@ Biplot # Here again, many other options can be turned on and off model.biplot(SPE=True, HT2=True, legend=1) + # Show the top features + results['topfeat'] + + # PC feature loading type + # 0 PC1 flavanoids 0.422934 best + # 1 PC2 color_intensity 0.529996 best + # 2 PC3 ash 0.626224 best + # 3 PC4 malic_acid 0.536890 best + # 4 PC5 magnesium 0.727049 best + # 5 PC6 malic_acid 0.536814 best + # 6 PC7 nonflavanoid_phenols 0.595447 best + # 7 PC8 hue 0.436624 best + # 8 PC9 proline 0.575786 best + # 9 PC10 od280/od315_of_diluted_wines 0.523706 best + # 10 PC9 alcohol -0.508619 weak + # 11 PC3 alcalinity_of_ash 0.612080 weak + # 12 PC8 total_phenols -0.405934 weak + # 13 PC6 proanthocyanins -0.533795 weak .. |figP5| image:: ../figs/wine_biplot.png .. |figP6| image:: ../figs/wine_biplot_with_outliers.png diff --git a/docs/pages/html/_sources/sponsor.rst.txt b/docs/pages/html/_sources/sponsor.rst.txt index a46c410..f006896 100644 --- a/docs/pages/html/_sources/sponsor.rst.txt +++ b/docs/pages/html/_sources/sponsor.rst.txt @@ -4,8 +4,10 @@ * Become a `Sponsor `_! * `Buy `_ me a coffee! I ❤️ coffee :) * `Donate `_ in Bitcoin. - * Follow me on medium! Go to my `medium profile `_ and press *follow*. + * Follow me on Medium! Go to my `medium profile `_ and press *follow*. + * Subscribe to me on Substack! Go to my `profile `_ where you can *subscribe*. * **Star** this repo at the github page. + * You can also buy a digital educational product over `here `_. * Other contributions can be in the form of feature requests, idea discussions, reporting bugs, opening pull requests. Cheers Mate. diff --git a/docs/pages/html/_static/_sphinx_javascript_frameworks_compat.js b/docs/pages/html/_static/_sphinx_javascript_frameworks_compat.js new file mode 100644 index 0000000..8141580 --- /dev/null +++ b/docs/pages/html/_static/_sphinx_javascript_frameworks_compat.js @@ -0,0 +1,123 @@ +/* Compatability shim for jQuery and underscores.js. + * + * Copyright Sphinx contributors + * Released under the two clause BSD licence + */ + +/** + * small helper function to urldecode strings + * + * See https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/decodeURIComponent#Decoding_query_parameters_from_a_URL + */ +jQuery.urldecode = function(x) { + if (!x) { + return x + } + return decodeURIComponent(x.replace(/\+/g, ' ')); +}; + +/** + * small helper function to urlencode strings + */ +jQuery.urlencode = encodeURIComponent; + +/** + * This function returns the parsed url parameters of the + * current request. Multiple values per key are supported, + * it will always return arrays of strings for the value parts. + */ +jQuery.getQueryParameters = function(s) { + if (typeof s === 'undefined') + s = document.location.search; + var parts = s.substr(s.indexOf('?') + 1).split('&'); + var result = {}; + for (var i = 0; i < parts.length; i++) { + var tmp = parts[i].split('=', 2); + var key = jQuery.urldecode(tmp[0]); + var value = jQuery.urldecode(tmp[1]); + if (key in result) + result[key].push(value); + else + result[key] = [value]; + } + return result; +}; + +/** + * highlight a given string on a jquery object by wrapping it in + * span elements with the given class name. + */ +jQuery.fn.highlightText = function(text, className) { + function highlight(node, addItems) { + if (node.nodeType === 3) { + var val = node.nodeValue; + var pos = val.toLowerCase().indexOf(text); + if (pos >= 0 && + !jQuery(node.parentNode).hasClass(className) && + !jQuery(node.parentNode).hasClass("nohighlight")) { + var span; + var isInSVG = jQuery(node).closest("body, svg, foreignObject").is("svg"); + if (isInSVG) { + span = document.createElementNS("http://www.w3.org/2000/svg", "tspan"); + } else { + span = document.createElement("span"); + span.className = className; + } + span.appendChild(document.createTextNode(val.substr(pos, text.length))); + node.parentNode.insertBefore(span, node.parentNode.insertBefore( + document.createTextNode(val.substr(pos + text.length)), + node.nextSibling)); + node.nodeValue = val.substr(0, pos); + if (isInSVG) { + var rect = document.createElementNS("http://www.w3.org/2000/svg", "rect"); + var bbox = node.parentElement.getBBox(); + rect.x.baseVal.value = bbox.x; + rect.y.baseVal.value = bbox.y; + rect.width.baseVal.value = bbox.width; + rect.height.baseVal.value = bbox.height; + rect.setAttribute('class', className); + addItems.push({ + "parent": node.parentNode, + "target": rect}); + } + } + } + else if (!jQuery(node).is("button, select, textarea")) { + jQuery.each(node.childNodes, function() { + highlight(this, addItems); + }); + } + } + var addItems = []; + var result = this.each(function() { + highlight(this, addItems); + }); + for (var i = 0; i < addItems.length; ++i) { + jQuery(addItems[i].parent).before(addItems[i].target); + } + return result; +}; + +/* + * backward compatibility for jQuery.browser + * This will be supported until firefox bug is fixed. + */ +if (!jQuery.browser) { + jQuery.uaMatch = function(ua) { + ua = ua.toLowerCase(); + + var match = /(chrome)[ \/]([\w.]+)/.exec(ua) || + /(webkit)[ \/]([\w.]+)/.exec(ua) || + /(opera)(?:.*version|)[ \/]([\w.]+)/.exec(ua) || + /(msie) ([\w.]+)/.exec(ua) || + ua.indexOf("compatible") < 0 && /(mozilla)(?:.*? rv:([\w.]+)|)/.exec(ua) || + []; + + return { + browser: match[ 1 ] || "", + version: match[ 2 ] || "0" + }; + }; + jQuery.browser = {}; + jQuery.browser[jQuery.uaMatch(navigator.userAgent).browser] = true; +} diff --git a/docs/pages/html/_static/basic.css b/docs/pages/html/_static/basic.css index 7577acb..7ebbd6d 100644 --- a/docs/pages/html/_static/basic.css +++ b/docs/pages/html/_static/basic.css @@ -1,12 +1,5 @@ /* - * basic.css - * ~~~~~~~~~ - * * Sphinx stylesheet -- basic theme. - * - * :copyright: Copyright 2007-2023 by the Sphinx team, see AUTHORS. - * :license: BSD, see LICENSE for details. - * */ /* -- main layout ----------------------------------------------------------- */ @@ -115,15 +108,11 @@ img { /* -- search page ----------------------------------------------------------- */ ul.search { - margin: 10px 0 0 20px; - padding: 0; + margin-top: 10px; } ul.search li { - padding: 5px 0 5px 20px; - background-image: url(file.png); - background-repeat: no-repeat; - background-position: 0 7px; + padding: 5px 0; } ul.search li a { @@ -237,6 +226,10 @@ a.headerlink { visibility: hidden; } +a:visited { + color: #551A8B; +} + h1:hover > a.headerlink, h2:hover > a.headerlink, h3:hover > a.headerlink, @@ -670,6 +663,16 @@ dd { 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config.projects.current, + ); + languages = languages.sort((a, b) => + a.language.name.localeCompare(b.language.name), + ); + + const languageSelect = ` + + ${languages + .map( + (language) => ` + + ${language.language.name} + `, + ) + .join("\n")} + + `; + + languageSwitch.innerHTML = languageSelect; + languageSwitch.firstElementChild.addEventListener("change", onSelectorSwitch); + } + else { + languageSwitch.remove(); + } + } + }); +} + +document.addEventListener("readthedocs-addons-data-ready", function (event) { + // Trigger the Read the Docs Addons Search modal when clicking on "Search docs" input from the topnav. + document + .querySelector("[role='search'] input") + .addEventListener("focusin", () => { + const event = new CustomEvent("readthedocs-search-show"); + document.dispatchEvent(event); + }); +}); \ No newline at end of file diff --git a/docs/pages/html/_static/language_data.js b/docs/pages/html/_static/language_data.js index 250f566..c7fe6c6 100644 --- a/docs/pages/html/_static/language_data.js +++ b/docs/pages/html/_static/language_data.js @@ -1,19 +1,12 @@ /* - * language_data.js - * ~~~~~~~~~~~~~~~~ - * * This script contains the language-specific data used by searchtools.js, * namely the list of stopwords, stemmer, scorer and splitter. - * - * :copyright: Copyright 2007-2023 by the Sphinx team, see AUTHORS. - * :license: BSD, see LICENSE for details. - * */ var stopwords = ["a", "and", "are", "as", "at", "be", "but", "by", "for", "if", "in", "into", "is", "it", "near", "no", "not", "of", "on", "or", "such", "that", "the", "their", "then", "there", "these", "they", "this", "to", "was", "will", "with"]; -/* Non-minified version is copied as a separate JS file, is available */ +/* Non-minified version is copied as a separate JS file, if available */ /** * Porter Stemmer diff --git a/docs/pages/html/_static/notebooks/pca_examples.html b/docs/pages/html/_static/notebooks/pca_examples.html index c9a75dc..7bb55a3 100644 --- a/docs/pages/html/_static/notebooks/pca_examples.html +++ b/docs/pages/html/_static/notebooks/pca_examples.html @@ -1,13 +1,9 @@ - - - + + + pca_examples - - - - - - - - - - - - - - + + + - - - - + void Promise.all([...diagrams].map(renderOneMarmaid)); + }); + + + + + + + - + pca A Python Package for Principal Component Analysis. The core of PCA is build on sklearn functionality to find maximum compatibility when combining with other packages. But this package can do a lot more. Besides the regular pca, it can also perform SparsePCA, and TruncatedSVD. Depending on your input data, the best approach will be choosen. Other functionalities are: @@ -15124,38 +7531,30 @@ github pca - - - + + -In [1]: +In [1]: - -!pip install pca + +!pip install pca - - - + - - - - - - - + + Requirement already satisfied: pca in /usr/local/lib/python3.7/dist-packages (1.7.2) Requirement already satisfied: matplotlib in /usr/local/lib/python3.7/dist-packages (from pca) (3.2.2) Requirement already satisfied: wget in /usr/local/lib/python3.7/dist-packages (from pca) (3.2) @@ -15180,179 +7579,149 @@ - - - - - + + - + Lets check the version - - - + + -In [2]: +In [2]: - -import pca + +import pca print(pca.__version__) - - - + - - - - - - - + + 1.7.2 - - - - - + + - + Import the pca library - - - + + -In [3]: +In [3]: - -from pca import pca + +from pca import pca import numpy as np import pandas as pd - - - - - + + + - + Here we will create a random dataset. - - - + + -In [4]: +In [4]: - -# Dataset + +# Dataset from sklearn.datasets import load_iris X = pd.DataFrame(data=load_iris().data, columns=load_iris().feature_names, index=load_iris().target) - - - - - + + + - + Initialize using specified parameters. The parameters here are the default parameters. - - - + + -In [5]: +In [5]: - -# Initialize + +# Initialize model = pca(n_components=3, normalize=True) - - - - - + + + -In [6]: +In [6]: - -# Fit transform + +# Fit transform out = model.fit_transform(X) - - - + - - - - - - - + + [pca] >Processing dataframe.. [pca] >Normalizing input data per feature (zero mean and unit variance).. [pca] >The PCA reduction is performed on the [4] columns of the input dataframe. @@ -15364,171 +7733,119 @@ - - - - - + + -In [7]: +In [7]: - -# Make plot with only the directions (no scatter) + +# Make plot with only the directions (no scatter) fig, ax = model.biplot(textlabel=True, legend=False, figsize=(10, 6)) - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 with loadings. - - - - - - - - + + + - - - - - - + + -In [8]: +In [8]: - -# Make plot with only the directions (no scatter) + +# Make plot with only the directions (no scatter) fig, ax = model.biplot(cmap=None, textlabel=False, legend=False, figsize=(10, 6)) - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 with loadings. - - - - - - - - + + + - - - - - - + + -In [9]: +In [9]: - -from pca import pca + +from pca import pca # Load example data from sklearn.datasets import load_iris X = pd.DataFrame(data=load_iris().data, columns=load_iris().feature_names, index=load_iris().target) - - - - - + + + -In [10]: +In [10]: - -# Initialize + +# Initialize model = pca(n_components=3) # Fit using PCA results = model.fit_transform(X) - - - + - - - - - - - + + [pca] >Processing dataframe.. [pca] >The PCA reduction is performed on the [4] columns of the input dataframe. [pca] >Fit using PCA. @@ -15539,20 +7856,17 @@ - - - - - + + -In [11]: +In [11]: - -# Make plots + +# Make plots # Scree plot fig, ax = model.plot(figsize=(10, 6)) @@ -15563,190 +7877,117 @@ # Biplot fig, ax = model.biplot(figsize=(10, 6)) - - - + - - - - - - - - - - + + + - - - - - - - - - + + + - - - - - - + + [pca] >Plot PC1 vs PC2 with loadings. - - - - - - - + + <Figure size 432x288 with 0 Axes> - - - - - - - - - + + + - - - - - - + + -In [17]: +In [17]: - -# Coloring on density to focus on the core samples. + +# Coloring on density to focus on the core samples. # Biplot -fig, ax = model.biplot(figsize=(10, 6), gradient='#ffffff') +fig, ax = model.biplot(figsize=(10, 6), gradient='#ffffff') - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 with loadings. - - - - - - - - + + + - - - - - - + + -In [18]: +In [18]: - -# Outliers are stored in results: -results['outliers'] + +# Outliers are stored in results: +results['outliers'] # Outliers based on T2 -print('--------T2------------') -print(results['outliers'].loc[results['outliers']['y_bool'], :]) +print('--------T2------------') +print(results['outliers'].loc[results['outliers']['y_bool'], :]) # Outliers based on SPE -print('--------SPE------------') -print(results['outliers'].loc[results['outliers']['y_bool_spe'], :]) +print('--------SPE------------') +print(results['outliers'].loc[results['outliers']['y_bool_spe'], :]) - - - + - - - - - - - + + --------T2------------ y_proba y_score y_bool y_bool_spe y_score_spe 2 0.040551 13.160880 True True 3.679935 @@ -15771,270 +8012,168 @@ - - - - - + + -In [20]: +In [20]: - -# Outlier detection + +# Outlier detection fig, ax = model.biplot(SPE=True, HT2=True, figsize=(10, 6)) - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 with loadings. - - - - - - - - + + + - - - - - - + + -In [21]: +In [21]: - -# 3D plots + +# 3D plots fig, ax = model.scatter3d(figsize=(10, 6)) fig, ax = model.biplot3d(figsize=(10, 6)) fig, ax = model.biplot3d(SPE=True, HT2=True, figsize=(10, 6)) - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 vs PC3 with loadings. - - - - - - - - + + + - - - - - - - - - + + + - - - - - - + + [pca] >Plot PC1 vs PC2 vs PC3 with loadings. - - - - - - - - + + + - - - - - - + + -In [22]: +In [22]: - -fig, ax = model.biplot3d(SPE=True, HT2=True, visible=False, figsize=(10, 6)) + +fig, ax = model.biplot3d(SPE=True, HT2=True, visible=False, figsize=(10, 6)) # Set the figure again to True and show the figure. fig.set_visible(True) fig - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 vs PC3 with loadings. - - Out[22]: - - - - - - +Out[22]: + + - - - - - - - - - + + + - - - - - - + + -In [23]: +In [23]: - -# Normalize out PCs + +
# 2D plot fig, ax = model.scatter() @@ -224,7 +224,7 @@ Scatter plot -Color on alcohol +Color on alcohol @@ -233,7 +233,7 @@ Scatter plot -Biplot +Biplot # 2D plot fig, ax = model.biplot(n_feat=4, PC=[0,1]) @@ -241,11 +241,12 @@ Biplotfig, ax = model.biplot3d(n_feat=2, PC=[0,1,2]) - + + -Demonstration of feature importance +Demonstration of feature importance This example is created to showcase the working of extracting features that are most important in a PCA reduction. We will create random variables with increasingly more variance. The first feature (f1) will have most of the variance, followed by feature 2 (f2) etc. # Print the top features. @@ -294,14 +295,15 @@ Demonstration of feature importance -Explained variance plot +Explained variance plot model.plot() - + + -Biplot +Biplot Make the biplot. It can be nicely seen that the first feature with most variance (f1), is almost horizontal in the plot, whereas the second most variance (f2) is almost vertical. This is expected because most of the variance is in f1, followed by f2 etc. Biplot in 3d. Here we see the nice addition of the expected f3 in the plot in the z-direction. # 2d plot ax = model.biplot(n_feat=10, legend=False) @@ -311,7 +313,7 @@ Biplot -Color on alcohol +Color on alcohol @@ -321,10 +323,10 @@ Biplot -Analyzing Discrete datasets +Analyzing Discrete datasets Analyzing datasets that have continuous and catagorical values can be challanging. To demonstrate how to do this, I will use the Titanic dataset. We need to pip install df2onehot first. -pip install df2onehot +pip install df2onehot import pca @@ -383,7 +385,7 @@ Analyzing Discrete datasets -Map unseen datapoints into fitted space +Map unseen datapoints into fitted space After fitting variables into the new principal component space, we can map new unseen samples into this space too. However, there is also normalization step which can be tricky because you now need standardize the values of the unseen samples first based on the previously performed standardization. This step is also integrated in the pca library by simply setting the parameter normalize=True. # Load libraries import matplotlib.pyplot as plt @@ -422,10 +424,11 @@ Map unseen datapoints into fitted spaceax.scatter(PCnew.iloc[:, 0], PCnew.iloc[:, 1], marker='x', s=200) - + + -Normalizing out PCs +Normalizing out PCs Normalize your data using the principal components. As an example, suppose there is (technical) variation in the fist component and you want that out. This function transforms the data using the components that you want, e.g., starting from the 2nd PC, up to the OC that contains at least 95% of the explained variance. print(X.shape) (178, 13) @@ -443,7 +446,7 @@ Normalizing out PCs -Colors in plots +Colors in plots The default colors that are used in the plots depend on how much information is provided at start. There are many parameters to change the colors in the plots. Here I will demonstrate some of the possibilities. First, we will load the data and import the libraries. @@ -476,7 +479,7 @@ Colors in plots -Left: Default plot using the provided classlabels. Right: Color on custom cmap. +Left: Default plot using the provided classlabels. Right: Color on custom cmap. @@ -498,7 +501,7 @@ Colors in plots -Left: Mark some points on y and use cmap. Right: Specify the colors manually. +Left: Mark some points on y and use cmap. Right: Specify the colors manually. @@ -514,7 +517,7 @@ Colors in plots -Left: Remove scatterpoints from plot. Right: Gradient with the used cmap. +Left: Remove scatterpoints from plot. Right: Gradient with the used cmap. @@ -539,7 +542,7 @@ Colors in plots -Fig as input to make iterative changes. +Fig as input to make iterative changes. diff --git a/docs/pages/html/Installation.html b/docs/pages/html/Installation.html index d2fd9ff..8a0f6d2 100644 --- a/docs/pages/html/Installation.html +++ b/docs/pages/html/Installation.html @@ -1,20 +1,22 @@ + + - + - + Installation — pca pca documentation - - - - + + + + - - - + + + + + @@ -33,9 +35,6 @@ pca - - 2.0.1 - @@ -138,9 +137,9 @@ -Installation +Installation -Create environment +Create environment If desired, install pca from an isolated Python environment using conda: conda create -n env_pca python=3.8 conda activate env_pca @@ -148,26 +147,26 @@ Create environment -Pip install -# Install from Pypi: +Pip install +# Install from Pypi: pip install pca -# Install directly from github +# Install directly from github pip install git+https://github.com/erdogant/pca -Uninstalling +Uninstalling Remove the environment with installation: -# List all the active environments. pca should be listed. +# List all the active environments. pca should be listed. conda env list -# Remove the pca environment +# Remove the pca environment conda env remove --name pca -# List all the active environments. pca should be absent. +# List all the active environments. pca should be absent. conda env list diff --git a/docs/pages/html/Outlier detection.html b/docs/pages/html/Outlier detection.html index 37bc204..fe764f4 100644 --- a/docs/pages/html/Outlier detection.html +++ b/docs/pages/html/Outlier detection.html @@ -1,20 +1,22 @@ + + - + - + Hotelling T2 — pca pca documentation - - - - + + + + - - - + + + + + @@ -33,9 +35,6 @@ pca - - 2.0.1 - @@ -134,7 +133,7 @@ -Hotelling T2 +Hotelling T2 To detect outliers across the multidimensional space of PCA, the hotellings T2 test is implemented. It works by computing the chi-square tests across the top n_components: default is PC1 to PC5. The reason for not using more PC’s is that it is expected that the highest variance (and thus the outliers) will be seen in the first few components. Going deeper into PC space may therefore not be required. Nevertheless, the depth is optional. The hotellings T2 test outputs a P-value matrix (samples x PCs), which are are subsequently combined using fishers method. This allows to determine outliers with its ranking (strongest to weak). The alpha parameter determines the detection of outliers (default: 0.05). @@ -192,7 +191,7 @@ Hotelling T2 -SPE/Dmodx +SPE/Dmodx Outlier can be detected using SPE/DmodX (distance to model) based on the mean and covariance of the first 2 dimensions of X. On the model plane (SPE ≈ 0). Note that the SPE or Hotelling’s T2 are complementary to each other. model.biplot(legend=True, SPE=True, HT2=True) @@ -204,7 +203,7 @@ SPE/Dmodx -Detected outliers +Detected outliers @@ -213,7 +212,7 @@ SPE/Dmodx -Selection of the Outliers +Selection of the Outliers Selecting the outliers can be usefull to remove them from the dataset or for deeper investigation. # Select the outliers Xoutliers = X[results['outliers']['y_bool'],:] @@ -224,7 +223,7 @@ Selection of the Outliers -Detect new unseen outliers +Detect new unseen outliers After fitting a model on the data, you may want to use the model in a later stage to detect outliers on unseen data. Detection of outliers is performed in the transform function and does not require any additional action. An example is shown in the code block below. # Import libraries @@ -252,7 +251,7 @@ Detect new unseen outliers -Detected outliers +Detected outliers @@ -288,7 +287,7 @@ Detect new unseen outliers -Detected outliers +Detected outliers @@ -296,7 +295,7 @@ Detect new unseen outliers -Detection of outliers without PCA +Detection of outliers without PCA If desired, the outliers can also be detected directly using the hotelling T2 and/or SPE/DmodX functionality. For demonstration purposes I use the PCs from the results but any other dataset would also work. import pca diff --git a/docs/pages/html/Plots.html b/docs/pages/html/Plots.html index c1677b6..f054370 100644 --- a/docs/pages/html/Plots.html +++ b/docs/pages/html/Plots.html @@ -1,20 +1,22 @@ + + - + - + Load dataset — pca pca documentation - - - - + + + + - - - + + + + + @@ -33,9 +35,6 @@ pca - - 2.0.1 - @@ -134,7 +133,7 @@ -Load dataset +Load dataset Let’s load the wine dataset to demonstrate the plots. # Load library from sklearn.datasets import load_wine @@ -166,7 +165,7 @@ Load dataset -Scatter plot +Scatter plot # Make scatterplot model.scatter() @@ -187,7 +186,7 @@ Scatter plot -Scatterplots +Scatterplots @@ -204,16 +203,40 @@ Scatter plot -Biplot +Biplot +The biplot draws the loadings (arrows) together with the samples (scatterplot). +The loadings can be colored red and blue which indicates the strength of the particular feature in the PC. +For each principal component (PC), the feature is determined with the largest absolute loading. This indicates which feature contributes the most to each PC and can occur in multiple PCs. +The highest loading values for the features are colored red in the biplot and described as “best” in the output dataframe. +The features that were not seen with highest loadings for any PC are considered weaker features, and are colored blue the biplot. In the output dataframe these features are described as “weak”. # Make biplot model.biplot() # Here again, many other options can be turned on and off model.biplot(SPE=True, HT2=True, legend=1) + +# Show the top features +results['topfeat'] + +# PC feature loading type +# 0 PC1 flavanoids 0.422934 best +# 1 PC2 color_intensity 0.529996 best +# 2 PC3 ash 0.626224 best +# 3 PC4 malic_acid 0.536890 best +# 4 PC5 magnesium 0.727049 best +# 5 PC6 malic_acid 0.536814 best +# 6 PC7 nonflavanoid_phenols 0.595447 best +# 7 PC8 hue 0.436624 best +# 8 PC9 proline 0.575786 best +# 9 PC10 od280/od315_of_diluted_wines 0.523706 best +# 10 PC9 alcohol -0.508619 weak +# 11 PC3 alcalinity_of_ash 0.612080 weak +# 12 PC8 total_phenols -0.405934 weak +# 13 PC6 proanthocyanins -0.533795 weak -Biplots +Biplots @@ -223,28 +246,30 @@ Biplot -Biplot (only arrows) +Biplot (only arrows) # Make plot with parameters: set cmap to None and label and legend to False. Only directions will be plotted. model.biplot(cmap=None, legend=False) - + + -Explained variance plot +Explained variance plot model.plot() - + + -Alpha Transparency +Alpha Transparency fig, ax = model.scatter(alpha=1) -Markers +Markers import numpy as np from sklearn.datasets import make_friedman1 from pca import pca @@ -272,7 +297,7 @@ Markers -Biplots with markers +Biplots with markers @@ -280,7 +305,7 @@ Markers -Control color/marker/size per sample +Control color/marker/size per sample import numpy as np import matplotlib.pyplot as plt import matplotlib.colors as mcolors @@ -329,7 +354,7 @@ Control color/marker/size per sample -Biplot with customized properties per sample. +Biplot with customized properties per sample. @@ -337,15 +362,16 @@ Control color/marker/size per sample -3D plots +3D plots All plots can also be created in 3D by setting the d3=True parameter. model.biplot3d() - + + -Toggle visible status +Toggle visible status The visible status for can be turned on and off. # Make plot but not visible. fig, ax = model.biplot(visible=False) diff --git a/docs/pages/html/_sources/Plots.rst.txt b/docs/pages/html/_sources/Plots.rst.txt index 33319b2..38cd2db 100644 --- a/docs/pages/html/_sources/Plots.rst.txt +++ b/docs/pages/html/_sources/Plots.rst.txt @@ -83,6 +83,14 @@ Scatter plot Biplot ############### +The biplot draws the loadings (arrows) together with the samples (scatterplot). +The loadings can be colored red and blue which indicates the strength of the particular feature in the PC. + +For each principal component (PC), the feature is determined with the largest absolute loading. This indicates which feature contributes the most to each PC and can occur in multiple PCs. +The highest loading values for the features are colored red in the biplot and described as "best" in the output dataframe. +The features that were not seen with highest loadings for any PC are considered weaker features, and are colored blue the biplot. In the output dataframe these features are described as "weak". + + .. code:: python # Make biplot @@ -91,6 +99,24 @@ Biplot # Here again, many other options can be turned on and off model.biplot(SPE=True, HT2=True, legend=1) + # Show the top features + results['topfeat'] + + # PC feature loading type + # 0 PC1 flavanoids 0.422934 best + # 1 PC2 color_intensity 0.529996 best + # 2 PC3 ash 0.626224 best + # 3 PC4 malic_acid 0.536890 best + # 4 PC5 magnesium 0.727049 best + # 5 PC6 malic_acid 0.536814 best + # 6 PC7 nonflavanoid_phenols 0.595447 best + # 7 PC8 hue 0.436624 best + # 8 PC9 proline 0.575786 best + # 9 PC10 od280/od315_of_diluted_wines 0.523706 best + # 10 PC9 alcohol -0.508619 weak + # 11 PC3 alcalinity_of_ash 0.612080 weak + # 12 PC8 total_phenols -0.405934 weak + # 13 PC6 proanthocyanins -0.533795 weak .. |figP5| image:: ../figs/wine_biplot.png .. |figP6| image:: ../figs/wine_biplot_with_outliers.png diff --git a/docs/pages/html/_sources/sponsor.rst.txt b/docs/pages/html/_sources/sponsor.rst.txt index a46c410..f006896 100644 --- a/docs/pages/html/_sources/sponsor.rst.txt +++ b/docs/pages/html/_sources/sponsor.rst.txt @@ -4,8 +4,10 @@ * Become a `Sponsor `_! * `Buy `_ me a coffee! I ❤️ coffee :) * `Donate `_ in Bitcoin. - * Follow me on medium! Go to my `medium profile `_ and press *follow*. + * Follow me on Medium! Go to my `medium profile `_ and press *follow*. + * Subscribe to me on Substack! Go to my `profile `_ where you can *subscribe*. * **Star** this repo at the github page. + * You can also buy a digital educational product over `here `_. * Other contributions can be in the form of feature requests, idea discussions, reporting bugs, opening pull requests. Cheers Mate. diff --git a/docs/pages/html/_static/_sphinx_javascript_frameworks_compat.js b/docs/pages/html/_static/_sphinx_javascript_frameworks_compat.js new file mode 100644 index 0000000..8141580 --- /dev/null +++ b/docs/pages/html/_static/_sphinx_javascript_frameworks_compat.js @@ -0,0 +1,123 @@ +/* Compatability shim for jQuery and underscores.js. + * + * Copyright Sphinx contributors + * Released under the two clause BSD licence + */ + +/** + * small helper function to urldecode strings + * + * See https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/decodeURIComponent#Decoding_query_parameters_from_a_URL + */ +jQuery.urldecode = function(x) { + if (!x) { + return x + } + return decodeURIComponent(x.replace(/\+/g, ' ')); +}; + +/** + * small helper function to urlencode strings + */ +jQuery.urlencode = encodeURIComponent; + +/** + * This function returns the parsed url parameters of the + * current request. Multiple values per key are supported, + * it will always return arrays of strings for the value parts. + */ +jQuery.getQueryParameters = function(s) { + if (typeof s === 'undefined') + s = document.location.search; + var parts = s.substr(s.indexOf('?') + 1).split('&'); + var result = {}; + for (var i = 0; i < parts.length; i++) { + var tmp = parts[i].split('=', 2); + var key = jQuery.urldecode(tmp[0]); + var value = jQuery.urldecode(tmp[1]); + if (key in result) + result[key].push(value); + else + result[key] = [value]; + } + return result; +}; + +/** + * highlight a given string on a jquery object by wrapping it in + * span elements with the given class name. + */ +jQuery.fn.highlightText = function(text, className) { + function highlight(node, addItems) { + if (node.nodeType === 3) { + var val = node.nodeValue; + var pos = val.toLowerCase().indexOf(text); + if (pos >= 0 && + !jQuery(node.parentNode).hasClass(className) && + !jQuery(node.parentNode).hasClass("nohighlight")) { + var span; + var isInSVG = jQuery(node).closest("body, svg, foreignObject").is("svg"); + if (isInSVG) { + span = document.createElementNS("http://www.w3.org/2000/svg", "tspan"); + } else { + span = document.createElement("span"); + span.className = className; + } + span.appendChild(document.createTextNode(val.substr(pos, text.length))); + node.parentNode.insertBefore(span, node.parentNode.insertBefore( + document.createTextNode(val.substr(pos + text.length)), + node.nextSibling)); + node.nodeValue = val.substr(0, pos); + if (isInSVG) { + var rect = document.createElementNS("http://www.w3.org/2000/svg", "rect"); + var bbox = node.parentElement.getBBox(); + rect.x.baseVal.value = bbox.x; + rect.y.baseVal.value = bbox.y; + rect.width.baseVal.value = bbox.width; + rect.height.baseVal.value = bbox.height; + rect.setAttribute('class', className); + addItems.push({ + "parent": node.parentNode, + "target": rect}); + } + } + } + else if (!jQuery(node).is("button, select, textarea")) { + jQuery.each(node.childNodes, function() { + highlight(this, addItems); + }); + } + } + var addItems = []; + var result = this.each(function() { + highlight(this, addItems); + }); + for (var i = 0; i < addItems.length; ++i) { + jQuery(addItems[i].parent).before(addItems[i].target); + } + return result; +}; + +/* + * backward compatibility for jQuery.browser + * This will be supported until firefox bug is fixed. + */ +if (!jQuery.browser) { + jQuery.uaMatch = function(ua) { + ua = ua.toLowerCase(); + + var match = /(chrome)[ \/]([\w.]+)/.exec(ua) || + /(webkit)[ \/]([\w.]+)/.exec(ua) || + /(opera)(?:.*version|)[ \/]([\w.]+)/.exec(ua) || + /(msie) ([\w.]+)/.exec(ua) || + ua.indexOf("compatible") < 0 && /(mozilla)(?:.*? rv:([\w.]+)|)/.exec(ua) || + []; + + return { + browser: match[ 1 ] || "", + version: match[ 2 ] || "0" + }; + }; + jQuery.browser = {}; + jQuery.browser[jQuery.uaMatch(navigator.userAgent).browser] = true; +} diff --git a/docs/pages/html/_static/basic.css b/docs/pages/html/_static/basic.css index 7577acb..7ebbd6d 100644 --- a/docs/pages/html/_static/basic.css +++ b/docs/pages/html/_static/basic.css @@ -1,12 +1,5 @@ /* - * basic.css - * ~~~~~~~~~ - * * Sphinx stylesheet -- basic theme. - * - * :copyright: Copyright 2007-2023 by the Sphinx team, see AUTHORS. - * :license: BSD, see LICENSE for details. - * */ /* -- main layout ----------------------------------------------------------- */ @@ -115,15 +108,11 @@ img { /* -- search page ----------------------------------------------------------- */ ul.search { - margin: 10px 0 0 20px; - padding: 0; + margin-top: 10px; } ul.search li { - padding: 5px 0 5px 20px; - background-image: url(file.png); - background-repeat: no-repeat; - background-position: 0 7px; + padding: 5px 0; } ul.search li a { @@ -237,6 +226,10 @@ a.headerlink { visibility: hidden; } +a:visited { + color: #551A8B; +} + h1:hover > a.headerlink, h2:hover > a.headerlink, h3:hover > a.headerlink, @@ -670,6 +663,16 @@ dd { 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{ + const config = event.detail.data(); + + const flyout = ` + + + Read the Docs + v: ${config.versions.current.slug} + + + + + ${renderLanguages(config)} + ${renderVersions(config)} + ${renderDownloads(config)} + + On Read the Docs + + Project Home + + + Builds + + + Downloads + + + + Search + + + + + + + + + Hosted by Read the Docs + + + + `; + + // Inject the generated flyout into the body HTML element. + document.body.insertAdjacentHTML("beforeend", flyout); + + // Trigger the Read the Docs Addons Search modal when clicking on the "Search docs" input from inside the flyout. + document + .querySelector("#flyout-search-form") + .addEventListener("focusin", () => { + const event = new CustomEvent("readthedocs-search-show"); + document.dispatchEvent(event); + }); + }) +} + +if (themeLanguageSelector || themeVersionSelector) { + function onSelectorSwitch(event) { + const option = event.target.selectedIndex; + const item = event.target.options[option]; + window.location.href = item.dataset.url; + } + + document.addEventListener("readthedocs-addons-data-ready", function (event) { + const config = event.detail.data(); + + const versionSwitch = document.querySelector( + "div.switch-menus > div.version-switch", + ); + if (themeVersionSelector) { + let versions = config.versions.active; + if (config.versions.current.hidden || config.versions.current.type === "external") { + versions.unshift(config.versions.current); + } + const versionSelect = ` + + ${versions + .map( + (version) => ` + + ${version.slug} + `, + ) + .join("\n")} + + `; + + versionSwitch.innerHTML = versionSelect; + versionSwitch.firstElementChild.addEventListener("change", onSelectorSwitch); + } + + const languageSwitch = document.querySelector( + "div.switch-menus > div.language-switch", + ); + + if (themeLanguageSelector) { + if (config.projects.translations.length) { + // Add the current language to the options on the selector + let languages = config.projects.translations.concat( + config.projects.current, + ); + languages = languages.sort((a, b) => + a.language.name.localeCompare(b.language.name), + ); + + const languageSelect = ` + + ${languages + .map( + (language) => ` + + ${language.language.name} + `, + ) + .join("\n")} + + `; + + languageSwitch.innerHTML = languageSelect; + languageSwitch.firstElementChild.addEventListener("change", onSelectorSwitch); + } + else { + languageSwitch.remove(); + } + } + }); +} + +document.addEventListener("readthedocs-addons-data-ready", function (event) { + // Trigger the Read the Docs Addons Search modal when clicking on "Search docs" input from the topnav. + document + .querySelector("[role='search'] input") + .addEventListener("focusin", () => { + const event = new CustomEvent("readthedocs-search-show"); + document.dispatchEvent(event); + }); +}); \ No newline at end of file diff --git a/docs/pages/html/_static/language_data.js b/docs/pages/html/_static/language_data.js index 250f566..c7fe6c6 100644 --- a/docs/pages/html/_static/language_data.js +++ b/docs/pages/html/_static/language_data.js @@ -1,19 +1,12 @@ /* - * language_data.js - * ~~~~~~~~~~~~~~~~ - * * This script contains the language-specific data used by searchtools.js, * namely the list of stopwords, stemmer, scorer and splitter. - * - * :copyright: Copyright 2007-2023 by the Sphinx team, see AUTHORS. - * :license: BSD, see LICENSE for details. - * */ var stopwords = ["a", "and", "are", "as", "at", "be", "but", "by", "for", "if", "in", "into", "is", "it", "near", "no", "not", "of", "on", "or", "such", "that", "the", "their", "then", "there", "these", "they", "this", "to", "was", "will", "with"]; -/* Non-minified version is copied as a separate JS file, is available */ +/* Non-minified version is copied as a separate JS file, if available */ /** * Porter Stemmer diff --git a/docs/pages/html/_static/notebooks/pca_examples.html b/docs/pages/html/_static/notebooks/pca_examples.html index c9a75dc..7bb55a3 100644 --- a/docs/pages/html/_static/notebooks/pca_examples.html +++ b/docs/pages/html/_static/notebooks/pca_examples.html @@ -1,13 +1,9 @@ - - - + + + pca_examples - - - - - - - - - - - - - - + + + - - - - + void Promise.all([...diagrams].map(renderOneMarmaid)); + }); + + + + + + + - + pca A Python Package for Principal Component Analysis. The core of PCA is build on sklearn functionality to find maximum compatibility when combining with other packages. But this package can do a lot more. Besides the regular pca, it can also perform SparsePCA, and TruncatedSVD. Depending on your input data, the best approach will be choosen. Other functionalities are: @@ -15124,38 +7531,30 @@ github pca - - - + + -In [1]: +In [1]: - -!pip install pca + +!pip install pca - - - + - - - - - - - + + Requirement already satisfied: pca in /usr/local/lib/python3.7/dist-packages (1.7.2) Requirement already satisfied: matplotlib in /usr/local/lib/python3.7/dist-packages (from pca) (3.2.2) Requirement already satisfied: wget in /usr/local/lib/python3.7/dist-packages (from pca) (3.2) @@ -15180,179 +7579,149 @@ - - - - - + + - + Lets check the version - - - + + -In [2]: +In [2]: - -import pca + +import pca print(pca.__version__) - - - + - - - - - - - + + 1.7.2 - - - - - + + - + Import the pca library - - - + + -In [3]: +In [3]: - -from pca import pca + +from pca import pca import numpy as np import pandas as pd - - - - - + + + - + Here we will create a random dataset. - - - + + -In [4]: +In [4]: - -# Dataset + +# Dataset from sklearn.datasets import load_iris X = pd.DataFrame(data=load_iris().data, columns=load_iris().feature_names, index=load_iris().target) - - - - - + + + - + Initialize using specified parameters. The parameters here are the default parameters. - - - + + -In [5]: +In [5]: - -# Initialize + +# Initialize model = pca(n_components=3, normalize=True) - - - - - + + + -In [6]: +In [6]: - -# Fit transform + +# Fit transform out = model.fit_transform(X) - - - + - - - - - - - + + [pca] >Processing dataframe.. [pca] >Normalizing input data per feature (zero mean and unit variance).. [pca] >The PCA reduction is performed on the [4] columns of the input dataframe. @@ -15364,171 +7733,119 @@ - - - - - + + -In [7]: +In [7]: - -# Make plot with only the directions (no scatter) + +# Make plot with only the directions (no scatter) fig, ax = model.biplot(textlabel=True, legend=False, figsize=(10, 6)) - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 with loadings. - - - - - - - - + + + - - - - - - + + -In [8]: +In [8]: - -# Make plot with only the directions (no scatter) + +# Make plot with only the directions (no scatter) fig, ax = model.biplot(cmap=None, textlabel=False, legend=False, figsize=(10, 6)) - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 with loadings. - - - - - - - - + + + - - - - - - + + -In [9]: +In [9]: - -from pca import pca + +from pca import pca # Load example data from sklearn.datasets import load_iris X = pd.DataFrame(data=load_iris().data, columns=load_iris().feature_names, index=load_iris().target) - - - - - + + + -In [10]: +In [10]: - -# Initialize + +# Initialize model = pca(n_components=3) # Fit using PCA results = model.fit_transform(X) - - - + - - - - - - - + + [pca] >Processing dataframe.. [pca] >The PCA reduction is performed on the [4] columns of the input dataframe. [pca] >Fit using PCA. @@ -15539,20 +7856,17 @@ - - - - - + + -In [11]: +In [11]: - -# Make plots + +# Make plots # Scree plot fig, ax = model.plot(figsize=(10, 6)) @@ -15563,190 +7877,117 @@ # Biplot fig, ax = model.biplot(figsize=(10, 6)) - - - + - - - - - - - - - - + + + - - - - - - - - - + + + - - - - - - + + [pca] >Plot PC1 vs PC2 with loadings. - - - - - - - + + <Figure size 432x288 with 0 Axes> - - - - - - - - - + + + - - - - - - + + -In [17]: +In [17]: - -# Coloring on density to focus on the core samples. + +# Coloring on density to focus on the core samples. # Biplot -fig, ax = model.biplot(figsize=(10, 6), gradient='#ffffff') +fig, ax = model.biplot(figsize=(10, 6), gradient='#ffffff') - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 with loadings. - - - - - - - - + + + - - - - - - + + -In [18]: +In [18]: - -# Outliers are stored in results: -results['outliers'] + +# Outliers are stored in results: +results['outliers'] # Outliers based on T2 -print('--------T2------------') -print(results['outliers'].loc[results['outliers']['y_bool'], :]) +print('--------T2------------') +print(results['outliers'].loc[results['outliers']['y_bool'], :]) # Outliers based on SPE -print('--------SPE------------') -print(results['outliers'].loc[results['outliers']['y_bool_spe'], :]) +print('--------SPE------------') +print(results['outliers'].loc[results['outliers']['y_bool_spe'], :]) - - - + - - - - - - - + + --------T2------------ y_proba y_score y_bool y_bool_spe y_score_spe 2 0.040551 13.160880 True True 3.679935 @@ -15771,270 +8012,168 @@ - - - - - + + -In [20]: +In [20]: - -# Outlier detection + +# Outlier detection fig, ax = model.biplot(SPE=True, HT2=True, figsize=(10, 6)) - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 with loadings. - - - - - - - - + + + - - - - - - + + -In [21]: +In [21]: - -# 3D plots + +# 3D plots fig, ax = model.scatter3d(figsize=(10, 6)) fig, ax = model.biplot3d(figsize=(10, 6)) fig, ax = model.biplot3d(SPE=True, HT2=True, figsize=(10, 6)) - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 vs PC3 with loadings. - - - - - - - - + + + - - - - - - - - - + + + - - - - - - + + [pca] >Plot PC1 vs PC2 vs PC3 with loadings. - - - - - - - - + + + - - - - - - + + -In [22]: +In [22]: - -fig, ax = model.biplot3d(SPE=True, HT2=True, visible=False, figsize=(10, 6)) + +fig, ax = model.biplot3d(SPE=True, HT2=True, visible=False, figsize=(10, 6)) # Set the figure again to True and show the figure. fig.set_visible(True) fig - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 vs PC3 with loadings. - - Out[22]: - - - - - - +Out[22]: + + - - - - - - - - - + + + - - - - - - + + -In [23]: +In [23]: - -# Normalize out PCs + +
# 2D plot fig, ax = model.biplot(n_feat=4, PC=[0,1]) @@ -241,11 +241,12 @@ Biplotfig, ax = model.biplot3d(n_feat=2, PC=[0,1,2])
This example is created to showcase the working of extracting features that are most important in a PCA reduction. We will create random variables with increasingly more variance. The first feature (f1) will have most of the variance, followed by feature 2 (f2) etc.
# Print the top features. @@ -294,14 +295,15 @@ Demonstration of feature importance -Explained variance plot +Explained variance plot model.plot() - + + -Biplot +Biplot Make the biplot. It can be nicely seen that the first feature with most variance (f1), is almost horizontal in the plot, whereas the second most variance (f2) is almost vertical. This is expected because most of the variance is in f1, followed by f2 etc. Biplot in 3d. Here we see the nice addition of the expected f3 in the plot in the z-direction. # 2d plot ax = model.biplot(n_feat=10, legend=False) @@ -311,7 +313,7 @@ Biplot -Color on alcohol +Color on alcohol @@ -321,10 +323,10 @@ Biplot -Analyzing Discrete datasets +Analyzing Discrete datasets Analyzing datasets that have continuous and catagorical values can be challanging. To demonstrate how to do this, I will use the Titanic dataset. We need to pip install df2onehot first. -pip install df2onehot +pip install df2onehot import pca @@ -383,7 +385,7 @@ Analyzing Discrete datasets -Map unseen datapoints into fitted space +Map unseen datapoints into fitted space After fitting variables into the new principal component space, we can map new unseen samples into this space too. However, there is also normalization step which can be tricky because you now need standardize the values of the unseen samples first based on the previously performed standardization. This step is also integrated in the pca library by simply setting the parameter normalize=True. # Load libraries import matplotlib.pyplot as plt @@ -422,10 +424,11 @@ Map unseen datapoints into fitted spaceax.scatter(PCnew.iloc[:, 0], PCnew.iloc[:, 1], marker='x', s=200) - + + -Normalizing out PCs +Normalizing out PCs Normalize your data using the principal components. As an example, suppose there is (technical) variation in the fist component and you want that out. This function transforms the data using the components that you want, e.g., starting from the 2nd PC, up to the OC that contains at least 95% of the explained variance. print(X.shape) (178, 13) @@ -443,7 +446,7 @@ Normalizing out PCs -Colors in plots +Colors in plots The default colors that are used in the plots depend on how much information is provided at start. There are many parameters to change the colors in the plots. Here I will demonstrate some of the possibilities. First, we will load the data and import the libraries. @@ -476,7 +479,7 @@ Colors in plots -Left: Default plot using the provided classlabels. Right: Color on custom cmap. +Left: Default plot using the provided classlabels. Right: Color on custom cmap. @@ -498,7 +501,7 @@ Colors in plots -Left: Mark some points on y and use cmap. Right: Specify the colors manually. +Left: Mark some points on y and use cmap. Right: Specify the colors manually. @@ -514,7 +517,7 @@ Colors in plots -Left: Remove scatterpoints from plot. Right: Gradient with the used cmap. +Left: Remove scatterpoints from plot. Right: Gradient with the used cmap. @@ -539,7 +542,7 @@ Colors in plots -Fig as input to make iterative changes. +Fig as input to make iterative changes. diff --git a/docs/pages/html/Installation.html b/docs/pages/html/Installation.html index d2fd9ff..8a0f6d2 100644 --- a/docs/pages/html/Installation.html +++ b/docs/pages/html/Installation.html @@ -1,20 +1,22 @@ + + - + - + Installation — pca pca documentation - - - - + + + + - - - + + + + + @@ -33,9 +35,6 @@ pca - - 2.0.1 - @@ -138,9 +137,9 @@ -Installation +Installation -Create environment +Create environment If desired, install pca from an isolated Python environment using conda: conda create -n env_pca python=3.8 conda activate env_pca @@ -148,26 +147,26 @@ Create environment -Pip install -# Install from Pypi: +Pip install +# Install from Pypi: pip install pca -# Install directly from github +# Install directly from github pip install git+https://github.com/erdogant/pca -Uninstalling +Uninstalling Remove the environment with installation: -# List all the active environments. pca should be listed. +# List all the active environments. pca should be listed. conda env list -# Remove the pca environment +# Remove the pca environment conda env remove --name pca -# List all the active environments. pca should be absent. +# List all the active environments. pca should be absent. conda env list diff --git a/docs/pages/html/Outlier detection.html b/docs/pages/html/Outlier detection.html index 37bc204..fe764f4 100644 --- a/docs/pages/html/Outlier detection.html +++ b/docs/pages/html/Outlier detection.html @@ -1,20 +1,22 @@ + + - + - + Hotelling T2 — pca pca documentation - - - - + + + + - - - + + + + + @@ -33,9 +35,6 @@ pca - - 2.0.1 - @@ -134,7 +133,7 @@ -Hotelling T2 +Hotelling T2 To detect outliers across the multidimensional space of PCA, the hotellings T2 test is implemented. It works by computing the chi-square tests across the top n_components: default is PC1 to PC5. The reason for not using more PC’s is that it is expected that the highest variance (and thus the outliers) will be seen in the first few components. Going deeper into PC space may therefore not be required. Nevertheless, the depth is optional. The hotellings T2 test outputs a P-value matrix (samples x PCs), which are are subsequently combined using fishers method. This allows to determine outliers with its ranking (strongest to weak). The alpha parameter determines the detection of outliers (default: 0.05). @@ -192,7 +191,7 @@ Hotelling T2 -SPE/Dmodx +SPE/Dmodx Outlier can be detected using SPE/DmodX (distance to model) based on the mean and covariance of the first 2 dimensions of X. On the model plane (SPE ≈ 0). Note that the SPE or Hotelling’s T2 are complementary to each other. model.biplot(legend=True, SPE=True, HT2=True) @@ -204,7 +203,7 @@ SPE/Dmodx -Detected outliers +Detected outliers @@ -213,7 +212,7 @@ SPE/Dmodx -Selection of the Outliers +Selection of the Outliers Selecting the outliers can be usefull to remove them from the dataset or for deeper investigation. # Select the outliers Xoutliers = X[results['outliers']['y_bool'],:] @@ -224,7 +223,7 @@ Selection of the Outliers -Detect new unseen outliers +Detect new unseen outliers After fitting a model on the data, you may want to use the model in a later stage to detect outliers on unseen data. Detection of outliers is performed in the transform function and does not require any additional action. An example is shown in the code block below. # Import libraries @@ -252,7 +251,7 @@ Detect new unseen outliers -Detected outliers +Detected outliers @@ -288,7 +287,7 @@ Detect new unseen outliers -Detected outliers +Detected outliers @@ -296,7 +295,7 @@ Detect new unseen outliers -Detection of outliers without PCA +Detection of outliers without PCA If desired, the outliers can also be detected directly using the hotelling T2 and/or SPE/DmodX functionality. For demonstration purposes I use the PCs from the results but any other dataset would also work. import pca diff --git a/docs/pages/html/Plots.html b/docs/pages/html/Plots.html index c1677b6..f054370 100644 --- a/docs/pages/html/Plots.html +++ b/docs/pages/html/Plots.html @@ -1,20 +1,22 @@ + + - + - + Load dataset — pca pca documentation - - - - + + + + - - - + + + + + @@ -33,9 +35,6 @@ pca - - 2.0.1 - @@ -134,7 +133,7 @@ -Load dataset +Load dataset Let’s load the wine dataset to demonstrate the plots. # Load library from sklearn.datasets import load_wine @@ -166,7 +165,7 @@ Load dataset -Scatter plot +Scatter plot # Make scatterplot model.scatter() @@ -187,7 +186,7 @@ Scatter plot -Scatterplots +Scatterplots @@ -204,16 +203,40 @@ Scatter plot -Biplot +Biplot +The biplot draws the loadings (arrows) together with the samples (scatterplot). +The loadings can be colored red and blue which indicates the strength of the particular feature in the PC. +For each principal component (PC), the feature is determined with the largest absolute loading. This indicates which feature contributes the most to each PC and can occur in multiple PCs. +The highest loading values for the features are colored red in the biplot and described as “best” in the output dataframe. +The features that were not seen with highest loadings for any PC are considered weaker features, and are colored blue the biplot. In the output dataframe these features are described as “weak”. # Make biplot model.biplot() # Here again, many other options can be turned on and off model.biplot(SPE=True, HT2=True, legend=1) + +# Show the top features +results['topfeat'] + +# PC feature loading type +# 0 PC1 flavanoids 0.422934 best +# 1 PC2 color_intensity 0.529996 best +# 2 PC3 ash 0.626224 best +# 3 PC4 malic_acid 0.536890 best +# 4 PC5 magnesium 0.727049 best +# 5 PC6 malic_acid 0.536814 best +# 6 PC7 nonflavanoid_phenols 0.595447 best +# 7 PC8 hue 0.436624 best +# 8 PC9 proline 0.575786 best +# 9 PC10 od280/od315_of_diluted_wines 0.523706 best +# 10 PC9 alcohol -0.508619 weak +# 11 PC3 alcalinity_of_ash 0.612080 weak +# 12 PC8 total_phenols -0.405934 weak +# 13 PC6 proanthocyanins -0.533795 weak -Biplots +Biplots @@ -223,28 +246,30 @@ Biplot -Biplot (only arrows) +Biplot (only arrows) # Make plot with parameters: set cmap to None and label and legend to False. Only directions will be plotted. model.biplot(cmap=None, legend=False) - + + -Explained variance plot +Explained variance plot model.plot() - + + -Alpha Transparency +Alpha Transparency fig, ax = model.scatter(alpha=1) -Markers +Markers import numpy as np from sklearn.datasets import make_friedman1 from pca import pca @@ -272,7 +297,7 @@ Markers -Biplots with markers +Biplots with markers @@ -280,7 +305,7 @@ Markers -Control color/marker/size per sample +Control color/marker/size per sample import numpy as np import matplotlib.pyplot as plt import matplotlib.colors as mcolors @@ -329,7 +354,7 @@ Control color/marker/size per sample -Biplot with customized properties per sample. +Biplot with customized properties per sample. @@ -337,15 +362,16 @@ Control color/marker/size per sample -3D plots +3D plots All plots can also be created in 3D by setting the d3=True parameter. model.biplot3d() - + + -Toggle visible status +Toggle visible status The visible status for can be turned on and off. # Make plot but not visible. fig, ax = model.biplot(visible=False) diff --git a/docs/pages/html/_sources/Plots.rst.txt b/docs/pages/html/_sources/Plots.rst.txt index 33319b2..38cd2db 100644 --- a/docs/pages/html/_sources/Plots.rst.txt +++ b/docs/pages/html/_sources/Plots.rst.txt @@ -83,6 +83,14 @@ Scatter plot Biplot ############### +The biplot draws the loadings (arrows) together with the samples (scatterplot). +The loadings can be colored red and blue which indicates the strength of the particular feature in the PC. + +For each principal component (PC), the feature is determined with the largest absolute loading. This indicates which feature contributes the most to each PC and can occur in multiple PCs. +The highest loading values for the features are colored red in the biplot and described as "best" in the output dataframe. +The features that were not seen with highest loadings for any PC are considered weaker features, and are colored blue the biplot. In the output dataframe these features are described as "weak". + + .. code:: python # Make biplot @@ -91,6 +99,24 @@ Biplot # Here again, many other options can be turned on and off model.biplot(SPE=True, HT2=True, legend=1) + # Show the top features + results['topfeat'] + + # PC feature loading type + # 0 PC1 flavanoids 0.422934 best + # 1 PC2 color_intensity 0.529996 best + # 2 PC3 ash 0.626224 best + # 3 PC4 malic_acid 0.536890 best + # 4 PC5 magnesium 0.727049 best + # 5 PC6 malic_acid 0.536814 best + # 6 PC7 nonflavanoid_phenols 0.595447 best + # 7 PC8 hue 0.436624 best + # 8 PC9 proline 0.575786 best + # 9 PC10 od280/od315_of_diluted_wines 0.523706 best + # 10 PC9 alcohol -0.508619 weak + # 11 PC3 alcalinity_of_ash 0.612080 weak + # 12 PC8 total_phenols -0.405934 weak + # 13 PC6 proanthocyanins -0.533795 weak .. |figP5| image:: ../figs/wine_biplot.png .. |figP6| image:: ../figs/wine_biplot_with_outliers.png diff --git a/docs/pages/html/_sources/sponsor.rst.txt b/docs/pages/html/_sources/sponsor.rst.txt index a46c410..f006896 100644 --- a/docs/pages/html/_sources/sponsor.rst.txt +++ b/docs/pages/html/_sources/sponsor.rst.txt @@ -4,8 +4,10 @@ * Become a `Sponsor `_! * `Buy `_ me a coffee! I ❤️ coffee :) * `Donate `_ in Bitcoin. - * Follow me on medium! Go to my `medium profile `_ and press *follow*. + * Follow me on Medium! Go to my `medium profile `_ and press *follow*. + * Subscribe to me on Substack! Go to my `profile `_ where you can *subscribe*. * **Star** this repo at the github page. + * You can also buy a digital educational product over `here `_. * Other contributions can be in the form of feature requests, idea discussions, reporting bugs, opening pull requests. Cheers Mate. diff --git a/docs/pages/html/_static/_sphinx_javascript_frameworks_compat.js b/docs/pages/html/_static/_sphinx_javascript_frameworks_compat.js new file mode 100644 index 0000000..8141580 --- /dev/null +++ b/docs/pages/html/_static/_sphinx_javascript_frameworks_compat.js @@ -0,0 +1,123 @@ +/* Compatability shim for jQuery and underscores.js. + * + * Copyright Sphinx contributors + * Released under the two clause BSD licence + */ + +/** + * small helper function to urldecode strings + * + * See https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/decodeURIComponent#Decoding_query_parameters_from_a_URL + */ +jQuery.urldecode = function(x) { + if (!x) { + return x + } + return decodeURIComponent(x.replace(/\+/g, ' ')); +}; + +/** + * small helper function to urlencode strings + */ +jQuery.urlencode = encodeURIComponent; + +/** + * This function returns the parsed url parameters of the + * current request. 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span; + var isInSVG = jQuery(node).closest("body, svg, foreignObject").is("svg"); + if (isInSVG) { + span = document.createElementNS("http://www.w3.org/2000/svg", "tspan"); + } else { + span = document.createElement("span"); + span.className = className; + } + span.appendChild(document.createTextNode(val.substr(pos, text.length))); + node.parentNode.insertBefore(span, node.parentNode.insertBefore( + document.createTextNode(val.substr(pos + text.length)), + node.nextSibling)); + node.nodeValue = val.substr(0, pos); + if (isInSVG) { + var rect = document.createElementNS("http://www.w3.org/2000/svg", "rect"); + var bbox = node.parentElement.getBBox(); + rect.x.baseVal.value = bbox.x; + rect.y.baseVal.value = bbox.y; + rect.width.baseVal.value = bbox.width; + rect.height.baseVal.value = bbox.height; + rect.setAttribute('class', className); + addItems.push({ + "parent": node.parentNode, + "target": rect}); + } + } + } + else if (!jQuery(node).is("button, select, textarea")) { + jQuery.each(node.childNodes, function() { + highlight(this, addItems); + }); + } + } + var addItems = []; + var result = this.each(function() { + highlight(this, addItems); + }); + for (var i = 0; i < addItems.length; ++i) { + jQuery(addItems[i].parent).before(addItems[i].target); + } + return result; +}; + +/* + * backward compatibility for jQuery.browser + * This will be supported until firefox bug is fixed. + */ +if (!jQuery.browser) { + jQuery.uaMatch = function(ua) { + ua = ua.toLowerCase(); + + var match = /(chrome)[ \/]([\w.]+)/.exec(ua) || + /(webkit)[ \/]([\w.]+)/.exec(ua) || + /(opera)(?:.*version|)[ \/]([\w.]+)/.exec(ua) || + /(msie) ([\w.]+)/.exec(ua) || + ua.indexOf("compatible") < 0 && /(mozilla)(?:.*? rv:([\w.]+)|)/.exec(ua) || + []; + + return { + browser: match[ 1 ] || "", + version: match[ 2 ] || "0" + }; + }; + jQuery.browser = {}; + jQuery.browser[jQuery.uaMatch(navigator.userAgent).browser] = true; +} diff --git a/docs/pages/html/_static/basic.css b/docs/pages/html/_static/basic.css index 7577acb..7ebbd6d 100644 --- a/docs/pages/html/_static/basic.css +++ b/docs/pages/html/_static/basic.css @@ -1,12 +1,5 @@ /* - * basic.css - * ~~~~~~~~~ - * * Sphinx stylesheet -- basic theme. - * - * :copyright: Copyright 2007-2023 by the Sphinx team, see AUTHORS. - * :license: BSD, see LICENSE for details. - * */ /* -- main layout ----------------------------------------------------------- */ @@ -115,15 +108,11 @@ img { /* -- search page ----------------------------------------------------------- */ ul.search { - margin: 10px 0 0 20px; - padding: 0; + margin-top: 10px; } ul.search li { - padding: 5px 0 5px 20px; - background-image: url(file.png); - background-repeat: no-repeat; - background-position: 0 7px; + padding: 5px 0; } ul.search li a { @@ -237,6 +226,10 @@ a.headerlink { visibility: hidden; } +a:visited { + color: #551A8B; +} + h1:hover > a.headerlink, h2:hover > a.headerlink, h3:hover > a.headerlink, @@ -670,6 +663,16 @@ dd { 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a/docs/pages/html/_static/language_data.js +++ b/docs/pages/html/_static/language_data.js @@ -1,19 +1,12 @@ /* - * language_data.js - * ~~~~~~~~~~~~~~~~ - * * This script contains the language-specific data used by searchtools.js, * namely the list of stopwords, stemmer, scorer and splitter. - * - * :copyright: Copyright 2007-2023 by the Sphinx team, see AUTHORS. - * :license: BSD, see LICENSE for details. - * */ var stopwords = ["a", "and", "are", "as", "at", "be", "but", "by", "for", "if", "in", "into", "is", "it", "near", "no", "not", "of", "on", "or", "such", "that", "the", "their", "then", "there", "these", "they", "this", "to", "was", "will", "with"]; -/* Non-minified version is copied as a separate JS file, is available */ +/* Non-minified version is copied as a separate JS file, if available */ /** * Porter Stemmer diff --git a/docs/pages/html/_static/notebooks/pca_examples.html b/docs/pages/html/_static/notebooks/pca_examples.html index c9a75dc..7bb55a3 100644 --- a/docs/pages/html/_static/notebooks/pca_examples.html +++ b/docs/pages/html/_static/notebooks/pca_examples.html @@ -1,13 +1,9 @@ - - - + + + pca_examples - - - - - - - - - - - - - - + + + - - - - + void Promise.all([...diagrams].map(renderOneMarmaid)); + }); + + + + + + + - + pca A Python Package for Principal Component Analysis. The core of PCA is build on sklearn functionality to find maximum compatibility when combining with other packages. But this package can do a lot more. Besides the regular pca, it can also perform SparsePCA, and TruncatedSVD. Depending on your input data, the best approach will be choosen. Other functionalities are: @@ -15124,38 +7531,30 @@ github pca - - - + + -In [1]: +In [1]: - -!pip install pca + +!pip install pca - - - + - - - - - - - + + Requirement already satisfied: pca in /usr/local/lib/python3.7/dist-packages (1.7.2) Requirement already satisfied: matplotlib in /usr/local/lib/python3.7/dist-packages (from pca) (3.2.2) Requirement already satisfied: wget in /usr/local/lib/python3.7/dist-packages (from pca) (3.2) @@ -15180,179 +7579,149 @@ - - - - - + + - + Lets check the version - - - + + -In [2]: +In [2]: - -import pca + +import pca print(pca.__version__) - - - + - - - - - - - + + 1.7.2 - - - - - + + - + Import the pca library - - - + + -In [3]: +In [3]: - -from pca import pca + +from pca import pca import numpy as np import pandas as pd - - - - - + + + - + Here we will create a random dataset. - - - + + -In [4]: +In [4]: - -# Dataset + +# Dataset from sklearn.datasets import load_iris X = pd.DataFrame(data=load_iris().data, columns=load_iris().feature_names, index=load_iris().target) - - - - - + + + - + Initialize using specified parameters. The parameters here are the default parameters. - - - + + -In [5]: +In [5]: - -# Initialize + +# Initialize model = pca(n_components=3, normalize=True) - - - - - + + + -In [6]: +In [6]: - -# Fit transform + +# Fit transform out = model.fit_transform(X) - - - + - - - - - - - + + [pca] >Processing dataframe.. [pca] >Normalizing input data per feature (zero mean and unit variance).. [pca] >The PCA reduction is performed on the [4] columns of the input dataframe. @@ -15364,171 +7733,119 @@ - - - - - + + -In [7]: +In [7]: - -# Make plot with only the directions (no scatter) + +# Make plot with only the directions (no scatter) fig, ax = model.biplot(textlabel=True, legend=False, figsize=(10, 6)) - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 with loadings. - - - - - - - - + + + - - - - - - + + -In [8]: +In [8]: - -# Make plot with only the directions (no scatter) + +# Make plot with only the directions (no scatter) fig, ax = model.biplot(cmap=None, textlabel=False, legend=False, figsize=(10, 6)) - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 with loadings. - - - - - - - - + + + - - - - - - + + -In [9]: +In [9]: - -from pca import pca + +from pca import pca # Load example data from sklearn.datasets import load_iris X = pd.DataFrame(data=load_iris().data, columns=load_iris().feature_names, index=load_iris().target) - - - - - + + + -In [10]: +In [10]: - -# Initialize + +# Initialize model = pca(n_components=3) # Fit using PCA results = model.fit_transform(X) - - - + - - - - - - - + + [pca] >Processing dataframe.. [pca] >The PCA reduction is performed on the [4] columns of the input dataframe. [pca] >Fit using PCA. @@ -15539,20 +7856,17 @@ - - - - - + + -In [11]: +In [11]: - -# Make plots + +# Make plots # Scree plot fig, ax = model.plot(figsize=(10, 6)) @@ -15563,190 +7877,117 @@ # Biplot fig, ax = model.biplot(figsize=(10, 6)) - - - + - - - - - - - - - - + + + - - - - - - - - - + + + - - - - - - + + [pca] >Plot PC1 vs PC2 with loadings. - - - - - - - + + <Figure size 432x288 with 0 Axes> - - - - - - - - - + + + - - - - - - + + -In [17]: +In [17]: - -# Coloring on density to focus on the core samples. + +# Coloring on density to focus on the core samples. # Biplot -fig, ax = model.biplot(figsize=(10, 6), gradient='#ffffff') +fig, ax = model.biplot(figsize=(10, 6), gradient='#ffffff') - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 with loadings. - - - - - - - - + + + - - - - - - + + -In [18]: +In [18]: - -# Outliers are stored in results: -results['outliers'] + +# Outliers are stored in results: +results['outliers'] # Outliers based on T2 -print('--------T2------------') -print(results['outliers'].loc[results['outliers']['y_bool'], :]) +print('--------T2------------') +print(results['outliers'].loc[results['outliers']['y_bool'], :]) # Outliers based on SPE -print('--------SPE------------') -print(results['outliers'].loc[results['outliers']['y_bool_spe'], :]) +print('--------SPE------------') +print(results['outliers'].loc[results['outliers']['y_bool_spe'], :]) - - - + - - - - - - - + + --------T2------------ y_proba y_score y_bool y_bool_spe y_score_spe 2 0.040551 13.160880 True True 3.679935 @@ -15771,270 +8012,168 @@ - - - - - + + -In [20]: +In [20]: - -# Outlier detection + +# Outlier detection fig, ax = model.biplot(SPE=True, HT2=True, figsize=(10, 6)) - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 with loadings. - - - - - - - - + + + - - - - - - + + -In [21]: +In [21]: - -# 3D plots + +# 3D plots fig, ax = model.scatter3d(figsize=(10, 6)) fig, ax = model.biplot3d(figsize=(10, 6)) fig, ax = model.biplot3d(SPE=True, HT2=True, figsize=(10, 6)) - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 vs PC3 with loadings. - - - - - - - - + + + - - - - - - - - - + + + - - - - - - + + [pca] >Plot PC1 vs PC2 vs PC3 with loadings. - - - - - - - - + + + - - - - - - + + -In [22]: +In [22]: - -fig, ax = model.biplot3d(SPE=True, HT2=True, visible=False, figsize=(10, 6)) + +fig, ax = model.biplot3d(SPE=True, HT2=True, visible=False, figsize=(10, 6)) # Set the figure again to True and show the figure. fig.set_visible(True) fig - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 vs PC3 with loadings. - - Out[22]: - - - - - - +Out[22]: + + - - - - - - - - - + + + - - - - - - + + -In [23]: +In [23]: - -# Normalize out PCs + +
model.plot()
Make the biplot. It can be nicely seen that the first feature with most variance (f1), is almost horizontal in the plot, whereas the second most variance (f2) is almost vertical. This is expected because most of the variance is in f1, followed by f2 etc. Biplot in 3d. Here we see the nice addition of the expected f3 in the plot in the z-direction.
# 2d plot ax = model.biplot(n_feat=10, legend=False) @@ -311,7 +313,7 @@ Biplot
Analyzing datasets that have continuous and catagorical values can be challanging. To demonstrate how to do this, I will use the Titanic dataset. We need to pip install df2onehot first.
pip install df2onehot +pip install df2onehot import pca @@ -383,7 +385,7 @@ Analyzing Discrete datasets -Map unseen datapoints into fitted space +Map unseen datapoints into fitted space After fitting variables into the new principal component space, we can map new unseen samples into this space too. However, there is also normalization step which can be tricky because you now need standardize the values of the unseen samples first based on the previously performed standardization. This step is also integrated in the pca library by simply setting the parameter normalize=True. # Load libraries import matplotlib.pyplot as plt @@ -422,10 +424,11 @@ Map unseen datapoints into fitted spaceax.scatter(PCnew.iloc[:, 0], PCnew.iloc[:, 1], marker='x', s=200) - + + -Normalizing out PCs +Normalizing out PCs Normalize your data using the principal components. As an example, suppose there is (technical) variation in the fist component and you want that out. This function transforms the data using the components that you want, e.g., starting from the 2nd PC, up to the OC that contains at least 95% of the explained variance. print(X.shape) (178, 13) @@ -443,7 +446,7 @@ Normalizing out PCs -Colors in plots +Colors in plots The default colors that are used in the plots depend on how much information is provided at start. There are many parameters to change the colors in the plots. Here I will demonstrate some of the possibilities. First, we will load the data and import the libraries. @@ -476,7 +479,7 @@ Colors in plots -Left: Default plot using the provided classlabels. Right: Color on custom cmap. +Left: Default plot using the provided classlabels. Right: Color on custom cmap. @@ -498,7 +501,7 @@ Colors in plots -Left: Mark some points on y and use cmap. Right: Specify the colors manually. +Left: Mark some points on y and use cmap. Right: Specify the colors manually. @@ -514,7 +517,7 @@ Colors in plots -Left: Remove scatterpoints from plot. Right: Gradient with the used cmap. +Left: Remove scatterpoints from plot. Right: Gradient with the used cmap. @@ -539,7 +542,7 @@ Colors in plots -Fig as input to make iterative changes. +Fig as input to make iterative changes. diff --git a/docs/pages/html/Installation.html b/docs/pages/html/Installation.html index d2fd9ff..8a0f6d2 100644 --- a/docs/pages/html/Installation.html +++ b/docs/pages/html/Installation.html @@ -1,20 +1,22 @@ + + - + - + Installation — pca pca documentation - - - - + + + + - - - + + + + + @@ -33,9 +35,6 @@ pca - - 2.0.1 - @@ -138,9 +137,9 @@ -Installation +Installation -Create environment +Create environment If desired, install pca from an isolated Python environment using conda: conda create -n env_pca python=3.8 conda activate env_pca @@ -148,26 +147,26 @@ Create environment -Pip install -# Install from Pypi: +Pip install +# Install from Pypi: pip install pca -# Install directly from github +# Install directly from github pip install git+https://github.com/erdogant/pca -Uninstalling +Uninstalling Remove the environment with installation: -# List all the active environments. pca should be listed. +# List all the active environments. pca should be listed. conda env list -# Remove the pca environment +# Remove the pca environment conda env remove --name pca -# List all the active environments. pca should be absent. +# List all the active environments. pca should be absent. conda env list diff --git a/docs/pages/html/Outlier detection.html b/docs/pages/html/Outlier detection.html index 37bc204..fe764f4 100644 --- a/docs/pages/html/Outlier detection.html +++ b/docs/pages/html/Outlier detection.html @@ -1,20 +1,22 @@ + + - + - + Hotelling T2 — pca pca documentation - - - - + + + + - - - + + + + + @@ -33,9 +35,6 @@ pca - - 2.0.1 - @@ -134,7 +133,7 @@ -Hotelling T2 +Hotelling T2 To detect outliers across the multidimensional space of PCA, the hotellings T2 test is implemented. It works by computing the chi-square tests across the top n_components: default is PC1 to PC5. The reason for not using more PC’s is that it is expected that the highest variance (and thus the outliers) will be seen in the first few components. Going deeper into PC space may therefore not be required. Nevertheless, the depth is optional. The hotellings T2 test outputs a P-value matrix (samples x PCs), which are are subsequently combined using fishers method. This allows to determine outliers with its ranking (strongest to weak). The alpha parameter determines the detection of outliers (default: 0.05). @@ -192,7 +191,7 @@ Hotelling T2 -SPE/Dmodx +SPE/Dmodx Outlier can be detected using SPE/DmodX (distance to model) based on the mean and covariance of the first 2 dimensions of X. On the model plane (SPE ≈ 0). Note that the SPE or Hotelling’s T2 are complementary to each other. model.biplot(legend=True, SPE=True, HT2=True) @@ -204,7 +203,7 @@ SPE/Dmodx -Detected outliers +Detected outliers @@ -213,7 +212,7 @@ SPE/Dmodx -Selection of the Outliers +Selection of the Outliers Selecting the outliers can be usefull to remove them from the dataset or for deeper investigation. # Select the outliers Xoutliers = X[results['outliers']['y_bool'],:] @@ -224,7 +223,7 @@ Selection of the Outliers -Detect new unseen outliers +Detect new unseen outliers After fitting a model on the data, you may want to use the model in a later stage to detect outliers on unseen data. Detection of outliers is performed in the transform function and does not require any additional action. An example is shown in the code block below. # Import libraries @@ -252,7 +251,7 @@ Detect new unseen outliers -Detected outliers +Detected outliers @@ -288,7 +287,7 @@ Detect new unseen outliers -Detected outliers +Detected outliers @@ -296,7 +295,7 @@ Detect new unseen outliers -Detection of outliers without PCA +Detection of outliers without PCA If desired, the outliers can also be detected directly using the hotelling T2 and/or SPE/DmodX functionality. For demonstration purposes I use the PCs from the results but any other dataset would also work. import pca diff --git a/docs/pages/html/Plots.html b/docs/pages/html/Plots.html index c1677b6..f054370 100644 --- a/docs/pages/html/Plots.html +++ b/docs/pages/html/Plots.html @@ -1,20 +1,22 @@ + + - + - + Load dataset — pca pca documentation - - - - + + + + - - - + + + + + @@ -33,9 +35,6 @@ pca - - 2.0.1 - @@ -134,7 +133,7 @@ -Load dataset +Load dataset Let’s load the wine dataset to demonstrate the plots. # Load library from sklearn.datasets import load_wine @@ -166,7 +165,7 @@ Load dataset -Scatter plot +Scatter plot # Make scatterplot model.scatter() @@ -187,7 +186,7 @@ Scatter plot -Scatterplots +Scatterplots @@ -204,16 +203,40 @@ Scatter plot -Biplot +Biplot +The biplot draws the loadings (arrows) together with the samples (scatterplot). +The loadings can be colored red and blue which indicates the strength of the particular feature in the PC. +For each principal component (PC), the feature is determined with the largest absolute loading. This indicates which feature contributes the most to each PC and can occur in multiple PCs. +The highest loading values for the features are colored red in the biplot and described as “best” in the output dataframe. +The features that were not seen with highest loadings for any PC are considered weaker features, and are colored blue the biplot. In the output dataframe these features are described as “weak”. # Make biplot model.biplot() # Here again, many other options can be turned on and off model.biplot(SPE=True, HT2=True, legend=1) + +# Show the top features +results['topfeat'] + +# PC feature loading type +# 0 PC1 flavanoids 0.422934 best +# 1 PC2 color_intensity 0.529996 best +# 2 PC3 ash 0.626224 best +# 3 PC4 malic_acid 0.536890 best +# 4 PC5 magnesium 0.727049 best +# 5 PC6 malic_acid 0.536814 best +# 6 PC7 nonflavanoid_phenols 0.595447 best +# 7 PC8 hue 0.436624 best +# 8 PC9 proline 0.575786 best +# 9 PC10 od280/od315_of_diluted_wines 0.523706 best +# 10 PC9 alcohol -0.508619 weak +# 11 PC3 alcalinity_of_ash 0.612080 weak +# 12 PC8 total_phenols -0.405934 weak +# 13 PC6 proanthocyanins -0.533795 weak -Biplots +Biplots @@ -223,28 +246,30 @@ Biplot -Biplot (only arrows) +Biplot (only arrows) # Make plot with parameters: set cmap to None and label and legend to False. Only directions will be plotted. model.biplot(cmap=None, legend=False) - + + -Explained variance plot +Explained variance plot model.plot() - + + -Alpha Transparency +Alpha Transparency fig, ax = model.scatter(alpha=1) -Markers +Markers import numpy as np from sklearn.datasets import make_friedman1 from pca import pca @@ -272,7 +297,7 @@ Markers -Biplots with markers +Biplots with markers @@ -280,7 +305,7 @@ Markers -Control color/marker/size per sample +Control color/marker/size per sample import numpy as np import matplotlib.pyplot as plt import matplotlib.colors as mcolors @@ -329,7 +354,7 @@ Control color/marker/size per sample -Biplot with customized properties per sample. +Biplot with customized properties per sample. @@ -337,15 +362,16 @@ Control color/marker/size per sample -3D plots +3D plots All plots can also be created in 3D by setting the d3=True parameter. model.biplot3d() - + + -Toggle visible status +Toggle visible status The visible status for can be turned on and off. # Make plot but not visible. fig, ax = model.biplot(visible=False) diff --git a/docs/pages/html/_sources/Plots.rst.txt b/docs/pages/html/_sources/Plots.rst.txt index 33319b2..38cd2db 100644 --- a/docs/pages/html/_sources/Plots.rst.txt +++ b/docs/pages/html/_sources/Plots.rst.txt @@ -83,6 +83,14 @@ Scatter plot Biplot ############### +The biplot draws the loadings (arrows) together with the samples (scatterplot). +The loadings can be colored red and blue which indicates the strength of the particular feature in the PC. + +For each principal component (PC), the feature is determined with the largest absolute loading. This indicates which feature contributes the most to each PC and can occur in multiple PCs. +The highest loading values for the features are colored red in the biplot and described as "best" in the output dataframe. +The features that were not seen with highest loadings for any PC are considered weaker features, and are colored blue the biplot. In the output dataframe these features are described as "weak". + + .. code:: python # Make biplot @@ -91,6 +99,24 @@ Biplot # Here again, many other options can be turned on and off model.biplot(SPE=True, HT2=True, legend=1) + # Show the top features + results['topfeat'] + + # PC feature loading type + # 0 PC1 flavanoids 0.422934 best + # 1 PC2 color_intensity 0.529996 best + # 2 PC3 ash 0.626224 best + # 3 PC4 malic_acid 0.536890 best + # 4 PC5 magnesium 0.727049 best + # 5 PC6 malic_acid 0.536814 best + # 6 PC7 nonflavanoid_phenols 0.595447 best + # 7 PC8 hue 0.436624 best + # 8 PC9 proline 0.575786 best + # 9 PC10 od280/od315_of_diluted_wines 0.523706 best + # 10 PC9 alcohol -0.508619 weak + # 11 PC3 alcalinity_of_ash 0.612080 weak + # 12 PC8 total_phenols -0.405934 weak + # 13 PC6 proanthocyanins -0.533795 weak .. |figP5| image:: ../figs/wine_biplot.png .. |figP6| image:: ../figs/wine_biplot_with_outliers.png diff --git a/docs/pages/html/_sources/sponsor.rst.txt b/docs/pages/html/_sources/sponsor.rst.txt index a46c410..f006896 100644 --- a/docs/pages/html/_sources/sponsor.rst.txt +++ b/docs/pages/html/_sources/sponsor.rst.txt @@ -4,8 +4,10 @@ * Become a `Sponsor `_! * `Buy `_ me a coffee! I ❤️ coffee :) * `Donate `_ in Bitcoin. - * Follow me on medium! Go to my `medium profile `_ and press *follow*. + * Follow me on Medium! Go to my `medium profile `_ and press *follow*. + * Subscribe to me on Substack! Go to my `profile `_ where you can *subscribe*. * **Star** this repo at the github page. + * You can also buy a digital educational product over `here `_. * Other contributions can be in the form of feature requests, idea discussions, reporting bugs, opening pull requests. Cheers Mate. diff --git a/docs/pages/html/_static/_sphinx_javascript_frameworks_compat.js b/docs/pages/html/_static/_sphinx_javascript_frameworks_compat.js new file mode 100644 index 0000000..8141580 --- /dev/null +++ b/docs/pages/html/_static/_sphinx_javascript_frameworks_compat.js @@ -0,0 +1,123 @@ +/* Compatability shim for jQuery and underscores.js. + * + * Copyright Sphinx contributors + * Released under the two clause BSD licence + */ + +/** + * small helper function to urldecode strings + * + * See https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/decodeURIComponent#Decoding_query_parameters_from_a_URL + */ +jQuery.urldecode = function(x) { + if (!x) { + return x + } + return decodeURIComponent(x.replace(/\+/g, ' ')); +}; + +/** + * small helper function to urlencode strings + */ +jQuery.urlencode = encodeURIComponent; + +/** + * This function returns the parsed url parameters of the + * current request. Multiple values per key are supported, + * it will always return arrays of strings for the value parts. + */ +jQuery.getQueryParameters = function(s) { + if (typeof s === 'undefined') + s = document.location.search; + var parts = s.substr(s.indexOf('?') + 1).split('&'); + var result = {}; + for (var i = 0; i < parts.length; i++) { + var tmp = parts[i].split('=', 2); + var key = jQuery.urldecode(tmp[0]); + var value = jQuery.urldecode(tmp[1]); + if (key in result) + result[key].push(value); + else + result[key] = [value]; + } + return result; +}; + +/** + * highlight a given string on a jquery object by wrapping it in + * span elements with the given class name. + */ +jQuery.fn.highlightText = function(text, className) { + function highlight(node, addItems) { + if (node.nodeType === 3) { + var val = node.nodeValue; + var pos = val.toLowerCase().indexOf(text); + if (pos >= 0 && + !jQuery(node.parentNode).hasClass(className) && + !jQuery(node.parentNode).hasClass("nohighlight")) { + var span; + var isInSVG = jQuery(node).closest("body, svg, foreignObject").is("svg"); + if (isInSVG) { + span = document.createElementNS("http://www.w3.org/2000/svg", "tspan"); + } else { + span = document.createElement("span"); + span.className = className; + } + span.appendChild(document.createTextNode(val.substr(pos, text.length))); + node.parentNode.insertBefore(span, node.parentNode.insertBefore( + document.createTextNode(val.substr(pos + text.length)), + node.nextSibling)); + node.nodeValue = val.substr(0, pos); + if (isInSVG) { + var rect = document.createElementNS("http://www.w3.org/2000/svg", "rect"); + var bbox = node.parentElement.getBBox(); + rect.x.baseVal.value = bbox.x; + rect.y.baseVal.value = bbox.y; + rect.width.baseVal.value = bbox.width; + rect.height.baseVal.value = bbox.height; + rect.setAttribute('class', className); + addItems.push({ + "parent": node.parentNode, + "target": rect}); + } + } + } + else if (!jQuery(node).is("button, select, textarea")) { + jQuery.each(node.childNodes, function() { + highlight(this, addItems); + }); + } + } + var addItems = []; + var result = this.each(function() { + highlight(this, addItems); + }); + for (var i = 0; i < addItems.length; ++i) { + jQuery(addItems[i].parent).before(addItems[i].target); + } + return result; +}; + +/* + * backward compatibility for jQuery.browser + * This will be supported until firefox bug is fixed. + */ +if (!jQuery.browser) { + jQuery.uaMatch = function(ua) { + ua = ua.toLowerCase(); + + var match = /(chrome)[ \/]([\w.]+)/.exec(ua) || + /(webkit)[ \/]([\w.]+)/.exec(ua) || + /(opera)(?:.*version|)[ \/]([\w.]+)/.exec(ua) || + /(msie) ([\w.]+)/.exec(ua) || + ua.indexOf("compatible") < 0 && /(mozilla)(?:.*? rv:([\w.]+)|)/.exec(ua) || + []; + + return { + browser: match[ 1 ] || "", + version: match[ 2 ] || "0" + }; + }; + jQuery.browser = {}; + jQuery.browser[jQuery.uaMatch(navigator.userAgent).browser] = true; +} diff --git a/docs/pages/html/_static/basic.css b/docs/pages/html/_static/basic.css index 7577acb..7ebbd6d 100644 --- a/docs/pages/html/_static/basic.css +++ b/docs/pages/html/_static/basic.css @@ -1,12 +1,5 @@ /* - * basic.css - * ~~~~~~~~~ - * * Sphinx stylesheet -- basic theme. - * - * :copyright: Copyright 2007-2023 by the Sphinx team, see AUTHORS. - * :license: BSD, see LICENSE for details. - * */ /* -- main layout ----------------------------------------------------------- */ @@ -115,15 +108,11 @@ img { /* -- search page ----------------------------------------------------------- */ ul.search { - margin: 10px 0 0 20px; - padding: 0; + margin-top: 10px; } ul.search li { - padding: 5px 0 5px 20px; - background-image: url(file.png); - background-repeat: no-repeat; - background-position: 0 7px; + padding: 5px 0; } ul.search li a { @@ -237,6 +226,10 @@ a.headerlink { visibility: hidden; } +a:visited { + color: #551A8B; +} + h1:hover > a.headerlink, h2:hover > a.headerlink, h3:hover > a.headerlink, @@ -670,6 +663,16 @@ dd { 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config.projects.current, + ); + languages = languages.sort((a, b) => + a.language.name.localeCompare(b.language.name), + ); + + const languageSelect = ` + + ${languages + .map( + (language) => ` + + ${language.language.name} + `, + ) + .join("\n")} + + `; + + languageSwitch.innerHTML = languageSelect; + languageSwitch.firstElementChild.addEventListener("change", onSelectorSwitch); + } + else { + languageSwitch.remove(); + } + } + }); +} + +document.addEventListener("readthedocs-addons-data-ready", function (event) { + // Trigger the Read the Docs Addons Search modal when clicking on "Search docs" input from the topnav. + document + .querySelector("[role='search'] input") + .addEventListener("focusin", () => { + const event = new CustomEvent("readthedocs-search-show"); + document.dispatchEvent(event); + }); +}); \ No newline at end of file diff --git a/docs/pages/html/_static/language_data.js b/docs/pages/html/_static/language_data.js index 250f566..c7fe6c6 100644 --- a/docs/pages/html/_static/language_data.js +++ b/docs/pages/html/_static/language_data.js @@ -1,19 +1,12 @@ /* - * language_data.js - * ~~~~~~~~~~~~~~~~ - * * This script contains the language-specific data used by searchtools.js, * namely the list of stopwords, stemmer, scorer and splitter. - * - * :copyright: Copyright 2007-2023 by the Sphinx team, see AUTHORS. - * :license: BSD, see LICENSE for details. - * */ var stopwords = ["a", "and", "are", "as", "at", "be", "but", "by", "for", "if", "in", "into", "is", "it", "near", "no", "not", "of", "on", "or", "such", "that", "the", "their", "then", "there", "these", "they", "this", "to", "was", "will", "with"]; -/* Non-minified version is copied as a separate JS file, is available */ +/* Non-minified version is copied as a separate JS file, if available */ /** * Porter Stemmer diff --git a/docs/pages/html/_static/notebooks/pca_examples.html b/docs/pages/html/_static/notebooks/pca_examples.html index c9a75dc..7bb55a3 100644 --- a/docs/pages/html/_static/notebooks/pca_examples.html +++ b/docs/pages/html/_static/notebooks/pca_examples.html @@ -1,13 +1,9 @@ - - - + + + pca_examples - - - - - - - - - - - - - - + + + - - - - + void Promise.all([...diagrams].map(renderOneMarmaid)); + }); + + + + + + + - + pca A Python Package for Principal Component Analysis. The core of PCA is build on sklearn functionality to find maximum compatibility when combining with other packages. But this package can do a lot more. Besides the regular pca, it can also perform SparsePCA, and TruncatedSVD. Depending on your input data, the best approach will be choosen. Other functionalities are: @@ -15124,38 +7531,30 @@ github pca - - - + + -In [1]: +In [1]: - -!pip install pca + +!pip install pca - - - + - - - - - - - + + Requirement already satisfied: pca in /usr/local/lib/python3.7/dist-packages (1.7.2) Requirement already satisfied: matplotlib in /usr/local/lib/python3.7/dist-packages (from pca) (3.2.2) Requirement already satisfied: wget in /usr/local/lib/python3.7/dist-packages (from pca) (3.2) @@ -15180,179 +7579,149 @@ - - - - - + + - + Lets check the version - - - + + -In [2]: +In [2]: - -import pca + +import pca print(pca.__version__) - - - + - - - - - - - + + 1.7.2 - - - - - + + - + Import the pca library - - - + + -In [3]: +In [3]: - -from pca import pca + +from pca import pca import numpy as np import pandas as pd - - - - - + + + - + Here we will create a random dataset. - - - + + -In [4]: +In [4]: - -# Dataset + +# Dataset from sklearn.datasets import load_iris X = pd.DataFrame(data=load_iris().data, columns=load_iris().feature_names, index=load_iris().target) - - - - - + + + - + Initialize using specified parameters. The parameters here are the default parameters. - - - + + -In [5]: +In [5]: - -# Initialize + +# Initialize model = pca(n_components=3, normalize=True) - - - - - + + + -In [6]: +In [6]: - -# Fit transform + +# Fit transform out = model.fit_transform(X) - - - + - - - - - - - + + [pca] >Processing dataframe.. [pca] >Normalizing input data per feature (zero mean and unit variance).. [pca] >The PCA reduction is performed on the [4] columns of the input dataframe. @@ -15364,171 +7733,119 @@ - - - - - + + -In [7]: +In [7]: - -# Make plot with only the directions (no scatter) + +# Make plot with only the directions (no scatter) fig, ax = model.biplot(textlabel=True, legend=False, figsize=(10, 6)) - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 with loadings. - - - - - - - - + + + - - - - - - + + -In [8]: +In [8]: - -# Make plot with only the directions (no scatter) + +# Make plot with only the directions (no scatter) fig, ax = model.biplot(cmap=None, textlabel=False, legend=False, figsize=(10, 6)) - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 with loadings. - - - - - - - - + + + - - - - - - + + -In [9]: +In [9]: - -from pca import pca + +from pca import pca # Load example data from sklearn.datasets import load_iris X = pd.DataFrame(data=load_iris().data, columns=load_iris().feature_names, index=load_iris().target) - - - - - + + + -In [10]: +In [10]: - -# Initialize + +# Initialize model = pca(n_components=3) # Fit using PCA results = model.fit_transform(X) - - - + - - - - - - - + + [pca] >Processing dataframe.. [pca] >The PCA reduction is performed on the [4] columns of the input dataframe. [pca] >Fit using PCA. @@ -15539,20 +7856,17 @@ - - - - - + + -In [11]: +In [11]: - -# Make plots + +# Make plots # Scree plot fig, ax = model.plot(figsize=(10, 6)) @@ -15563,190 +7877,117 @@ # Biplot fig, ax = model.biplot(figsize=(10, 6)) - - - + - - - - - - - - - - + + + - - - - - - - - - + + + - - - - - - + + [pca] >Plot PC1 vs PC2 with loadings. - - - - - - - + + <Figure size 432x288 with 0 Axes> - - - - - - - - - + + + - - - - - - + + -In [17]: +In [17]: - -# Coloring on density to focus on the core samples. + +# Coloring on density to focus on the core samples. # Biplot -fig, ax = model.biplot(figsize=(10, 6), gradient='#ffffff') +fig, ax = model.biplot(figsize=(10, 6), gradient='#ffffff') - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 with loadings. - - - - - - - - + + + - - - - - - + + -In [18]: +In [18]: - -# Outliers are stored in results: -results['outliers'] + +# Outliers are stored in results: +results['outliers'] # Outliers based on T2 -print('--------T2------------') -print(results['outliers'].loc[results['outliers']['y_bool'], :]) +print('--------T2------------') +print(results['outliers'].loc[results['outliers']['y_bool'], :]) # Outliers based on SPE -print('--------SPE------------') -print(results['outliers'].loc[results['outliers']['y_bool_spe'], :]) +print('--------SPE------------') +print(results['outliers'].loc[results['outliers']['y_bool_spe'], :]) - - - + - - - - - - - + + --------T2------------ y_proba y_score y_bool y_bool_spe y_score_spe 2 0.040551 13.160880 True True 3.679935 @@ -15771,270 +8012,168 @@ - - - - - + + -In [20]: +In [20]: - -# Outlier detection + +# Outlier detection fig, ax = model.biplot(SPE=True, HT2=True, figsize=(10, 6)) - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 with loadings. - - - - - - - - + + + - - - - - - + + -In [21]: +In [21]: - -# 3D plots + +# 3D plots fig, ax = model.scatter3d(figsize=(10, 6)) fig, ax = model.biplot3d(figsize=(10, 6)) fig, ax = model.biplot3d(SPE=True, HT2=True, figsize=(10, 6)) - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 vs PC3 with loadings. - - - - - - - - + + + - - - - - - - - - + + + - - - - - - + + [pca] >Plot PC1 vs PC2 vs PC3 with loadings. - - - - - - - - + + + - - - - - - + + -In [22]: +In [22]: - -fig, ax = model.biplot3d(SPE=True, HT2=True, visible=False, figsize=(10, 6)) + +fig, ax = model.biplot3d(SPE=True, HT2=True, visible=False, figsize=(10, 6)) # Set the figure again to True and show the figure. fig.set_visible(True) fig - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 vs PC3 with loadings. - - Out[22]: - - - - - - +Out[22]: + + - - - - - - - - - + + + - - - - - - + + -In [23]: +In [23]: - -# Normalize out PCs + +
pip install df2onehot
import pca @@ -383,7 +385,7 @@ Analyzing Discrete datasets -Map unseen datapoints into fitted space +Map unseen datapoints into fitted space After fitting variables into the new principal component space, we can map new unseen samples into this space too. However, there is also normalization step which can be tricky because you now need standardize the values of the unseen samples first based on the previously performed standardization. This step is also integrated in the pca library by simply setting the parameter normalize=True. # Load libraries import matplotlib.pyplot as plt @@ -422,10 +424,11 @@ Map unseen datapoints into fitted spaceax.scatter(PCnew.iloc[:, 0], PCnew.iloc[:, 1], marker='x', s=200) - + + -Normalizing out PCs +Normalizing out PCs Normalize your data using the principal components. As an example, suppose there is (technical) variation in the fist component and you want that out. This function transforms the data using the components that you want, e.g., starting from the 2nd PC, up to the OC that contains at least 95% of the explained variance. print(X.shape) (178, 13) @@ -443,7 +446,7 @@ Normalizing out PCs -Colors in plots +Colors in plots The default colors that are used in the plots depend on how much information is provided at start. There are many parameters to change the colors in the plots. Here I will demonstrate some of the possibilities. First, we will load the data and import the libraries. @@ -476,7 +479,7 @@ Colors in plots -Left: Default plot using the provided classlabels. Right: Color on custom cmap. +Left: Default plot using the provided classlabels. Right: Color on custom cmap. @@ -498,7 +501,7 @@ Colors in plots -Left: Mark some points on y and use cmap. Right: Specify the colors manually. +Left: Mark some points on y and use cmap. Right: Specify the colors manually. @@ -514,7 +517,7 @@ Colors in plots -Left: Remove scatterpoints from plot. Right: Gradient with the used cmap. +Left: Remove scatterpoints from plot. Right: Gradient with the used cmap. @@ -539,7 +542,7 @@ Colors in plots -Fig as input to make iterative changes. +Fig as input to make iterative changes. diff --git a/docs/pages/html/Installation.html b/docs/pages/html/Installation.html index d2fd9ff..8a0f6d2 100644 --- a/docs/pages/html/Installation.html +++ b/docs/pages/html/Installation.html @@ -1,20 +1,22 @@ + + - + - + Installation — pca pca documentation - - - - + + + + - - - + + + + + @@ -33,9 +35,6 @@ pca - - 2.0.1 - @@ -138,9 +137,9 @@ -Installation +Installation -Create environment +Create environment If desired, install pca from an isolated Python environment using conda: conda create -n env_pca python=3.8 conda activate env_pca @@ -148,26 +147,26 @@ Create environment -Pip install -# Install from Pypi: +Pip install +# Install from Pypi: pip install pca -# Install directly from github +# Install directly from github pip install git+https://github.com/erdogant/pca -Uninstalling +Uninstalling Remove the environment with installation: -# List all the active environments. pca should be listed. +# List all the active environments. pca should be listed. conda env list -# Remove the pca environment +# Remove the pca environment conda env remove --name pca -# List all the active environments. pca should be absent. +# List all the active environments. pca should be absent. conda env list diff --git a/docs/pages/html/Outlier detection.html b/docs/pages/html/Outlier detection.html index 37bc204..fe764f4 100644 --- a/docs/pages/html/Outlier detection.html +++ b/docs/pages/html/Outlier detection.html @@ -1,20 +1,22 @@ + + - + - + Hotelling T2 — pca pca documentation - - - - + + + + - - - + + + + + @@ -33,9 +35,6 @@ pca - - 2.0.1 - @@ -134,7 +133,7 @@ -Hotelling T2 +Hotelling T2 To detect outliers across the multidimensional space of PCA, the hotellings T2 test is implemented. It works by computing the chi-square tests across the top n_components: default is PC1 to PC5. The reason for not using more PC’s is that it is expected that the highest variance (and thus the outliers) will be seen in the first few components. Going deeper into PC space may therefore not be required. Nevertheless, the depth is optional. The hotellings T2 test outputs a P-value matrix (samples x PCs), which are are subsequently combined using fishers method. This allows to determine outliers with its ranking (strongest to weak). The alpha parameter determines the detection of outliers (default: 0.05). @@ -192,7 +191,7 @@ Hotelling T2 -SPE/Dmodx +SPE/Dmodx Outlier can be detected using SPE/DmodX (distance to model) based on the mean and covariance of the first 2 dimensions of X. On the model plane (SPE ≈ 0). Note that the SPE or Hotelling’s T2 are complementary to each other. model.biplot(legend=True, SPE=True, HT2=True) @@ -204,7 +203,7 @@ SPE/Dmodx -Detected outliers +Detected outliers @@ -213,7 +212,7 @@ SPE/Dmodx -Selection of the Outliers +Selection of the Outliers Selecting the outliers can be usefull to remove them from the dataset or for deeper investigation. # Select the outliers Xoutliers = X[results['outliers']['y_bool'],:] @@ -224,7 +223,7 @@ Selection of the Outliers -Detect new unseen outliers +Detect new unseen outliers After fitting a model on the data, you may want to use the model in a later stage to detect outliers on unseen data. Detection of outliers is performed in the transform function and does not require any additional action. An example is shown in the code block below. # Import libraries @@ -252,7 +251,7 @@ Detect new unseen outliers -Detected outliers +Detected outliers @@ -288,7 +287,7 @@ Detect new unseen outliers -Detected outliers +Detected outliers @@ -296,7 +295,7 @@ Detect new unseen outliers -Detection of outliers without PCA +Detection of outliers without PCA If desired, the outliers can also be detected directly using the hotelling T2 and/or SPE/DmodX functionality. For demonstration purposes I use the PCs from the results but any other dataset would also work. import pca diff --git a/docs/pages/html/Plots.html b/docs/pages/html/Plots.html index c1677b6..f054370 100644 --- a/docs/pages/html/Plots.html +++ b/docs/pages/html/Plots.html @@ -1,20 +1,22 @@ + + - + - + Load dataset — pca pca documentation - - - - + + + + - - - + + + + + @@ -33,9 +35,6 @@ pca - - 2.0.1 - @@ -134,7 +133,7 @@ -Load dataset +Load dataset Let’s load the wine dataset to demonstrate the plots. # Load library from sklearn.datasets import load_wine @@ -166,7 +165,7 @@ Load dataset -Scatter plot +Scatter plot # Make scatterplot model.scatter() @@ -187,7 +186,7 @@ Scatter plot -Scatterplots +Scatterplots @@ -204,16 +203,40 @@ Scatter plot -Biplot +Biplot +The biplot draws the loadings (arrows) together with the samples (scatterplot). +The loadings can be colored red and blue which indicates the strength of the particular feature in the PC. +For each principal component (PC), the feature is determined with the largest absolute loading. This indicates which feature contributes the most to each PC and can occur in multiple PCs. +The highest loading values for the features are colored red in the biplot and described as “best” in the output dataframe. +The features that were not seen with highest loadings for any PC are considered weaker features, and are colored blue the biplot. In the output dataframe these features are described as “weak”. # Make biplot model.biplot() # Here again, many other options can be turned on and off model.biplot(SPE=True, HT2=True, legend=1) + +# Show the top features +results['topfeat'] + +# PC feature loading type +# 0 PC1 flavanoids 0.422934 best +# 1 PC2 color_intensity 0.529996 best +# 2 PC3 ash 0.626224 best +# 3 PC4 malic_acid 0.536890 best +# 4 PC5 magnesium 0.727049 best +# 5 PC6 malic_acid 0.536814 best +# 6 PC7 nonflavanoid_phenols 0.595447 best +# 7 PC8 hue 0.436624 best +# 8 PC9 proline 0.575786 best +# 9 PC10 od280/od315_of_diluted_wines 0.523706 best +# 10 PC9 alcohol -0.508619 weak +# 11 PC3 alcalinity_of_ash 0.612080 weak +# 12 PC8 total_phenols -0.405934 weak +# 13 PC6 proanthocyanins -0.533795 weak -Biplots +Biplots @@ -223,28 +246,30 @@ Biplot -Biplot (only arrows) +Biplot (only arrows) # Make plot with parameters: set cmap to None and label and legend to False. Only directions will be plotted. model.biplot(cmap=None, legend=False) - + + -Explained variance plot +Explained variance plot model.plot() - + + -Alpha Transparency +Alpha Transparency fig, ax = model.scatter(alpha=1) -Markers +Markers import numpy as np from sklearn.datasets import make_friedman1 from pca import pca @@ -272,7 +297,7 @@ Markers -Biplots with markers +Biplots with markers @@ -280,7 +305,7 @@ Markers -Control color/marker/size per sample +Control color/marker/size per sample import numpy as np import matplotlib.pyplot as plt import matplotlib.colors as mcolors @@ -329,7 +354,7 @@ Control color/marker/size per sample -Biplot with customized properties per sample. +Biplot with customized properties per sample. @@ -337,15 +362,16 @@ Control color/marker/size per sample -3D plots +3D plots All plots can also be created in 3D by setting the d3=True parameter. model.biplot3d() - + + -Toggle visible status +Toggle visible status The visible status for can be turned on and off. # Make plot but not visible. fig, ax = model.biplot(visible=False) diff --git a/docs/pages/html/_sources/Plots.rst.txt b/docs/pages/html/_sources/Plots.rst.txt index 33319b2..38cd2db 100644 --- a/docs/pages/html/_sources/Plots.rst.txt +++ b/docs/pages/html/_sources/Plots.rst.txt @@ -83,6 +83,14 @@ Scatter plot Biplot ############### +The biplot draws the loadings (arrows) together with the samples (scatterplot). +The loadings can be colored red and blue which indicates the strength of the particular feature in the PC. + +For each principal component (PC), the feature is determined with the largest absolute loading. This indicates which feature contributes the most to each PC and can occur in multiple PCs. +The highest loading values for the features are colored red in the biplot and described as "best" in the output dataframe. +The features that were not seen with highest loadings for any PC are considered weaker features, and are colored blue the biplot. In the output dataframe these features are described as "weak". + + .. code:: python # Make biplot @@ -91,6 +99,24 @@ Biplot # Here again, many other options can be turned on and off model.biplot(SPE=True, HT2=True, legend=1) + # Show the top features + results['topfeat'] + + # PC feature loading type + # 0 PC1 flavanoids 0.422934 best + # 1 PC2 color_intensity 0.529996 best + # 2 PC3 ash 0.626224 best + # 3 PC4 malic_acid 0.536890 best + # 4 PC5 magnesium 0.727049 best + # 5 PC6 malic_acid 0.536814 best + # 6 PC7 nonflavanoid_phenols 0.595447 best + # 7 PC8 hue 0.436624 best + # 8 PC9 proline 0.575786 best + # 9 PC10 od280/od315_of_diluted_wines 0.523706 best + # 10 PC9 alcohol -0.508619 weak + # 11 PC3 alcalinity_of_ash 0.612080 weak + # 12 PC8 total_phenols -0.405934 weak + # 13 PC6 proanthocyanins -0.533795 weak .. |figP5| image:: ../figs/wine_biplot.png .. |figP6| image:: ../figs/wine_biplot_with_outliers.png diff --git a/docs/pages/html/_sources/sponsor.rst.txt b/docs/pages/html/_sources/sponsor.rst.txt index a46c410..f006896 100644 --- a/docs/pages/html/_sources/sponsor.rst.txt +++ b/docs/pages/html/_sources/sponsor.rst.txt @@ -4,8 +4,10 @@ * Become a `Sponsor `_! * `Buy `_ me a coffee! I ❤️ coffee :) * `Donate `_ in Bitcoin. - * Follow me on medium! Go to my `medium profile `_ and press *follow*. + * Follow me on Medium! Go to my `medium profile `_ and press *follow*. + * Subscribe to me on Substack! Go to my `profile `_ where you can *subscribe*. * **Star** this repo at the github page. + * You can also buy a digital educational product over `here `_. * Other contributions can be in the form of feature requests, idea discussions, reporting bugs, opening pull requests. Cheers Mate. diff --git a/docs/pages/html/_static/_sphinx_javascript_frameworks_compat.js b/docs/pages/html/_static/_sphinx_javascript_frameworks_compat.js new file mode 100644 index 0000000..8141580 --- /dev/null +++ b/docs/pages/html/_static/_sphinx_javascript_frameworks_compat.js @@ -0,0 +1,123 @@ +/* Compatability shim for jQuery and underscores.js. + * + * Copyright Sphinx contributors + * Released under the two clause BSD licence + */ + +/** + * small helper function to urldecode strings + * + * See https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/decodeURIComponent#Decoding_query_parameters_from_a_URL + */ +jQuery.urldecode = function(x) { + if (!x) { + return x + } + return decodeURIComponent(x.replace(/\+/g, ' ')); +}; + +/** + * small helper function to urlencode strings + */ +jQuery.urlencode = encodeURIComponent; + +/** + * This function returns the parsed url parameters of the + * current request. Multiple values per key are supported, + * it will always return arrays of strings for the value parts. + */ +jQuery.getQueryParameters = function(s) { + if (typeof s === 'undefined') + s = document.location.search; + var parts = s.substr(s.indexOf('?') + 1).split('&'); + var result = {}; + for (var i = 0; i < parts.length; i++) { + var tmp = parts[i].split('=', 2); + var key = jQuery.urldecode(tmp[0]); + var value = jQuery.urldecode(tmp[1]); + if (key in result) + result[key].push(value); + else + result[key] = [value]; + } + return result; +}; + +/** + * highlight a given string on a jquery object by wrapping it in + * span elements with the given class name. + */ +jQuery.fn.highlightText = function(text, className) { + function highlight(node, addItems) { + if (node.nodeType === 3) { + var val = node.nodeValue; + var pos = val.toLowerCase().indexOf(text); + if (pos >= 0 && + !jQuery(node.parentNode).hasClass(className) && + !jQuery(node.parentNode).hasClass("nohighlight")) { + var span; + var isInSVG = jQuery(node).closest("body, svg, foreignObject").is("svg"); + if (isInSVG) { + span = document.createElementNS("http://www.w3.org/2000/svg", "tspan"); + } else { + span = document.createElement("span"); + span.className = className; + } + span.appendChild(document.createTextNode(val.substr(pos, text.length))); + node.parentNode.insertBefore(span, node.parentNode.insertBefore( + document.createTextNode(val.substr(pos + text.length)), + node.nextSibling)); + node.nodeValue = val.substr(0, pos); + if (isInSVG) { + var rect = document.createElementNS("http://www.w3.org/2000/svg", "rect"); + var bbox = node.parentElement.getBBox(); + rect.x.baseVal.value = bbox.x; + rect.y.baseVal.value = bbox.y; + rect.width.baseVal.value = bbox.width; + rect.height.baseVal.value = bbox.height; + rect.setAttribute('class', className); + addItems.push({ + "parent": node.parentNode, + "target": rect}); + } + } + } + else if (!jQuery(node).is("button, select, textarea")) { + jQuery.each(node.childNodes, function() { + highlight(this, addItems); + }); + } + } + var addItems = []; + var result = this.each(function() { + highlight(this, addItems); + }); + for (var i = 0; i < addItems.length; ++i) { + jQuery(addItems[i].parent).before(addItems[i].target); + } + return result; +}; + +/* + * backward compatibility for jQuery.browser + * This will be supported until firefox bug is fixed. + */ +if (!jQuery.browser) { + jQuery.uaMatch = function(ua) { + ua = ua.toLowerCase(); + + var match = /(chrome)[ \/]([\w.]+)/.exec(ua) || + /(webkit)[ \/]([\w.]+)/.exec(ua) || + /(opera)(?:.*version|)[ \/]([\w.]+)/.exec(ua) || + /(msie) ([\w.]+)/.exec(ua) || + ua.indexOf("compatible") < 0 && /(mozilla)(?:.*? rv:([\w.]+)|)/.exec(ua) || + []; + + return { + browser: match[ 1 ] || "", + version: match[ 2 ] || "0" + }; + }; + jQuery.browser = {}; + jQuery.browser[jQuery.uaMatch(navigator.userAgent).browser] = true; +} diff --git a/docs/pages/html/_static/basic.css b/docs/pages/html/_static/basic.css index 7577acb..7ebbd6d 100644 --- a/docs/pages/html/_static/basic.css +++ b/docs/pages/html/_static/basic.css @@ -1,12 +1,5 @@ /* - * basic.css - * ~~~~~~~~~ - * * Sphinx stylesheet -- basic theme. - * - * :copyright: Copyright 2007-2023 by the Sphinx team, see AUTHORS. - * :license: BSD, see LICENSE for details. - * */ /* -- main layout ----------------------------------------------------------- */ @@ -115,15 +108,11 @@ img { /* -- search page ----------------------------------------------------------- */ ul.search { - margin: 10px 0 0 20px; - padding: 0; + margin-top: 10px; } ul.search li { - padding: 5px 0 5px 20px; - background-image: url(file.png); - background-repeat: no-repeat; - background-position: 0 7px; + padding: 5px 0; } ul.search li a { @@ -237,6 +226,10 @@ a.headerlink { visibility: hidden; } +a:visited { + color: #551A8B; +} + h1:hover > a.headerlink, h2:hover > a.headerlink, h3:hover > a.headerlink, @@ -670,6 +663,16 @@ dd { 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{ + const config = event.detail.data(); + + const flyout = ` + + + Read the Docs + v: ${config.versions.current.slug} + + + + + ${renderLanguages(config)} + ${renderVersions(config)} + ${renderDownloads(config)} + + On Read the Docs + + Project Home + + + Builds + + + Downloads + + + + Search + + + + + + + + + Hosted by Read the Docs + + + + `; + + // Inject the generated flyout into the body HTML element. + document.body.insertAdjacentHTML("beforeend", flyout); + + // Trigger the Read the Docs Addons Search modal when clicking on the "Search docs" input from inside the flyout. + document + .querySelector("#flyout-search-form") + .addEventListener("focusin", () => { + const event = new CustomEvent("readthedocs-search-show"); + document.dispatchEvent(event); + }); + }) +} + +if (themeLanguageSelector || themeVersionSelector) { + function onSelectorSwitch(event) { + const option = event.target.selectedIndex; + const item = event.target.options[option]; + window.location.href = item.dataset.url; + } + + document.addEventListener("readthedocs-addons-data-ready", function (event) { + const config = event.detail.data(); + + const versionSwitch = document.querySelector( + "div.switch-menus > div.version-switch", + ); + if (themeVersionSelector) { + let versions = config.versions.active; + if (config.versions.current.hidden || config.versions.current.type === "external") { + versions.unshift(config.versions.current); + } + const versionSelect = ` + + ${versions + .map( + (version) => ` + + ${version.slug} + `, + ) + .join("\n")} + + `; + + versionSwitch.innerHTML = versionSelect; + versionSwitch.firstElementChild.addEventListener("change", onSelectorSwitch); + } + + const languageSwitch = document.querySelector( + "div.switch-menus > div.language-switch", + ); + + if (themeLanguageSelector) { + if (config.projects.translations.length) { + // Add the current language to the options on the selector + let languages = config.projects.translations.concat( + config.projects.current, + ); + languages = languages.sort((a, b) => + a.language.name.localeCompare(b.language.name), + ); + + const languageSelect = ` + + ${languages + .map( + (language) => ` + + ${language.language.name} + `, + ) + .join("\n")} + + `; + + languageSwitch.innerHTML = languageSelect; + languageSwitch.firstElementChild.addEventListener("change", onSelectorSwitch); + } + else { + languageSwitch.remove(); + } + } + }); +} + +document.addEventListener("readthedocs-addons-data-ready", function (event) { + // Trigger the Read the Docs Addons Search modal when clicking on "Search docs" input from the topnav. + document + .querySelector("[role='search'] input") + .addEventListener("focusin", () => { + const event = new CustomEvent("readthedocs-search-show"); + document.dispatchEvent(event); + }); +}); \ No newline at end of file diff --git a/docs/pages/html/_static/language_data.js b/docs/pages/html/_static/language_data.js index 250f566..c7fe6c6 100644 --- a/docs/pages/html/_static/language_data.js +++ b/docs/pages/html/_static/language_data.js @@ -1,19 +1,12 @@ /* - * language_data.js - * ~~~~~~~~~~~~~~~~ - * * This script contains the language-specific data used by searchtools.js, * namely the list of stopwords, stemmer, scorer and splitter. - * - * :copyright: Copyright 2007-2023 by the Sphinx team, see AUTHORS. - * :license: BSD, see LICENSE for details. - * */ var stopwords = ["a", "and", "are", "as", "at", "be", "but", "by", "for", "if", "in", "into", "is", "it", "near", "no", "not", "of", "on", "or", "such", "that", "the", "their", "then", "there", "these", "they", "this", "to", "was", "will", "with"]; -/* Non-minified version is copied as a separate JS file, is available */ +/* Non-minified version is copied as a separate JS file, if available */ /** * Porter Stemmer diff --git a/docs/pages/html/_static/notebooks/pca_examples.html b/docs/pages/html/_static/notebooks/pca_examples.html index c9a75dc..7bb55a3 100644 --- a/docs/pages/html/_static/notebooks/pca_examples.html +++ b/docs/pages/html/_static/notebooks/pca_examples.html @@ -1,13 +1,9 @@ - - - + + + pca_examples - - - - - - - - - - - - - - + + + - - - - + void Promise.all([...diagrams].map(renderOneMarmaid)); + }); + + + + + + + - + pca A Python Package for Principal Component Analysis. The core of PCA is build on sklearn functionality to find maximum compatibility when combining with other packages. But this package can do a lot more. Besides the regular pca, it can also perform SparsePCA, and TruncatedSVD. Depending on your input data, the best approach will be choosen. Other functionalities are: @@ -15124,38 +7531,30 @@ github pca - - - + + -In [1]: +In [1]: - -!pip install pca + +!pip install pca - - - + - - - - - - - + + Requirement already satisfied: pca in /usr/local/lib/python3.7/dist-packages (1.7.2) Requirement already satisfied: matplotlib in /usr/local/lib/python3.7/dist-packages (from pca) (3.2.2) Requirement already satisfied: wget in /usr/local/lib/python3.7/dist-packages (from pca) (3.2) @@ -15180,179 +7579,149 @@ - - - - - + + - + Lets check the version - - - + + -In [2]: +In [2]: - -import pca + +import pca print(pca.__version__) - - - + - - - - - - - + + 1.7.2 - - - - - + + - + Import the pca library - - - + + -In [3]: +In [3]: - -from pca import pca + +from pca import pca import numpy as np import pandas as pd - - - - - + + + - + Here we will create a random dataset. - - - + + -In [4]: +In [4]: - -# Dataset + +# Dataset from sklearn.datasets import load_iris X = pd.DataFrame(data=load_iris().data, columns=load_iris().feature_names, index=load_iris().target) - - - - - + + + - + Initialize using specified parameters. The parameters here are the default parameters. - - - + + -In [5]: +In [5]: - -# Initialize + +# Initialize model = pca(n_components=3, normalize=True) - - - - - + + + -In [6]: +In [6]: - -# Fit transform + +# Fit transform out = model.fit_transform(X) - - - + - - - - - - - + + [pca] >Processing dataframe.. [pca] >Normalizing input data per feature (zero mean and unit variance).. [pca] >The PCA reduction is performed on the [4] columns of the input dataframe. @@ -15364,171 +7733,119 @@ - - - - - + + -In [7]: +In [7]: - -# Make plot with only the directions (no scatter) + +# Make plot with only the directions (no scatter) fig, ax = model.biplot(textlabel=True, legend=False, figsize=(10, 6)) - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 with loadings. - - - - - - - - + + + - - - - - - + + -In [8]: +In [8]: - -# Make plot with only the directions (no scatter) + +# Make plot with only the directions (no scatter) fig, ax = model.biplot(cmap=None, textlabel=False, legend=False, figsize=(10, 6)) - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 with loadings. - - - - - - - - + + + - - - - - - + + -In [9]: +In [9]: - -from pca import pca + +from pca import pca # Load example data from sklearn.datasets import load_iris X = pd.DataFrame(data=load_iris().data, columns=load_iris().feature_names, index=load_iris().target) - - - - - + + + -In [10]: +In [10]: - -# Initialize + +# Initialize model = pca(n_components=3) # Fit using PCA results = model.fit_transform(X) - - - + - - - - - - - + + [pca] >Processing dataframe.. [pca] >The PCA reduction is performed on the [4] columns of the input dataframe. [pca] >Fit using PCA. @@ -15539,20 +7856,17 @@ - - - - - + + -In [11]: +In [11]: - -# Make plots + +# Make plots # Scree plot fig, ax = model.plot(figsize=(10, 6)) @@ -15563,190 +7877,117 @@ # Biplot fig, ax = model.biplot(figsize=(10, 6)) - - - + - - - - - - - - - - + + + - - - - - - - - - + + + - - - - - - + + [pca] >Plot PC1 vs PC2 with loadings. - - - - - - - + + <Figure size 432x288 with 0 Axes> - - - - - - - - - + + + - - - - - - + + -In [17]: +In [17]: - -# Coloring on density to focus on the core samples. + +# Coloring on density to focus on the core samples. # Biplot -fig, ax = model.biplot(figsize=(10, 6), gradient='#ffffff') +fig, ax = model.biplot(figsize=(10, 6), gradient='#ffffff') - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 with loadings. - - - - - - - - + + + - - - - - - + + -In [18]: +In [18]: - -# Outliers are stored in results: -results['outliers'] + +# Outliers are stored in results: +results['outliers'] # Outliers based on T2 -print('--------T2------------') -print(results['outliers'].loc[results['outliers']['y_bool'], :]) +print('--------T2------------') +print(results['outliers'].loc[results['outliers']['y_bool'], :]) # Outliers based on SPE -print('--------SPE------------') -print(results['outliers'].loc[results['outliers']['y_bool_spe'], :]) +print('--------SPE------------') +print(results['outliers'].loc[results['outliers']['y_bool_spe'], :]) - - - + - - - - - - - + + --------T2------------ y_proba y_score y_bool y_bool_spe y_score_spe 2 0.040551 13.160880 True True 3.679935 @@ -15771,270 +8012,168 @@ - - - - - + + -In [20]: +In [20]: - -# Outlier detection + +# Outlier detection fig, ax = model.biplot(SPE=True, HT2=True, figsize=(10, 6)) - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 with loadings. - - - - - - - - + + + - - - - - - + + -In [21]: +In [21]: - -# 3D plots + +# 3D plots fig, ax = model.scatter3d(figsize=(10, 6)) fig, ax = model.biplot3d(figsize=(10, 6)) fig, ax = model.biplot3d(SPE=True, HT2=True, figsize=(10, 6)) - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 vs PC3 with loadings. - - - - - - - - + + + - - - - - - - - - + + + - - - - - - + + [pca] >Plot PC1 vs PC2 vs PC3 with loadings. - - - - - - - - + + + - - - - - - + + -In [22]: +In [22]: - -fig, ax = model.biplot3d(SPE=True, HT2=True, visible=False, figsize=(10, 6)) + +fig, ax = model.biplot3d(SPE=True, HT2=True, visible=False, figsize=(10, 6)) # Set the figure again to True and show the figure. fig.set_visible(True) fig - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 vs PC3 with loadings. - - Out[22]: - - - - - - +Out[22]: + + - - - - - - - - - + + + - - - - - - + + -In [23]: +In [23]: - -# Normalize out PCs + +
After fitting variables into the new principal component space, we can map new unseen samples into this space too. However, there is also normalization step which can be tricky because you now need standardize the values of the unseen samples first based on the previously performed standardization. This step is also integrated in the pca library by simply setting the parameter normalize=True.
normalize=True
# Load libraries import matplotlib.pyplot as plt @@ -422,10 +424,11 @@ Map unseen datapoints into fitted spaceax.scatter(PCnew.iloc[:, 0], PCnew.iloc[:, 1], marker='x', s=200)
Normalize your data using the principal components. As an example, suppose there is (technical) variation in the fist component and you want that out. This function transforms the data using the components that you want, e.g., starting from the 2nd PC, up to the OC that contains at least 95% of the explained variance.
print(X.shape) (178, 13) @@ -443,7 +446,7 @@ Normalizing out PCs -Colors in plots +Colors in plots The default colors that are used in the plots depend on how much information is provided at start. There are many parameters to change the colors in the plots. Here I will demonstrate some of the possibilities. First, we will load the data and import the libraries. @@ -476,7 +479,7 @@ Colors in plots -Left: Default plot using the provided classlabels. Right: Color on custom cmap. +Left: Default plot using the provided classlabels. Right: Color on custom cmap. @@ -498,7 +501,7 @@ Colors in plots -Left: Mark some points on y and use cmap. Right: Specify the colors manually. +Left: Mark some points on y and use cmap. Right: Specify the colors manually. @@ -514,7 +517,7 @@ Colors in plots -Left: Remove scatterpoints from plot. Right: Gradient with the used cmap. +Left: Remove scatterpoints from plot. Right: Gradient with the used cmap. @@ -539,7 +542,7 @@ Colors in plots -Fig as input to make iterative changes. +Fig as input to make iterative changes. diff --git a/docs/pages/html/Installation.html b/docs/pages/html/Installation.html index d2fd9ff..8a0f6d2 100644 --- a/docs/pages/html/Installation.html +++ b/docs/pages/html/Installation.html @@ -1,20 +1,22 @@ + + - + - + Installation — pca pca documentation - - - - + + + + - - - + + + + + @@ -33,9 +35,6 @@ pca - - 2.0.1 - @@ -138,9 +137,9 @@ -Installation +Installation -Create environment +Create environment If desired, install pca from an isolated Python environment using conda: conda create -n env_pca python=3.8 conda activate env_pca @@ -148,26 +147,26 @@ Create environment -Pip install -# Install from Pypi: +Pip install +# Install from Pypi: pip install pca -# Install directly from github +# Install directly from github pip install git+https://github.com/erdogant/pca -Uninstalling +Uninstalling Remove the environment with installation: -# List all the active environments. pca should be listed. +# List all the active environments. pca should be listed. conda env list -# Remove the pca environment +# Remove the pca environment conda env remove --name pca -# List all the active environments. pca should be absent. +# List all the active environments. pca should be absent. conda env list diff --git a/docs/pages/html/Outlier detection.html b/docs/pages/html/Outlier detection.html index 37bc204..fe764f4 100644 --- a/docs/pages/html/Outlier detection.html +++ b/docs/pages/html/Outlier detection.html @@ -1,20 +1,22 @@ + + - + - + Hotelling T2 — pca pca documentation - - - - + + + + - - - + + + + + @@ -33,9 +35,6 @@ pca - - 2.0.1 - @@ -134,7 +133,7 @@ -Hotelling T2 +Hotelling T2 To detect outliers across the multidimensional space of PCA, the hotellings T2 test is implemented. It works by computing the chi-square tests across the top n_components: default is PC1 to PC5. The reason for not using more PC’s is that it is expected that the highest variance (and thus the outliers) will be seen in the first few components. Going deeper into PC space may therefore not be required. Nevertheless, the depth is optional. The hotellings T2 test outputs a P-value matrix (samples x PCs), which are are subsequently combined using fishers method. This allows to determine outliers with its ranking (strongest to weak). The alpha parameter determines the detection of outliers (default: 0.05). @@ -192,7 +191,7 @@ Hotelling T2 -SPE/Dmodx +SPE/Dmodx Outlier can be detected using SPE/DmodX (distance to model) based on the mean and covariance of the first 2 dimensions of X. On the model plane (SPE ≈ 0). Note that the SPE or Hotelling’s T2 are complementary to each other. model.biplot(legend=True, SPE=True, HT2=True) @@ -204,7 +203,7 @@ SPE/Dmodx -Detected outliers +Detected outliers @@ -213,7 +212,7 @@ SPE/Dmodx -Selection of the Outliers +Selection of the Outliers Selecting the outliers can be usefull to remove them from the dataset or for deeper investigation. # Select the outliers Xoutliers = X[results['outliers']['y_bool'],:] @@ -224,7 +223,7 @@ Selection of the Outliers -Detect new unseen outliers +Detect new unseen outliers After fitting a model on the data, you may want to use the model in a later stage to detect outliers on unseen data. Detection of outliers is performed in the transform function and does not require any additional action. An example is shown in the code block below. # Import libraries @@ -252,7 +251,7 @@ Detect new unseen outliers -Detected outliers +Detected outliers @@ -288,7 +287,7 @@ Detect new unseen outliers -Detected outliers +Detected outliers @@ -296,7 +295,7 @@ Detect new unseen outliers -Detection of outliers without PCA +Detection of outliers without PCA If desired, the outliers can also be detected directly using the hotelling T2 and/or SPE/DmodX functionality. For demonstration purposes I use the PCs from the results but any other dataset would also work. import pca diff --git a/docs/pages/html/Plots.html b/docs/pages/html/Plots.html index c1677b6..f054370 100644 --- a/docs/pages/html/Plots.html +++ b/docs/pages/html/Plots.html @@ -1,20 +1,22 @@ + + - + - + Load dataset — pca pca documentation - - - - + + + + - - - + + + + + @@ -33,9 +35,6 @@ pca - - 2.0.1 - @@ -134,7 +133,7 @@ -Load dataset +Load dataset Let’s load the wine dataset to demonstrate the plots. # Load library from sklearn.datasets import load_wine @@ -166,7 +165,7 @@ Load dataset -Scatter plot +Scatter plot # Make scatterplot model.scatter() @@ -187,7 +186,7 @@ Scatter plot -Scatterplots +Scatterplots @@ -204,16 +203,40 @@ Scatter plot -Biplot +Biplot +The biplot draws the loadings (arrows) together with the samples (scatterplot). +The loadings can be colored red and blue which indicates the strength of the particular feature in the PC. +For each principal component (PC), the feature is determined with the largest absolute loading. This indicates which feature contributes the most to each PC and can occur in multiple PCs. +The highest loading values for the features are colored red in the biplot and described as “best” in the output dataframe. +The features that were not seen with highest loadings for any PC are considered weaker features, and are colored blue the biplot. In the output dataframe these features are described as “weak”. # Make biplot model.biplot() # Here again, many other options can be turned on and off model.biplot(SPE=True, HT2=True, legend=1) + +# Show the top features +results['topfeat'] + +# PC feature loading type +# 0 PC1 flavanoids 0.422934 best +# 1 PC2 color_intensity 0.529996 best +# 2 PC3 ash 0.626224 best +# 3 PC4 malic_acid 0.536890 best +# 4 PC5 magnesium 0.727049 best +# 5 PC6 malic_acid 0.536814 best +# 6 PC7 nonflavanoid_phenols 0.595447 best +# 7 PC8 hue 0.436624 best +# 8 PC9 proline 0.575786 best +# 9 PC10 od280/od315_of_diluted_wines 0.523706 best +# 10 PC9 alcohol -0.508619 weak +# 11 PC3 alcalinity_of_ash 0.612080 weak +# 12 PC8 total_phenols -0.405934 weak +# 13 PC6 proanthocyanins -0.533795 weak -Biplots +Biplots @@ -223,28 +246,30 @@ Biplot -Biplot (only arrows) +Biplot (only arrows) # Make plot with parameters: set cmap to None and label and legend to False. Only directions will be plotted. model.biplot(cmap=None, legend=False) - + + -Explained variance plot +Explained variance plot model.plot() - + + -Alpha Transparency +Alpha Transparency fig, ax = model.scatter(alpha=1) -Markers +Markers import numpy as np from sklearn.datasets import make_friedman1 from pca import pca @@ -272,7 +297,7 @@ Markers -Biplots with markers +Biplots with markers @@ -280,7 +305,7 @@ Markers -Control color/marker/size per sample +Control color/marker/size per sample import numpy as np import matplotlib.pyplot as plt import matplotlib.colors as mcolors @@ -329,7 +354,7 @@ Control color/marker/size per sample -Biplot with customized properties per sample. +Biplot with customized properties per sample. @@ -337,15 +362,16 @@ Control color/marker/size per sample -3D plots +3D plots All plots can also be created in 3D by setting the d3=True parameter. model.biplot3d() - + + -Toggle visible status +Toggle visible status The visible status for can be turned on and off. # Make plot but not visible. fig, ax = model.biplot(visible=False) diff --git a/docs/pages/html/_sources/Plots.rst.txt b/docs/pages/html/_sources/Plots.rst.txt index 33319b2..38cd2db 100644 --- a/docs/pages/html/_sources/Plots.rst.txt +++ b/docs/pages/html/_sources/Plots.rst.txt @@ -83,6 +83,14 @@ Scatter plot Biplot ############### +The biplot draws the loadings (arrows) together with the samples (scatterplot). +The loadings can be colored red and blue which indicates the strength of the particular feature in the PC. + +For each principal component (PC), the feature is determined with the largest absolute loading. This indicates which feature contributes the most to each PC and can occur in multiple PCs. +The highest loading values for the features are colored red in the biplot and described as "best" in the output dataframe. +The features that were not seen with highest loadings for any PC are considered weaker features, and are colored blue the biplot. In the output dataframe these features are described as "weak". + + .. code:: python # Make biplot @@ -91,6 +99,24 @@ Biplot # Here again, many other options can be turned on and off model.biplot(SPE=True, HT2=True, legend=1) + # Show the top features + results['topfeat'] + + # PC feature loading type + # 0 PC1 flavanoids 0.422934 best + # 1 PC2 color_intensity 0.529996 best + # 2 PC3 ash 0.626224 best + # 3 PC4 malic_acid 0.536890 best + # 4 PC5 magnesium 0.727049 best + # 5 PC6 malic_acid 0.536814 best + # 6 PC7 nonflavanoid_phenols 0.595447 best + # 7 PC8 hue 0.436624 best + # 8 PC9 proline 0.575786 best + # 9 PC10 od280/od315_of_diluted_wines 0.523706 best + # 10 PC9 alcohol -0.508619 weak + # 11 PC3 alcalinity_of_ash 0.612080 weak + # 12 PC8 total_phenols -0.405934 weak + # 13 PC6 proanthocyanins -0.533795 weak .. |figP5| image:: ../figs/wine_biplot.png .. |figP6| image:: ../figs/wine_biplot_with_outliers.png diff --git a/docs/pages/html/_sources/sponsor.rst.txt b/docs/pages/html/_sources/sponsor.rst.txt index a46c410..f006896 100644 --- a/docs/pages/html/_sources/sponsor.rst.txt +++ b/docs/pages/html/_sources/sponsor.rst.txt @@ -4,8 +4,10 @@ * Become a `Sponsor `_! * `Buy `_ me a coffee! I ❤️ coffee :) * `Donate `_ in Bitcoin. - * Follow me on medium! Go to my `medium profile `_ and press *follow*. + * Follow me on Medium! Go to my `medium profile `_ and press *follow*. + * Subscribe to me on Substack! Go to my `profile `_ where you can *subscribe*. * **Star** this repo at the github page. + * You can also buy a digital educational product over `here `_. * Other contributions can be in the form of feature requests, idea discussions, reporting bugs, opening pull requests. 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b/docs/pages/html/_static/basic.css index 7577acb..7ebbd6d 100644 --- a/docs/pages/html/_static/basic.css +++ b/docs/pages/html/_static/basic.css @@ -1,12 +1,5 @@ /* - * basic.css - * ~~~~~~~~~ - * * Sphinx stylesheet -- basic theme. - * - * :copyright: Copyright 2007-2023 by the Sphinx team, see AUTHORS. - * :license: BSD, see LICENSE for details. - * */ /* -- main layout ----------------------------------------------------------- */ @@ -115,15 +108,11 @@ img { /* -- search page ----------------------------------------------------------- */ ul.search { - margin: 10px 0 0 20px; - padding: 0; + margin-top: 10px; } ul.search li { - padding: 5px 0 5px 20px; - background-image: url(file.png); - background-repeat: no-repeat; - background-position: 0 7px; + padding: 5px 0; } ul.search li a { @@ -237,6 +226,10 @@ a.headerlink { visibility: hidden; } +a:visited { + color: #551A8B; +} + h1:hover > a.headerlink, h2:hover > a.headerlink, h3:hover > a.headerlink, @@ -670,6 +663,16 @@ dd { 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a/docs/pages/html/_static/language_data.js +++ b/docs/pages/html/_static/language_data.js @@ -1,19 +1,12 @@ /* - * language_data.js - * ~~~~~~~~~~~~~~~~ - * * This script contains the language-specific data used by searchtools.js, * namely the list of stopwords, stemmer, scorer and splitter. - * - * :copyright: Copyright 2007-2023 by the Sphinx team, see AUTHORS. - * :license: BSD, see LICENSE for details. - * */ var stopwords = ["a", "and", "are", "as", "at", "be", "but", "by", "for", "if", "in", "into", "is", "it", "near", "no", "not", "of", "on", "or", "such", "that", "the", "their", "then", "there", "these", "they", "this", "to", "was", "will", "with"]; -/* Non-minified version is copied as a separate JS file, is available */ +/* Non-minified version is copied as a separate JS file, if available */ /** * Porter Stemmer diff --git a/docs/pages/html/_static/notebooks/pca_examples.html b/docs/pages/html/_static/notebooks/pca_examples.html index c9a75dc..7bb55a3 100644 --- a/docs/pages/html/_static/notebooks/pca_examples.html +++ b/docs/pages/html/_static/notebooks/pca_examples.html @@ -1,13 +1,9 @@ - - - + + + pca_examples - - - - - - - - - - - - - - + + + - - - - + void Promise.all([...diagrams].map(renderOneMarmaid)); + }); + + + + + + + - + pca A Python Package for Principal Component Analysis. The core of PCA is build on sklearn functionality to find maximum compatibility when combining with other packages. But this package can do a lot more. Besides the regular pca, it can also perform SparsePCA, and TruncatedSVD. Depending on your input data, the best approach will be choosen. Other functionalities are: @@ -15124,38 +7531,30 @@ github pca - - - + + -In [1]: +In [1]: - -!pip install pca + +!pip install pca - - - + - - - - - - - + + Requirement already satisfied: pca in /usr/local/lib/python3.7/dist-packages (1.7.2) Requirement already satisfied: matplotlib in /usr/local/lib/python3.7/dist-packages (from pca) (3.2.2) Requirement already satisfied: wget in /usr/local/lib/python3.7/dist-packages (from pca) (3.2) @@ -15180,179 +7579,149 @@ - - - - - + + - + Lets check the version - - - + + -In [2]: +In [2]: - -import pca + +import pca print(pca.__version__) - - - + - - - - - - - + + 1.7.2 - - - - - + + - + Import the pca library - - - + + -In [3]: +In [3]: - -from pca import pca + +from pca import pca import numpy as np import pandas as pd - - - - - + + + - + Here we will create a random dataset. - - - + + -In [4]: +In [4]: - -# Dataset + +# Dataset from sklearn.datasets import load_iris X = pd.DataFrame(data=load_iris().data, columns=load_iris().feature_names, index=load_iris().target) - - - - - + + + - + Initialize using specified parameters. The parameters here are the default parameters. - - - + + -In [5]: +In [5]: - -# Initialize + +# Initialize model = pca(n_components=3, normalize=True) - - - - - + + + -In [6]: +In [6]: - -# Fit transform + +# Fit transform out = model.fit_transform(X) - - - + - - - - - - - + + [pca] >Processing dataframe.. [pca] >Normalizing input data per feature (zero mean and unit variance).. [pca] >The PCA reduction is performed on the [4] columns of the input dataframe. @@ -15364,171 +7733,119 @@ - - - - - + + -In [7]: +In [7]: - -# Make plot with only the directions (no scatter) + +# Make plot with only the directions (no scatter) fig, ax = model.biplot(textlabel=True, legend=False, figsize=(10, 6)) - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 with loadings. - - - - - - - - + + + - - - - - - + + -In [8]: +In [8]: - -# Make plot with only the directions (no scatter) + +# Make plot with only the directions (no scatter) fig, ax = model.biplot(cmap=None, textlabel=False, legend=False, figsize=(10, 6)) - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 with loadings. - - - - - - - - + + + - - - - - - + + -In [9]: +In [9]: - -from pca import pca + +from pca import pca # Load example data from sklearn.datasets import load_iris X = pd.DataFrame(data=load_iris().data, columns=load_iris().feature_names, index=load_iris().target) - - - - - + + + -In [10]: +In [10]: - -# Initialize + +# Initialize model = pca(n_components=3) # Fit using PCA results = model.fit_transform(X) - - - + - - - - - - - + + [pca] >Processing dataframe.. [pca] >The PCA reduction is performed on the [4] columns of the input dataframe. [pca] >Fit using PCA. @@ -15539,20 +7856,17 @@ - - - - - + + -In [11]: +In [11]: - -# Make plots + +# Make plots # Scree plot fig, ax = model.plot(figsize=(10, 6)) @@ -15563,190 +7877,117 @@ # Biplot fig, ax = model.biplot(figsize=(10, 6)) - - - + - - - - - - - - - - + + + - - - - - - - - - + + + - - - - - - + + [pca] >Plot PC1 vs PC2 with loadings. - - - - - - - + + <Figure size 432x288 with 0 Axes> - - - - - - - - - + + + - - - - - - + + -In [17]: +In [17]: - -# Coloring on density to focus on the core samples. + +# Coloring on density to focus on the core samples. # Biplot -fig, ax = model.biplot(figsize=(10, 6), gradient='#ffffff') +fig, ax = model.biplot(figsize=(10, 6), gradient='#ffffff') - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 with loadings. - - - - - - - - + + + - - - - - - + + -In [18]: +In [18]: - -# Outliers are stored in results: -results['outliers'] + +# Outliers are stored in results: +results['outliers'] # Outliers based on T2 -print('--------T2------------') -print(results['outliers'].loc[results['outliers']['y_bool'], :]) +print('--------T2------------') +print(results['outliers'].loc[results['outliers']['y_bool'], :]) # Outliers based on SPE -print('--------SPE------------') -print(results['outliers'].loc[results['outliers']['y_bool_spe'], :]) +print('--------SPE------------') +print(results['outliers'].loc[results['outliers']['y_bool_spe'], :]) - - - + - - - - - - - + + --------T2------------ y_proba y_score y_bool y_bool_spe y_score_spe 2 0.040551 13.160880 True True 3.679935 @@ -15771,270 +8012,168 @@ - - - - - + + -In [20]: +In [20]: - -# Outlier detection + +# Outlier detection fig, ax = model.biplot(SPE=True, HT2=True, figsize=(10, 6)) - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 with loadings. - - - - - - - - + + + - - - - - - + + -In [21]: +In [21]: - -# 3D plots + +# 3D plots fig, ax = model.scatter3d(figsize=(10, 6)) fig, ax = model.biplot3d(figsize=(10, 6)) fig, ax = model.biplot3d(SPE=True, HT2=True, figsize=(10, 6)) - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 vs PC3 with loadings. - - - - - - - - + + + - - - - - - - - - + + + - - - - - - + + [pca] >Plot PC1 vs PC2 vs PC3 with loadings. - - - - - - - - + + + - - - - - - + + -In [22]: +In [22]: - -fig, ax = model.biplot3d(SPE=True, HT2=True, visible=False, figsize=(10, 6)) + +fig, ax = model.biplot3d(SPE=True, HT2=True, visible=False, figsize=(10, 6)) # Set the figure again to True and show the figure. fig.set_visible(True) fig - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 vs PC3 with loadings. - - Out[22]: - - - - - - +Out[22]: + + - - - - - - - - - + + + - - - - - - + + -In [23]: +In [23]: - -# Normalize out PCs + +
The default colors that are used in the plots depend on how much information is provided at start. There are many parameters to change the colors in the plots. Here I will demonstrate some of the possibilities.
First, we will load the data and import the libraries.
If desired, install pca from an isolated Python environment using conda:
conda create -n env_pca python=3.8 conda activate env_pca @@ -148,26 +147,26 @@ Create environment -Pip install -# Install from Pypi: +Pip install +# Install from Pypi: pip install pca -# Install directly from github +# Install directly from github pip install git+https://github.com/erdogant/pca -Uninstalling +Uninstalling Remove the environment with installation: -# List all the active environments. pca should be listed. +# List all the active environments. pca should be listed. conda env list -# Remove the pca environment +# Remove the pca environment conda env remove --name pca -# List all the active environments. pca should be absent. +# List all the active environments. pca should be absent. conda env list diff --git a/docs/pages/html/Outlier detection.html b/docs/pages/html/Outlier detection.html index 37bc204..fe764f4 100644 --- a/docs/pages/html/Outlier detection.html +++ b/docs/pages/html/Outlier detection.html @@ -1,20 +1,22 @@ + + - + - + Hotelling T2 — pca pca documentation - - - - + + + + - - - + + + + + @@ -33,9 +35,6 @@ pca - - 2.0.1 - @@ -134,7 +133,7 @@ -Hotelling T2 +Hotelling T2 To detect outliers across the multidimensional space of PCA, the hotellings T2 test is implemented. It works by computing the chi-square tests across the top n_components: default is PC1 to PC5. The reason for not using more PC’s is that it is expected that the highest variance (and thus the outliers) will be seen in the first few components. Going deeper into PC space may therefore not be required. Nevertheless, the depth is optional. The hotellings T2 test outputs a P-value matrix (samples x PCs), which are are subsequently combined using fishers method. This allows to determine outliers with its ranking (strongest to weak). The alpha parameter determines the detection of outliers (default: 0.05). @@ -192,7 +191,7 @@ Hotelling T2 -SPE/Dmodx +SPE/Dmodx Outlier can be detected using SPE/DmodX (distance to model) based on the mean and covariance of the first 2 dimensions of X. On the model plane (SPE ≈ 0). Note that the SPE or Hotelling’s T2 are complementary to each other. model.biplot(legend=True, SPE=True, HT2=True) @@ -204,7 +203,7 @@ SPE/Dmodx -Detected outliers +Detected outliers @@ -213,7 +212,7 @@ SPE/Dmodx -Selection of the Outliers +Selection of the Outliers Selecting the outliers can be usefull to remove them from the dataset or for deeper investigation. # Select the outliers Xoutliers = X[results['outliers']['y_bool'],:] @@ -224,7 +223,7 @@ Selection of the Outliers -Detect new unseen outliers +Detect new unseen outliers After fitting a model on the data, you may want to use the model in a later stage to detect outliers on unseen data. Detection of outliers is performed in the transform function and does not require any additional action. An example is shown in the code block below. # Import libraries @@ -252,7 +251,7 @@ Detect new unseen outliers -Detected outliers +Detected outliers @@ -288,7 +287,7 @@ Detect new unseen outliers -Detected outliers +Detected outliers @@ -296,7 +295,7 @@ Detect new unseen outliers -Detection of outliers without PCA +Detection of outliers without PCA If desired, the outliers can also be detected directly using the hotelling T2 and/or SPE/DmodX functionality. For demonstration purposes I use the PCs from the results but any other dataset would also work. import pca diff --git a/docs/pages/html/Plots.html b/docs/pages/html/Plots.html index c1677b6..f054370 100644 --- a/docs/pages/html/Plots.html +++ b/docs/pages/html/Plots.html @@ -1,20 +1,22 @@ + + - + - + Load dataset — pca pca documentation - - - - + + + + - - - + + + + + @@ -33,9 +35,6 @@ pca - - 2.0.1 - @@ -134,7 +133,7 @@ -Load dataset +Load dataset Let’s load the wine dataset to demonstrate the plots. # Load library from sklearn.datasets import load_wine @@ -166,7 +165,7 @@ Load dataset -Scatter plot +Scatter plot # Make scatterplot model.scatter() @@ -187,7 +186,7 @@ Scatter plot -Scatterplots +Scatterplots @@ -204,16 +203,40 @@ Scatter plot -Biplot +Biplot +The biplot draws the loadings (arrows) together with the samples (scatterplot). +The loadings can be colored red and blue which indicates the strength of the particular feature in the PC. +For each principal component (PC), the feature is determined with the largest absolute loading. This indicates which feature contributes the most to each PC and can occur in multiple PCs. +The highest loading values for the features are colored red in the biplot and described as “best” in the output dataframe. +The features that were not seen with highest loadings for any PC are considered weaker features, and are colored blue the biplot. In the output dataframe these features are described as “weak”. # Make biplot model.biplot() # Here again, many other options can be turned on and off model.biplot(SPE=True, HT2=True, legend=1) + +# Show the top features +results['topfeat'] + +# PC feature loading type +# 0 PC1 flavanoids 0.422934 best +# 1 PC2 color_intensity 0.529996 best +# 2 PC3 ash 0.626224 best +# 3 PC4 malic_acid 0.536890 best +# 4 PC5 magnesium 0.727049 best +# 5 PC6 malic_acid 0.536814 best +# 6 PC7 nonflavanoid_phenols 0.595447 best +# 7 PC8 hue 0.436624 best +# 8 PC9 proline 0.575786 best +# 9 PC10 od280/od315_of_diluted_wines 0.523706 best +# 10 PC9 alcohol -0.508619 weak +# 11 PC3 alcalinity_of_ash 0.612080 weak +# 12 PC8 total_phenols -0.405934 weak +# 13 PC6 proanthocyanins -0.533795 weak -Biplots +Biplots @@ -223,28 +246,30 @@ Biplot -Biplot (only arrows) +Biplot (only arrows) # Make plot with parameters: set cmap to None and label and legend to False. Only directions will be plotted. model.biplot(cmap=None, legend=False) - + + -Explained variance plot +Explained variance plot model.plot() - + + -Alpha Transparency +Alpha Transparency fig, ax = model.scatter(alpha=1) -Markers +Markers import numpy as np from sklearn.datasets import make_friedman1 from pca import pca @@ -272,7 +297,7 @@ Markers -Biplots with markers +Biplots with markers @@ -280,7 +305,7 @@ Markers -Control color/marker/size per sample +Control color/marker/size per sample import numpy as np import matplotlib.pyplot as plt import matplotlib.colors as mcolors @@ -329,7 +354,7 @@ Control color/marker/size per sample -Biplot with customized properties per sample. +Biplot with customized properties per sample. @@ -337,15 +362,16 @@ Control color/marker/size per sample -3D plots +3D plots All plots can also be created in 3D by setting the d3=True parameter. model.biplot3d() - + + -Toggle visible status +Toggle visible status The visible status for can be turned on and off. # Make plot but not visible. fig, ax = model.biplot(visible=False) diff --git a/docs/pages/html/_sources/Plots.rst.txt b/docs/pages/html/_sources/Plots.rst.txt index 33319b2..38cd2db 100644 --- a/docs/pages/html/_sources/Plots.rst.txt +++ b/docs/pages/html/_sources/Plots.rst.txt @@ -83,6 +83,14 @@ Scatter plot Biplot ############### +The biplot draws the loadings (arrows) together with the samples (scatterplot). +The loadings can be colored red and blue which indicates the strength of the particular feature in the PC. + +For each principal component (PC), the feature is determined with the largest absolute loading. This indicates which feature contributes the most to each PC and can occur in multiple PCs. +The highest loading values for the features are colored red in the biplot and described as "best" in the output dataframe. +The features that were not seen with highest loadings for any PC are considered weaker features, and are colored blue the biplot. In the output dataframe these features are described as "weak". + + .. code:: python # Make biplot @@ -91,6 +99,24 @@ Biplot # Here again, many other options can be turned on and off model.biplot(SPE=True, HT2=True, legend=1) + # Show the top features + results['topfeat'] + + # PC feature loading type + # 0 PC1 flavanoids 0.422934 best + # 1 PC2 color_intensity 0.529996 best + # 2 PC3 ash 0.626224 best + # 3 PC4 malic_acid 0.536890 best + # 4 PC5 magnesium 0.727049 best + # 5 PC6 malic_acid 0.536814 best + # 6 PC7 nonflavanoid_phenols 0.595447 best + # 7 PC8 hue 0.436624 best + # 8 PC9 proline 0.575786 best + # 9 PC10 od280/od315_of_diluted_wines 0.523706 best + # 10 PC9 alcohol -0.508619 weak + # 11 PC3 alcalinity_of_ash 0.612080 weak + # 12 PC8 total_phenols -0.405934 weak + # 13 PC6 proanthocyanins -0.533795 weak .. |figP5| image:: ../figs/wine_biplot.png .. |figP6| image:: ../figs/wine_biplot_with_outliers.png diff --git a/docs/pages/html/_sources/sponsor.rst.txt b/docs/pages/html/_sources/sponsor.rst.txt index a46c410..f006896 100644 --- a/docs/pages/html/_sources/sponsor.rst.txt +++ b/docs/pages/html/_sources/sponsor.rst.txt @@ -4,8 +4,10 @@ * Become a `Sponsor `_! * `Buy `_ me a coffee! I ❤️ coffee :) * `Donate `_ in Bitcoin. - * Follow me on medium! Go to my `medium profile `_ and press *follow*. + * Follow me on Medium! Go to my `medium profile `_ and press *follow*. + * Subscribe to me on Substack! Go to my `profile `_ where you can *subscribe*. * **Star** this repo at the github page. + * You can also buy a digital educational product over `here `_. * Other contributions can be in the form of feature requests, idea discussions, reporting bugs, opening pull requests. Cheers Mate. diff --git a/docs/pages/html/_static/_sphinx_javascript_frameworks_compat.js b/docs/pages/html/_static/_sphinx_javascript_frameworks_compat.js new file mode 100644 index 0000000..8141580 --- /dev/null +++ b/docs/pages/html/_static/_sphinx_javascript_frameworks_compat.js @@ -0,0 +1,123 @@ +/* Compatability shim for jQuery and underscores.js. + * + * Copyright Sphinx contributors + * Released under the two clause BSD licence + */ + +/** + * small helper function to urldecode strings + * + * See https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/decodeURIComponent#Decoding_query_parameters_from_a_URL + */ +jQuery.urldecode = function(x) { + if (!x) { + return x + } + return decodeURIComponent(x.replace(/\+/g, ' ')); +}; + +/** + * small helper function to urlencode strings + */ +jQuery.urlencode = encodeURIComponent; + +/** + * This function returns the parsed url parameters of the + * current request. Multiple values per key are supported, + * it will always return arrays of strings for the value parts. + */ +jQuery.getQueryParameters = function(s) { + if (typeof s === 'undefined') + s = document.location.search; + var parts = s.substr(s.indexOf('?') + 1).split('&'); + var result = {}; + for (var i = 0; i < parts.length; i++) { + var tmp = parts[i].split('=', 2); + var key = jQuery.urldecode(tmp[0]); + var value = jQuery.urldecode(tmp[1]); + if (key in result) + result[key].push(value); + else + result[key] = [value]; + } + return result; +}; + +/** + * highlight a given string on a jquery object by wrapping it in + * span elements with the given class name. + */ +jQuery.fn.highlightText = function(text, className) { + function highlight(node, addItems) { + if (node.nodeType === 3) { + var val = node.nodeValue; + var pos = val.toLowerCase().indexOf(text); + if (pos >= 0 && + !jQuery(node.parentNode).hasClass(className) && + !jQuery(node.parentNode).hasClass("nohighlight")) { + var span; + var isInSVG = jQuery(node).closest("body, svg, foreignObject").is("svg"); + if (isInSVG) { + span = document.createElementNS("http://www.w3.org/2000/svg", "tspan"); + } else { + span = document.createElement("span"); + span.className = className; + } + span.appendChild(document.createTextNode(val.substr(pos, text.length))); + node.parentNode.insertBefore(span, node.parentNode.insertBefore( + document.createTextNode(val.substr(pos + text.length)), + node.nextSibling)); + node.nodeValue = val.substr(0, pos); + if (isInSVG) { + var rect = document.createElementNS("http://www.w3.org/2000/svg", "rect"); + var bbox = node.parentElement.getBBox(); + rect.x.baseVal.value = bbox.x; + rect.y.baseVal.value = bbox.y; + rect.width.baseVal.value = bbox.width; + rect.height.baseVal.value = bbox.height; + rect.setAttribute('class', className); + addItems.push({ + "parent": node.parentNode, + "target": rect}); + } + } + } + else if (!jQuery(node).is("button, select, textarea")) { + jQuery.each(node.childNodes, function() { + highlight(this, addItems); + }); + } + } + var addItems = []; + var result = this.each(function() { + highlight(this, addItems); + }); + for (var i = 0; i < addItems.length; ++i) { + jQuery(addItems[i].parent).before(addItems[i].target); + } + return result; +}; + +/* + * backward compatibility for jQuery.browser + * This will be supported until firefox bug is fixed. + */ +if (!jQuery.browser) { + jQuery.uaMatch = function(ua) { + ua = ua.toLowerCase(); + + var match = /(chrome)[ \/]([\w.]+)/.exec(ua) || + /(webkit)[ \/]([\w.]+)/.exec(ua) || + /(opera)(?:.*version|)[ \/]([\w.]+)/.exec(ua) || + /(msie) ([\w.]+)/.exec(ua) || + ua.indexOf("compatible") < 0 && /(mozilla)(?:.*? rv:([\w.]+)|)/.exec(ua) || + []; + + return { + browser: match[ 1 ] || "", + version: match[ 2 ] || "0" + }; + }; + jQuery.browser = {}; + jQuery.browser[jQuery.uaMatch(navigator.userAgent).browser] = true; +} diff --git a/docs/pages/html/_static/basic.css b/docs/pages/html/_static/basic.css index 7577acb..7ebbd6d 100644 --- a/docs/pages/html/_static/basic.css +++ b/docs/pages/html/_static/basic.css @@ -1,12 +1,5 @@ /* - * basic.css - * ~~~~~~~~~ - * * Sphinx stylesheet -- basic theme. - * - * :copyright: Copyright 2007-2023 by the Sphinx team, see AUTHORS. - * :license: BSD, see LICENSE for details. - * */ /* -- main layout ----------------------------------------------------------- */ @@ -115,15 +108,11 @@ img { /* -- search page ----------------------------------------------------------- */ ul.search { - margin: 10px 0 0 20px; - padding: 0; + margin-top: 10px; } ul.search li { - padding: 5px 0 5px 20px; - background-image: url(file.png); - background-repeat: no-repeat; - background-position: 0 7px; + padding: 5px 0; } ul.search li a { @@ -237,6 +226,10 @@ a.headerlink { visibility: hidden; } +a:visited { + color: #551A8B; +} + h1:hover > a.headerlink, h2:hover > a.headerlink, h3:hover > a.headerlink, @@ -670,6 +663,16 @@ dd { 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video",version:m,shivCSS:n.shivCSS!==!1,supportsUnknownElements:l,shivMethods:n.shivMethods!==!1,type:"default",shivDocument:j,createElement:g,createDocumentFragment:h,addElements:e};a.html5=t,j(b),"object"==typeof module&&module.exports&&(module.exports=t)}("undefined"!=typeof window?window:this,document); \ No newline at end of file diff --git a/docs/pages/html/_static/js/versions.js b/docs/pages/html/_static/js/versions.js new file mode 100644 index 0000000..4958195 --- /dev/null +++ b/docs/pages/html/_static/js/versions.js @@ -0,0 +1,228 @@ +const themeFlyoutDisplay = "hidden"; +const themeVersionSelector = true; +const themeLanguageSelector = true; + +if (themeFlyoutDisplay === "attached") { + function renderLanguages(config) { + if (!config.projects.translations.length) { + return ""; + } + + // Insert the current language to the options on the selector + let languages = config.projects.translations.concat(config.projects.current); + languages = languages.sort((a, b) => a.language.name.localeCompare(b.language.name)); + + const languagesHTML = ` + + Languages + ${languages + .map( + (translation) => ` + + ${translation.language.code} + + `, + ) + .join("\n")} + + `; + return languagesHTML; + } + + function renderVersions(config) { + if (!config.versions.active.length) { + return ""; + } + const versionsHTML = ` + + Versions + ${config.versions.active + .map( + (version) => ` + + ${version.slug} + + `, + ) + .join("\n")} + + `; + return versionsHTML; + } + + function renderDownloads(config) { + if (!Object.keys(config.versions.current.downloads).length) { + return ""; + } + const downloadsNameDisplay = { + pdf: "PDF", + epub: "Epub", + htmlzip: "HTML", + }; + + const downloadsHTML = ` + + Downloads + ${Object.entries(config.versions.current.downloads) + .map( + ([name, url]) => ` + + ${downloadsNameDisplay[name]} + + `, + ) + .join("\n")} + + `; + return downloadsHTML; + } + + document.addEventListener("readthedocs-addons-data-ready", function (event) { + const config = event.detail.data(); + + const flyout = ` + + + Read the Docs + v: ${config.versions.current.slug} + + + + + ${renderLanguages(config)} + ${renderVersions(config)} + ${renderDownloads(config)} + + On Read the Docs + + Project Home + + + Builds + + + Downloads + + + + Search + + + + + + + + + Hosted by Read the Docs + + + + `; + + // Inject the generated flyout into the body HTML element. + document.body.insertAdjacentHTML("beforeend", flyout); + + // Trigger the Read the Docs Addons Search modal when clicking on the "Search docs" input from inside the flyout. + document + .querySelector("#flyout-search-form") + .addEventListener("focusin", () => { + const event = new CustomEvent("readthedocs-search-show"); + document.dispatchEvent(event); + }); + }) +} + +if (themeLanguageSelector || themeVersionSelector) { + function onSelectorSwitch(event) { + const option = event.target.selectedIndex; + const item = event.target.options[option]; + window.location.href = item.dataset.url; + } + + document.addEventListener("readthedocs-addons-data-ready", function (event) { + const config = event.detail.data(); + + const versionSwitch = document.querySelector( + "div.switch-menus > div.version-switch", + ); + if (themeVersionSelector) { + let versions = config.versions.active; + if (config.versions.current.hidden || config.versions.current.type === "external") { + versions.unshift(config.versions.current); + } + const versionSelect = ` + + ${versions + .map( + (version) => ` + + ${version.slug} + `, + ) + .join("\n")} + + `; + + versionSwitch.innerHTML = versionSelect; + versionSwitch.firstElementChild.addEventListener("change", onSelectorSwitch); + } + + const languageSwitch = document.querySelector( + "div.switch-menus > div.language-switch", + ); + + if (themeLanguageSelector) { + if (config.projects.translations.length) { + // Add the current language to the options on the selector + let languages = config.projects.translations.concat( + config.projects.current, + ); + languages = languages.sort((a, b) => + a.language.name.localeCompare(b.language.name), + ); + + const languageSelect = ` + + ${languages + .map( + (language) => ` + + ${language.language.name} + `, + ) + .join("\n")} + + `; + + languageSwitch.innerHTML = languageSelect; + languageSwitch.firstElementChild.addEventListener("change", onSelectorSwitch); + } + else { + languageSwitch.remove(); + } + } + }); +} + +document.addEventListener("readthedocs-addons-data-ready", function (event) { + // Trigger the Read the Docs Addons Search modal when clicking on "Search docs" input from the topnav. + document + .querySelector("[role='search'] input") + .addEventListener("focusin", () => { + const event = new CustomEvent("readthedocs-search-show"); + document.dispatchEvent(event); + }); +}); \ No newline at end of file diff --git a/docs/pages/html/_static/language_data.js b/docs/pages/html/_static/language_data.js index 250f566..c7fe6c6 100644 --- a/docs/pages/html/_static/language_data.js +++ b/docs/pages/html/_static/language_data.js @@ -1,19 +1,12 @@ /* - * language_data.js - * ~~~~~~~~~~~~~~~~ - * * This script contains the language-specific data used by searchtools.js, * namely the list of stopwords, stemmer, scorer and splitter. - * - * :copyright: Copyright 2007-2023 by the Sphinx team, see AUTHORS. - * :license: BSD, see LICENSE for details. - * */ var stopwords = ["a", "and", "are", "as", "at", "be", "but", "by", "for", "if", "in", "into", "is", "it", "near", "no", "not", "of", "on", "or", "such", "that", "the", "their", "then", "there", "these", "they", "this", "to", "was", "will", "with"]; -/* Non-minified version is copied as a separate JS file, is available */ +/* Non-minified version is copied as a separate JS file, if available */ /** * Porter Stemmer diff --git a/docs/pages/html/_static/notebooks/pca_examples.html b/docs/pages/html/_static/notebooks/pca_examples.html index c9a75dc..7bb55a3 100644 --- a/docs/pages/html/_static/notebooks/pca_examples.html +++ b/docs/pages/html/_static/notebooks/pca_examples.html @@ -1,13 +1,9 @@ - - - + + + pca_examples - - - - - - - - - - - - - - + + + - - - - + void Promise.all([...diagrams].map(renderOneMarmaid)); + }); + + + + + + + - + pca A Python Package for Principal Component Analysis. The core of PCA is build on sklearn functionality to find maximum compatibility when combining with other packages. But this package can do a lot more. Besides the regular pca, it can also perform SparsePCA, and TruncatedSVD. Depending on your input data, the best approach will be choosen. Other functionalities are: @@ -15124,38 +7531,30 @@ github pca - - - + + -In [1]: +In [1]: - -!pip install pca + +!pip install pca - - - + - - - - - - - + + Requirement already satisfied: pca in /usr/local/lib/python3.7/dist-packages (1.7.2) Requirement already satisfied: matplotlib in /usr/local/lib/python3.7/dist-packages (from pca) (3.2.2) Requirement already satisfied: wget in /usr/local/lib/python3.7/dist-packages (from pca) (3.2) @@ -15180,179 +7579,149 @@ - - - - - + + - + Lets check the version - - - + + -In [2]: +In [2]: - -import pca + +import pca print(pca.__version__) - - - + - - - - - - - + + 1.7.2 - - - - - + + - + Import the pca library - - - + + -In [3]: +In [3]: - -from pca import pca + +from pca import pca import numpy as np import pandas as pd - - - - - + + + - + Here we will create a random dataset. - - - + + -In [4]: +In [4]: - -# Dataset + +# Dataset from sklearn.datasets import load_iris X = pd.DataFrame(data=load_iris().data, columns=load_iris().feature_names, index=load_iris().target) - - - - - + + + - + Initialize using specified parameters. The parameters here are the default parameters. - - - + + -In [5]: +In [5]: - -# Initialize + +# Initialize model = pca(n_components=3, normalize=True) - - - - - + + + -In [6]: +In [6]: - -# Fit transform + +# Fit transform out = model.fit_transform(X) - - - + - - - - - - - + + [pca] >Processing dataframe.. [pca] >Normalizing input data per feature (zero mean and unit variance).. [pca] >The PCA reduction is performed on the [4] columns of the input dataframe. @@ -15364,171 +7733,119 @@ - - - - - + + -In [7]: +In [7]: - -# Make plot with only the directions (no scatter) + +# Make plot with only the directions (no scatter) fig, ax = model.biplot(textlabel=True, legend=False, figsize=(10, 6)) - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 with loadings. - - - - - - - - + + + - - - - - - + + -In [8]: +In [8]: - -# Make plot with only the directions (no scatter) + +# Make plot with only the directions (no scatter) fig, ax = model.biplot(cmap=None, textlabel=False, legend=False, figsize=(10, 6)) - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 with loadings. - - - - - - - - + + + - - - - - - + + -In [9]: +In [9]: - -from pca import pca + +from pca import pca # Load example data from sklearn.datasets import load_iris X = pd.DataFrame(data=load_iris().data, columns=load_iris().feature_names, index=load_iris().target) - - - - - + + + -In [10]: +In [10]: - -# Initialize + +# Initialize model = pca(n_components=3) # Fit using PCA results = model.fit_transform(X) - - - + - - - - - - - + + [pca] >Processing dataframe.. [pca] >The PCA reduction is performed on the [4] columns of the input dataframe. [pca] >Fit using PCA. @@ -15539,20 +7856,17 @@ - - - - - + + -In [11]: +In [11]: - -# Make plots + +# Make plots # Scree plot fig, ax = model.plot(figsize=(10, 6)) @@ -15563,190 +7877,117 @@ # Biplot fig, ax = model.biplot(figsize=(10, 6)) - - - + - - - - - - - - - - + + + - - - - - - - - - + + + - - - - - - + + [pca] >Plot PC1 vs PC2 with loadings. - - - - - - - + + <Figure size 432x288 with 0 Axes> - - - - - - - - - + + + - - - - - - + + -In [17]: +In [17]: - -# Coloring on density to focus on the core samples. + +# Coloring on density to focus on the core samples. # Biplot -fig, ax = model.biplot(figsize=(10, 6), gradient='#ffffff') +fig, ax = model.biplot(figsize=(10, 6), gradient='#ffffff') - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 with loadings. - - - - - - - - + + + - - - - - - + + -In [18]: +In [18]: - -# Outliers are stored in results: -results['outliers'] + +# Outliers are stored in results: +results['outliers'] # Outliers based on T2 -print('--------T2------------') -print(results['outliers'].loc[results['outliers']['y_bool'], :]) +print('--------T2------------') +print(results['outliers'].loc[results['outliers']['y_bool'], :]) # Outliers based on SPE -print('--------SPE------------') -print(results['outliers'].loc[results['outliers']['y_bool_spe'], :]) +print('--------SPE------------') +print(results['outliers'].loc[results['outliers']['y_bool_spe'], :]) - - - + - - - - - - - + + --------T2------------ y_proba y_score y_bool y_bool_spe y_score_spe 2 0.040551 13.160880 True True 3.679935 @@ -15771,270 +8012,168 @@ - - - - - + + -In [20]: +In [20]: - -# Outlier detection + +# Outlier detection fig, ax = model.biplot(SPE=True, HT2=True, figsize=(10, 6)) - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 with loadings. - - - - - - - - + + + - - - - - - + + -In [21]: +In [21]: - -# 3D plots + +# 3D plots fig, ax = model.scatter3d(figsize=(10, 6)) fig, ax = model.biplot3d(figsize=(10, 6)) fig, ax = model.biplot3d(SPE=True, HT2=True, figsize=(10, 6)) - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 vs PC3 with loadings. - - - - - - - - + + + - - - - - - - - - + + + - - - - - - + + [pca] >Plot PC1 vs PC2 vs PC3 with loadings. - - - - - - - - + + + - - - - - - + + -In [22]: +In [22]: - -fig, ax = model.biplot3d(SPE=True, HT2=True, visible=False, figsize=(10, 6)) + +fig, ax = model.biplot3d(SPE=True, HT2=True, visible=False, figsize=(10, 6)) # Set the figure again to True and show the figure. fig.set_visible(True) fig - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 vs PC3 with loadings. - - Out[22]: - - - - - - +Out[22]: + + - - - - - - - - - + + + - - - - - - + + -In [23]: +In [23]: - -# Normalize out PCs + +
# Install from Pypi: +Pip install +# Install from Pypi: pip install pca -# Install directly from github +# Install directly from github pip install git+https://github.com/erdogant/pca -Uninstalling +Uninstalling Remove the environment with installation: -# List all the active environments. pca should be listed. +# List all the active environments. pca should be listed. conda env list -# Remove the pca environment +# Remove the pca environment conda env remove --name pca -# List all the active environments. pca should be absent. +# List all the active environments. pca should be absent. conda env list diff --git a/docs/pages/html/Outlier detection.html b/docs/pages/html/Outlier detection.html index 37bc204..fe764f4 100644 --- a/docs/pages/html/Outlier detection.html +++ b/docs/pages/html/Outlier detection.html @@ -1,20 +1,22 @@ + + - + - + Hotelling T2 — pca pca documentation - - - - + + + + - - - + + + + + @@ -33,9 +35,6 @@ pca - - 2.0.1 - @@ -134,7 +133,7 @@ -Hotelling T2 +Hotelling T2 To detect outliers across the multidimensional space of PCA, the hotellings T2 test is implemented. It works by computing the chi-square tests across the top n_components: default is PC1 to PC5. The reason for not using more PC’s is that it is expected that the highest variance (and thus the outliers) will be seen in the first few components. Going deeper into PC space may therefore not be required. Nevertheless, the depth is optional. The hotellings T2 test outputs a P-value matrix (samples x PCs), which are are subsequently combined using fishers method. This allows to determine outliers with its ranking (strongest to weak). The alpha parameter determines the detection of outliers (default: 0.05). @@ -192,7 +191,7 @@ Hotelling T2 -SPE/Dmodx +SPE/Dmodx Outlier can be detected using SPE/DmodX (distance to model) based on the mean and covariance of the first 2 dimensions of X. On the model plane (SPE ≈ 0). Note that the SPE or Hotelling’s T2 are complementary to each other. model.biplot(legend=True, SPE=True, HT2=True) @@ -204,7 +203,7 @@ SPE/Dmodx -Detected outliers +Detected outliers @@ -213,7 +212,7 @@ SPE/Dmodx -Selection of the Outliers +Selection of the Outliers Selecting the outliers can be usefull to remove them from the dataset or for deeper investigation. # Select the outliers Xoutliers = X[results['outliers']['y_bool'],:] @@ -224,7 +223,7 @@ Selection of the Outliers -Detect new unseen outliers +Detect new unseen outliers After fitting a model on the data, you may want to use the model in a later stage to detect outliers on unseen data. Detection of outliers is performed in the transform function and does not require any additional action. An example is shown in the code block below. # Import libraries @@ -252,7 +251,7 @@ Detect new unseen outliers -Detected outliers +Detected outliers @@ -288,7 +287,7 @@ Detect new unseen outliers -Detected outliers +Detected outliers @@ -296,7 +295,7 @@ Detect new unseen outliers -Detection of outliers without PCA +Detection of outliers without PCA If desired, the outliers can also be detected directly using the hotelling T2 and/or SPE/DmodX functionality. For demonstration purposes I use the PCs from the results but any other dataset would also work. import pca diff --git a/docs/pages/html/Plots.html b/docs/pages/html/Plots.html index c1677b6..f054370 100644 --- a/docs/pages/html/Plots.html +++ b/docs/pages/html/Plots.html @@ -1,20 +1,22 @@ + + - + - + Load dataset — pca pca documentation - - - - + + + + - - - + + + + + @@ -33,9 +35,6 @@ pca - - 2.0.1 - @@ -134,7 +133,7 @@ -Load dataset +Load dataset Let’s load the wine dataset to demonstrate the plots. # Load library from sklearn.datasets import load_wine @@ -166,7 +165,7 @@ Load dataset -Scatter plot +Scatter plot # Make scatterplot model.scatter() @@ -187,7 +186,7 @@ Scatter plot -Scatterplots +Scatterplots @@ -204,16 +203,40 @@ Scatter plot -Biplot +Biplot +The biplot draws the loadings (arrows) together with the samples (scatterplot). +The loadings can be colored red and blue which indicates the strength of the particular feature in the PC. +For each principal component (PC), the feature is determined with the largest absolute loading. This indicates which feature contributes the most to each PC and can occur in multiple PCs. +The highest loading values for the features are colored red in the biplot and described as “best” in the output dataframe. +The features that were not seen with highest loadings for any PC are considered weaker features, and are colored blue the biplot. In the output dataframe these features are described as “weak”. # Make biplot model.biplot() # Here again, many other options can be turned on and off model.biplot(SPE=True, HT2=True, legend=1) + +# Show the top features +results['topfeat'] + +# PC feature loading type +# 0 PC1 flavanoids 0.422934 best +# 1 PC2 color_intensity 0.529996 best +# 2 PC3 ash 0.626224 best +# 3 PC4 malic_acid 0.536890 best +# 4 PC5 magnesium 0.727049 best +# 5 PC6 malic_acid 0.536814 best +# 6 PC7 nonflavanoid_phenols 0.595447 best +# 7 PC8 hue 0.436624 best +# 8 PC9 proline 0.575786 best +# 9 PC10 od280/od315_of_diluted_wines 0.523706 best +# 10 PC9 alcohol -0.508619 weak +# 11 PC3 alcalinity_of_ash 0.612080 weak +# 12 PC8 total_phenols -0.405934 weak +# 13 PC6 proanthocyanins -0.533795 weak -Biplots +Biplots @@ -223,28 +246,30 @@ Biplot -Biplot (only arrows) +Biplot (only arrows) # Make plot with parameters: set cmap to None and label and legend to False. Only directions will be plotted. model.biplot(cmap=None, legend=False) - + + -Explained variance plot +Explained variance plot model.plot() - + + -Alpha Transparency +Alpha Transparency fig, ax = model.scatter(alpha=1) -Markers +Markers import numpy as np from sklearn.datasets import make_friedman1 from pca import pca @@ -272,7 +297,7 @@ Markers -Biplots with markers +Biplots with markers @@ -280,7 +305,7 @@ Markers -Control color/marker/size per sample +Control color/marker/size per sample import numpy as np import matplotlib.pyplot as plt import matplotlib.colors as mcolors @@ -329,7 +354,7 @@ Control color/marker/size per sample -Biplot with customized properties per sample. +Biplot with customized properties per sample. @@ -337,15 +362,16 @@ Control color/marker/size per sample -3D plots +3D plots All plots can also be created in 3D by setting the d3=True parameter. model.biplot3d() - + + -Toggle visible status +Toggle visible status The visible status for can be turned on and off. # Make plot but not visible. fig, ax = model.biplot(visible=False) diff --git a/docs/pages/html/_sources/Plots.rst.txt b/docs/pages/html/_sources/Plots.rst.txt index 33319b2..38cd2db 100644 --- a/docs/pages/html/_sources/Plots.rst.txt +++ b/docs/pages/html/_sources/Plots.rst.txt @@ -83,6 +83,14 @@ Scatter plot Biplot ############### +The biplot draws the loadings (arrows) together with the samples (scatterplot). +The loadings can be colored red and blue which indicates the strength of the particular feature in the PC. + +For each principal component (PC), the feature is determined with the largest absolute loading. This indicates which feature contributes the most to each PC and can occur in multiple PCs. +The highest loading values for the features are colored red in the biplot and described as "best" in the output dataframe. +The features that were not seen with highest loadings for any PC are considered weaker features, and are colored blue the biplot. In the output dataframe these features are described as "weak". + + .. code:: python # Make biplot @@ -91,6 +99,24 @@ Biplot # Here again, many other options can be turned on and off model.biplot(SPE=True, HT2=True, legend=1) + # Show the top features + results['topfeat'] + + # PC feature loading type + # 0 PC1 flavanoids 0.422934 best + # 1 PC2 color_intensity 0.529996 best + # 2 PC3 ash 0.626224 best + # 3 PC4 malic_acid 0.536890 best + # 4 PC5 magnesium 0.727049 best + # 5 PC6 malic_acid 0.536814 best + # 6 PC7 nonflavanoid_phenols 0.595447 best + # 7 PC8 hue 0.436624 best + # 8 PC9 proline 0.575786 best + # 9 PC10 od280/od315_of_diluted_wines 0.523706 best + # 10 PC9 alcohol -0.508619 weak + # 11 PC3 alcalinity_of_ash 0.612080 weak + # 12 PC8 total_phenols -0.405934 weak + # 13 PC6 proanthocyanins -0.533795 weak .. |figP5| image:: ../figs/wine_biplot.png .. |figP6| image:: ../figs/wine_biplot_with_outliers.png diff --git a/docs/pages/html/_sources/sponsor.rst.txt b/docs/pages/html/_sources/sponsor.rst.txt index a46c410..f006896 100644 --- a/docs/pages/html/_sources/sponsor.rst.txt +++ b/docs/pages/html/_sources/sponsor.rst.txt @@ -4,8 +4,10 @@ * Become a `Sponsor `_! * `Buy `_ me a coffee! I ❤️ coffee :) * `Donate `_ in Bitcoin. - * Follow me on medium! Go to my `medium profile `_ and press *follow*. + * Follow me on Medium! Go to my `medium profile `_ and press *follow*. + * Subscribe to me on Substack! Go to my `profile `_ where you can *subscribe*. * **Star** this repo at the github page. + * You can also buy a digital educational product over `here `_. * Other contributions can be in the form of feature requests, idea discussions, reporting bugs, opening pull requests. Cheers Mate. diff --git a/docs/pages/html/_static/_sphinx_javascript_frameworks_compat.js b/docs/pages/html/_static/_sphinx_javascript_frameworks_compat.js new file mode 100644 index 0000000..8141580 --- /dev/null +++ b/docs/pages/html/_static/_sphinx_javascript_frameworks_compat.js @@ -0,0 +1,123 @@ +/* Compatability shim for jQuery and underscores.js. + * + * Copyright Sphinx contributors + * Released under the two clause BSD licence + */ + +/** + * small helper function to urldecode strings + * + * See https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/decodeURIComponent#Decoding_query_parameters_from_a_URL + */ +jQuery.urldecode = function(x) { + if (!x) { + return x + } + return decodeURIComponent(x.replace(/\+/g, ' ')); +}; + +/** + * small helper function to urlencode strings + */ +jQuery.urlencode = encodeURIComponent; + +/** + * This function returns the parsed url parameters of the + * current request. Multiple values per key are supported, + * it will always return arrays of strings for the value parts. + */ +jQuery.getQueryParameters = function(s) { + if (typeof s === 'undefined') + s = document.location.search; + var parts = s.substr(s.indexOf('?') + 1).split('&'); + var result = {}; + for (var i = 0; i < parts.length; i++) { + var tmp = parts[i].split('=', 2); + var key = jQuery.urldecode(tmp[0]); + var value = jQuery.urldecode(tmp[1]); + if (key in result) + result[key].push(value); + else + result[key] = [value]; + } + return result; +}; + +/** + * highlight a given string on a jquery object by wrapping it in + * span elements with the given class name. + */ +jQuery.fn.highlightText = function(text, className) { + function highlight(node, addItems) { + if (node.nodeType === 3) { + var val = node.nodeValue; + var pos = val.toLowerCase().indexOf(text); + if (pos >= 0 && + !jQuery(node.parentNode).hasClass(className) && + !jQuery(node.parentNode).hasClass("nohighlight")) { + var span; + var isInSVG = jQuery(node).closest("body, svg, foreignObject").is("svg"); + if (isInSVG) { + span = document.createElementNS("http://www.w3.org/2000/svg", "tspan"); + } else { + span = document.createElement("span"); + span.className = className; + } + span.appendChild(document.createTextNode(val.substr(pos, text.length))); + node.parentNode.insertBefore(span, node.parentNode.insertBefore( + document.createTextNode(val.substr(pos + text.length)), + node.nextSibling)); + node.nodeValue = val.substr(0, pos); + if (isInSVG) { + var rect = document.createElementNS("http://www.w3.org/2000/svg", "rect"); + var bbox = node.parentElement.getBBox(); + rect.x.baseVal.value = bbox.x; + rect.y.baseVal.value = bbox.y; + rect.width.baseVal.value = bbox.width; + rect.height.baseVal.value = bbox.height; + rect.setAttribute('class', className); + addItems.push({ + "parent": node.parentNode, + "target": rect}); + } + } + } + else if (!jQuery(node).is("button, select, textarea")) { + jQuery.each(node.childNodes, function() { + highlight(this, addItems); + }); + } + } + var addItems = []; + var result = this.each(function() { + highlight(this, addItems); + }); + for (var i = 0; i < addItems.length; ++i) { + jQuery(addItems[i].parent).before(addItems[i].target); + } + return result; +}; + +/* + * backward compatibility for jQuery.browser + * This will be supported until firefox bug is fixed. + */ +if (!jQuery.browser) { + jQuery.uaMatch = function(ua) { + ua = ua.toLowerCase(); + + var match = /(chrome)[ \/]([\w.]+)/.exec(ua) || + /(webkit)[ \/]([\w.]+)/.exec(ua) || + /(opera)(?:.*version|)[ \/]([\w.]+)/.exec(ua) || + /(msie) ([\w.]+)/.exec(ua) || + ua.indexOf("compatible") < 0 && /(mozilla)(?:.*? rv:([\w.]+)|)/.exec(ua) || + []; + + return { + browser: match[ 1 ] || "", + version: match[ 2 ] || "0" + }; + }; + jQuery.browser = {}; + jQuery.browser[jQuery.uaMatch(navigator.userAgent).browser] = true; +} diff --git a/docs/pages/html/_static/basic.css b/docs/pages/html/_static/basic.css index 7577acb..7ebbd6d 100644 --- a/docs/pages/html/_static/basic.css +++ b/docs/pages/html/_static/basic.css @@ -1,12 +1,5 @@ /* - * basic.css - * ~~~~~~~~~ - * * Sphinx stylesheet -- basic theme. - * - * :copyright: Copyright 2007-2023 by the Sphinx team, see AUTHORS. - * :license: BSD, see LICENSE for details. - * */ /* -- main layout ----------------------------------------------------------- */ @@ -115,15 +108,11 @@ img { /* -- search page ----------------------------------------------------------- */ ul.search { - margin: 10px 0 0 20px; - padding: 0; + margin-top: 10px; } ul.search li { - padding: 5px 0 5px 20px; - background-image: url(file.png); - background-repeat: no-repeat; - background-position: 0 7px; + padding: 5px 0; } ul.search li a { @@ -237,6 +226,10 @@ a.headerlink { visibility: hidden; } +a:visited { + color: #551A8B; +} + h1:hover > a.headerlink, h2:hover > a.headerlink, h3:hover > a.headerlink, @@ -670,6 +663,16 @@ dd { margin-left: 30px; } +.sig dd { + margin-top: 0px; + margin-bottom: 0px; +} + +.sig dl { + margin-top: 0px; + margin-bottom: 0px; +} + dl > dd:last-child, dl > dd:last-child > :last-child { margin-bottom: 0; @@ -738,6 +741,14 @@ abbr, acronym { cursor: help; } +.translated { + background-color: rgba(207, 255, 207, 0.2) +} + +.untranslated { + background-color: rgba(255, 207, 207, 0.2) +} + /* -- code displays --------------------------------------------------------- */ pre { diff --git a/docs/pages/html/_static/css/badge_only.css b/docs/pages/html/_static/css/badge_only.css index c718cee..88ba55b 100644 --- a/docs/pages/html/_static/css/badge_only.css +++ b/docs/pages/html/_static/css/badge_only.css @@ -1 +1 @@ -.clearfix{*zoom:1}.clearfix:after,.clearfix:before{display:table;content:""}.clearfix:after{clear:both}@font-face{font-family:FontAwesome;font-style:normal;font-weight:400;src:url(fonts/fontawesome-webfont.eot?674f50d287a8c48dc19ba404d20fe713?#iefix) 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config.projects.current, + ); + languages = languages.sort((a, b) => + a.language.name.localeCompare(b.language.name), + ); + + const languageSelect = ` + + ${languages + .map( + (language) => ` + + ${language.language.name} + `, + ) + .join("\n")} + + `; + + languageSwitch.innerHTML = languageSelect; + languageSwitch.firstElementChild.addEventListener("change", onSelectorSwitch); + } + else { + languageSwitch.remove(); + } + } + }); +} + +document.addEventListener("readthedocs-addons-data-ready", function (event) { + // Trigger the Read the Docs Addons Search modal when clicking on "Search docs" input from the topnav. + document + .querySelector("[role='search'] input") + .addEventListener("focusin", () => { + const event = new CustomEvent("readthedocs-search-show"); + document.dispatchEvent(event); + }); +}); \ No newline at end of file diff --git a/docs/pages/html/_static/language_data.js b/docs/pages/html/_static/language_data.js index 250f566..c7fe6c6 100644 --- a/docs/pages/html/_static/language_data.js +++ b/docs/pages/html/_static/language_data.js @@ -1,19 +1,12 @@ /* - * language_data.js - * ~~~~~~~~~~~~~~~~ - * * This script contains the language-specific data used by searchtools.js, * namely the list of stopwords, stemmer, scorer and splitter. - * - * :copyright: Copyright 2007-2023 by the Sphinx team, see AUTHORS. - * :license: BSD, see LICENSE for details. - * */ var stopwords = ["a", "and", "are", "as", "at", "be", "but", "by", "for", "if", "in", "into", "is", "it", "near", "no", "not", "of", "on", "or", "such", "that", "the", "their", "then", "there", "these", "they", "this", "to", "was", "will", "with"]; -/* Non-minified version is copied as a separate JS file, is available */ +/* Non-minified version is copied as a separate JS file, if available */ /** * Porter Stemmer diff --git a/docs/pages/html/_static/notebooks/pca_examples.html b/docs/pages/html/_static/notebooks/pca_examples.html index c9a75dc..7bb55a3 100644 --- a/docs/pages/html/_static/notebooks/pca_examples.html +++ b/docs/pages/html/_static/notebooks/pca_examples.html @@ -1,13 +1,9 @@ - - - + + + pca_examples - - - - - - - - - - - - - - + + + - - - - + void Promise.all([...diagrams].map(renderOneMarmaid)); + }); + + + + + + + - + pca A Python Package for Principal Component Analysis. The core of PCA is build on sklearn functionality to find maximum compatibility when combining with other packages. But this package can do a lot more. Besides the regular pca, it can also perform SparsePCA, and TruncatedSVD. Depending on your input data, the best approach will be choosen. Other functionalities are: @@ -15124,38 +7531,30 @@ github pca - - - + + -In [1]: +In [1]: - -!pip install pca + +!pip install pca - - - + - - - - - - - + + Requirement already satisfied: pca in /usr/local/lib/python3.7/dist-packages (1.7.2) Requirement already satisfied: matplotlib in /usr/local/lib/python3.7/dist-packages (from pca) (3.2.2) Requirement already satisfied: wget in /usr/local/lib/python3.7/dist-packages (from pca) (3.2) @@ -15180,179 +7579,149 @@ - - - - - + + - + Lets check the version - - - + + -In [2]: +In [2]: - -import pca + +import pca print(pca.__version__) - - - + - - - - - - - + + 1.7.2 - - - - - + + - + Import the pca library - - - + + -In [3]: +In [3]: - -from pca import pca + +from pca import pca import numpy as np import pandas as pd - - - - - + + + - + Here we will create a random dataset. - - - + + -In [4]: +In [4]: - -# Dataset + +# Dataset from sklearn.datasets import load_iris X = pd.DataFrame(data=load_iris().data, columns=load_iris().feature_names, index=load_iris().target) - - - - - + + + - + Initialize using specified parameters. The parameters here are the default parameters. - - - + + -In [5]: +In [5]: - -# Initialize + +# Initialize model = pca(n_components=3, normalize=True) - - - - - + + + -In [6]: +In [6]: - -# Fit transform + +# Fit transform out = model.fit_transform(X) - - - + - - - - - - - + + [pca] >Processing dataframe.. [pca] >Normalizing input data per feature (zero mean and unit variance).. [pca] >The PCA reduction is performed on the [4] columns of the input dataframe. @@ -15364,171 +7733,119 @@ - - - - - + + -In [7]: +In [7]: - -# Make plot with only the directions (no scatter) + +# Make plot with only the directions (no scatter) fig, ax = model.biplot(textlabel=True, legend=False, figsize=(10, 6)) - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 with loadings. - - - - - - - - + + + - - - - - - + + -In [8]: +In [8]: - -# Make plot with only the directions (no scatter) + +# Make plot with only the directions (no scatter) fig, ax = model.biplot(cmap=None, textlabel=False, legend=False, figsize=(10, 6)) - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 with loadings. - - - - - - - - + + + - - - - - - + + -In [9]: +In [9]: - -from pca import pca + +from pca import pca # Load example data from sklearn.datasets import load_iris X = pd.DataFrame(data=load_iris().data, columns=load_iris().feature_names, index=load_iris().target) - - - - - + + + -In [10]: +In [10]: - -# Initialize + +# Initialize model = pca(n_components=3) # Fit using PCA results = model.fit_transform(X) - - - + - - - - - - - + + [pca] >Processing dataframe.. [pca] >The PCA reduction is performed on the [4] columns of the input dataframe. [pca] >Fit using PCA. @@ -15539,20 +7856,17 @@ - - - - - + + -In [11]: +In [11]: - -# Make plots + +# Make plots # Scree plot fig, ax = model.plot(figsize=(10, 6)) @@ -15563,190 +7877,117 @@ # Biplot fig, ax = model.biplot(figsize=(10, 6)) - - - + - - - - - - - - - - + + + - - - - - - - - - + + + - - - - - - + + [pca] >Plot PC1 vs PC2 with loadings. - - - - - - - + + <Figure size 432x288 with 0 Axes> - - - - - - - - - + + + - - - - - - + + -In [17]: +In [17]: - -# Coloring on density to focus on the core samples. + +# Coloring on density to focus on the core samples. # Biplot -fig, ax = model.biplot(figsize=(10, 6), gradient='#ffffff') +fig, ax = model.biplot(figsize=(10, 6), gradient='#ffffff') - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 with loadings. - - - - - - - - + + + - - - - - - + + -In [18]: +In [18]: - -# Outliers are stored in results: -results['outliers'] + +# Outliers are stored in results: +results['outliers'] # Outliers based on T2 -print('--------T2------------') -print(results['outliers'].loc[results['outliers']['y_bool'], :]) +print('--------T2------------') +print(results['outliers'].loc[results['outliers']['y_bool'], :]) # Outliers based on SPE -print('--------SPE------------') -print(results['outliers'].loc[results['outliers']['y_bool_spe'], :]) +print('--------SPE------------') +print(results['outliers'].loc[results['outliers']['y_bool_spe'], :]) - - - + - - - - - - - + + --------T2------------ y_proba y_score y_bool y_bool_spe y_score_spe 2 0.040551 13.160880 True True 3.679935 @@ -15771,270 +8012,168 @@ - - - - - + + -In [20]: +In [20]: - -# Outlier detection + +# Outlier detection fig, ax = model.biplot(SPE=True, HT2=True, figsize=(10, 6)) - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 with loadings. - - - - - - - - + + + - - - - - - + + -In [21]: +In [21]: - -# 3D plots + +# 3D plots fig, ax = model.scatter3d(figsize=(10, 6)) fig, ax = model.biplot3d(figsize=(10, 6)) fig, ax = model.biplot3d(SPE=True, HT2=True, figsize=(10, 6)) - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 vs PC3 with loadings. - - - - - - - - + + + - - - - - - - - - + + + - - - - - - + + [pca] >Plot PC1 vs PC2 vs PC3 with loadings. - - - - - - - - + + + - - - - - - + + -In [22]: +In [22]: - -fig, ax = model.biplot3d(SPE=True, HT2=True, visible=False, figsize=(10, 6)) + +fig, ax = model.biplot3d(SPE=True, HT2=True, visible=False, figsize=(10, 6)) # Set the figure again to True and show the figure. fig.set_visible(True) fig - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 vs PC3 with loadings. - - Out[22]: - - - - - - +Out[22]: + + - - - - - - - - - + + + - - - - - - + + -In [23]: +In [23]: - -# Normalize out PCs + +
# Install from Pypi: pip install pca -# Install directly from github +# Install directly from github pip install git+https://github.com/erdogant/pca
Remove the environment with installation:
# List all the active environments. pca should be listed. +# List all the active environments. pca should be listed. conda env list -# Remove the pca environment +# Remove the pca environment conda env remove --name pca -# List all the active environments. pca should be absent. +# List all the active environments. pca should be absent. conda env list diff --git a/docs/pages/html/Outlier detection.html b/docs/pages/html/Outlier detection.html index 37bc204..fe764f4 100644 --- a/docs/pages/html/Outlier detection.html +++ b/docs/pages/html/Outlier detection.html @@ -1,20 +1,22 @@ + + - + - + Hotelling T2 — pca pca documentation - - - - + + + + - - - + + + + + @@ -33,9 +35,6 @@ pca - - 2.0.1 - @@ -134,7 +133,7 @@ -Hotelling T2 +Hotelling T2 To detect outliers across the multidimensional space of PCA, the hotellings T2 test is implemented. It works by computing the chi-square tests across the top n_components: default is PC1 to PC5. The reason for not using more PC’s is that it is expected that the highest variance (and thus the outliers) will be seen in the first few components. Going deeper into PC space may therefore not be required. Nevertheless, the depth is optional. The hotellings T2 test outputs a P-value matrix (samples x PCs), which are are subsequently combined using fishers method. This allows to determine outliers with its ranking (strongest to weak). The alpha parameter determines the detection of outliers (default: 0.05). @@ -192,7 +191,7 @@ Hotelling T2 -SPE/Dmodx +SPE/Dmodx Outlier can be detected using SPE/DmodX (distance to model) based on the mean and covariance of the first 2 dimensions of X. On the model plane (SPE ≈ 0). Note that the SPE or Hotelling’s T2 are complementary to each other. model.biplot(legend=True, SPE=True, HT2=True) @@ -204,7 +203,7 @@ SPE/Dmodx -Detected outliers +Detected outliers @@ -213,7 +212,7 @@ SPE/Dmodx -Selection of the Outliers +Selection of the Outliers Selecting the outliers can be usefull to remove them from the dataset or for deeper investigation. # Select the outliers Xoutliers = X[results['outliers']['y_bool'],:] @@ -224,7 +223,7 @@ Selection of the Outliers -Detect new unseen outliers +Detect new unseen outliers After fitting a model on the data, you may want to use the model in a later stage to detect outliers on unseen data. Detection of outliers is performed in the transform function and does not require any additional action. An example is shown in the code block below. # Import libraries @@ -252,7 +251,7 @@ Detect new unseen outliers -Detected outliers +Detected outliers @@ -288,7 +287,7 @@ Detect new unseen outliers -Detected outliers +Detected outliers @@ -296,7 +295,7 @@ Detect new unseen outliers -Detection of outliers without PCA +Detection of outliers without PCA If desired, the outliers can also be detected directly using the hotelling T2 and/or SPE/DmodX functionality. For demonstration purposes I use the PCs from the results but any other dataset would also work. import pca diff --git a/docs/pages/html/Plots.html b/docs/pages/html/Plots.html index c1677b6..f054370 100644 --- a/docs/pages/html/Plots.html +++ b/docs/pages/html/Plots.html @@ -1,20 +1,22 @@ + + - + - + Load dataset — pca pca documentation - - - - + + + + - - - + + + + + @@ -33,9 +35,6 @@ pca - - 2.0.1 - @@ -134,7 +133,7 @@ -Load dataset +Load dataset Let’s load the wine dataset to demonstrate the plots. # Load library from sklearn.datasets import load_wine @@ -166,7 +165,7 @@ Load dataset -Scatter plot +Scatter plot # Make scatterplot model.scatter() @@ -187,7 +186,7 @@ Scatter plot -Scatterplots +Scatterplots @@ -204,16 +203,40 @@ Scatter plot -Biplot +Biplot +The biplot draws the loadings (arrows) together with the samples (scatterplot). +The loadings can be colored red and blue which indicates the strength of the particular feature in the PC. +For each principal component (PC), the feature is determined with the largest absolute loading. This indicates which feature contributes the most to each PC and can occur in multiple PCs. +The highest loading values for the features are colored red in the biplot and described as “best” in the output dataframe. +The features that were not seen with highest loadings for any PC are considered weaker features, and are colored blue the biplot. In the output dataframe these features are described as “weak”. # Make biplot model.biplot() # Here again, many other options can be turned on and off model.biplot(SPE=True, HT2=True, legend=1) + +# Show the top features +results['topfeat'] + +# PC feature loading type +# 0 PC1 flavanoids 0.422934 best +# 1 PC2 color_intensity 0.529996 best +# 2 PC3 ash 0.626224 best +# 3 PC4 malic_acid 0.536890 best +# 4 PC5 magnesium 0.727049 best +# 5 PC6 malic_acid 0.536814 best +# 6 PC7 nonflavanoid_phenols 0.595447 best +# 7 PC8 hue 0.436624 best +# 8 PC9 proline 0.575786 best +# 9 PC10 od280/od315_of_diluted_wines 0.523706 best +# 10 PC9 alcohol -0.508619 weak +# 11 PC3 alcalinity_of_ash 0.612080 weak +# 12 PC8 total_phenols -0.405934 weak +# 13 PC6 proanthocyanins -0.533795 weak -Biplots +Biplots @@ -223,28 +246,30 @@ Biplot -Biplot (only arrows) +Biplot (only arrows) # Make plot with parameters: set cmap to None and label and legend to False. Only directions will be plotted. model.biplot(cmap=None, legend=False) - + + -Explained variance plot +Explained variance plot model.plot() - + + -Alpha Transparency +Alpha Transparency fig, ax = model.scatter(alpha=1) -Markers +Markers import numpy as np from sklearn.datasets import make_friedman1 from pca import pca @@ -272,7 +297,7 @@ Markers -Biplots with markers +Biplots with markers @@ -280,7 +305,7 @@ Markers -Control color/marker/size per sample +Control color/marker/size per sample import numpy as np import matplotlib.pyplot as plt import matplotlib.colors as mcolors @@ -329,7 +354,7 @@ Control color/marker/size per sample -Biplot with customized properties per sample. +Biplot with customized properties per sample. @@ -337,15 +362,16 @@ Control color/marker/size per sample -3D plots +3D plots All plots can also be created in 3D by setting the d3=True parameter. model.biplot3d() - + + -Toggle visible status +Toggle visible status The visible status for can be turned on and off. # Make plot but not visible. fig, ax = model.biplot(visible=False) diff --git a/docs/pages/html/_sources/Plots.rst.txt b/docs/pages/html/_sources/Plots.rst.txt index 33319b2..38cd2db 100644 --- a/docs/pages/html/_sources/Plots.rst.txt +++ b/docs/pages/html/_sources/Plots.rst.txt @@ -83,6 +83,14 @@ Scatter plot Biplot ############### +The biplot draws the loadings (arrows) together with the samples (scatterplot). +The loadings can be colored red and blue which indicates the strength of the particular feature in the PC. + +For each principal component (PC), the feature is determined with the largest absolute loading. This indicates which feature contributes the most to each PC and can occur in multiple PCs. +The highest loading values for the features are colored red in the biplot and described as "best" in the output dataframe. +The features that were not seen with highest loadings for any PC are considered weaker features, and are colored blue the biplot. In the output dataframe these features are described as "weak". + + .. code:: python # Make biplot @@ -91,6 +99,24 @@ Biplot # Here again, many other options can be turned on and off model.biplot(SPE=True, HT2=True, legend=1) + # Show the top features + results['topfeat'] + + # PC feature loading type + # 0 PC1 flavanoids 0.422934 best + # 1 PC2 color_intensity 0.529996 best + # 2 PC3 ash 0.626224 best + # 3 PC4 malic_acid 0.536890 best + # 4 PC5 magnesium 0.727049 best + # 5 PC6 malic_acid 0.536814 best + # 6 PC7 nonflavanoid_phenols 0.595447 best + # 7 PC8 hue 0.436624 best + # 8 PC9 proline 0.575786 best + # 9 PC10 od280/od315_of_diluted_wines 0.523706 best + # 10 PC9 alcohol -0.508619 weak + # 11 PC3 alcalinity_of_ash 0.612080 weak + # 12 PC8 total_phenols -0.405934 weak + # 13 PC6 proanthocyanins -0.533795 weak .. |figP5| image:: ../figs/wine_biplot.png .. |figP6| image:: ../figs/wine_biplot_with_outliers.png diff --git a/docs/pages/html/_sources/sponsor.rst.txt b/docs/pages/html/_sources/sponsor.rst.txt index a46c410..f006896 100644 --- a/docs/pages/html/_sources/sponsor.rst.txt +++ b/docs/pages/html/_sources/sponsor.rst.txt @@ -4,8 +4,10 @@ * Become a `Sponsor `_! * `Buy `_ me a coffee! I ❤️ coffee :) * `Donate `_ in Bitcoin. - * Follow me on medium! Go to my `medium profile `_ and press *follow*. + * Follow me on Medium! Go to my `medium profile `_ and press *follow*. + * Subscribe to me on Substack! Go to my `profile `_ where you can *subscribe*. * **Star** this repo at the github page. + * You can also buy a digital educational product over `here `_. * Other contributions can be in the form of feature requests, idea discussions, reporting bugs, opening pull requests. Cheers Mate. diff --git a/docs/pages/html/_static/_sphinx_javascript_frameworks_compat.js b/docs/pages/html/_static/_sphinx_javascript_frameworks_compat.js new file mode 100644 index 0000000..8141580 --- /dev/null +++ b/docs/pages/html/_static/_sphinx_javascript_frameworks_compat.js @@ -0,0 +1,123 @@ +/* Compatability shim for jQuery and underscores.js. + * + * Copyright Sphinx contributors + * Released under the two clause BSD licence + */ + +/** + * small helper function to urldecode strings + * + * See https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/decodeURIComponent#Decoding_query_parameters_from_a_URL + */ +jQuery.urldecode = function(x) { + if (!x) { + return x + } + return decodeURIComponent(x.replace(/\+/g, ' ')); +}; + +/** + * small helper function to urlencode strings + */ +jQuery.urlencode = encodeURIComponent; + +/** + * This function returns the parsed url parameters of the + * current request. Multiple values per key are supported, + * it will always return arrays of strings for the value parts. + */ +jQuery.getQueryParameters = function(s) { + if (typeof s === 'undefined') + s = document.location.search; + var parts = s.substr(s.indexOf('?') + 1).split('&'); + var result = {}; + for (var i = 0; i < parts.length; i++) { + var tmp = parts[i].split('=', 2); + var key = jQuery.urldecode(tmp[0]); + var value = jQuery.urldecode(tmp[1]); + if (key in result) + result[key].push(value); + else + result[key] = [value]; + } + return result; +}; + +/** + * highlight a given string on a jquery object by wrapping it in + * span elements with the given class name. + */ +jQuery.fn.highlightText = function(text, className) { + function highlight(node, addItems) { + if (node.nodeType === 3) { + var val = node.nodeValue; + var pos = val.toLowerCase().indexOf(text); + if (pos >= 0 && + !jQuery(node.parentNode).hasClass(className) && + !jQuery(node.parentNode).hasClass("nohighlight")) { + var span; + var isInSVG = jQuery(node).closest("body, svg, foreignObject").is("svg"); + if (isInSVG) { + span = document.createElementNS("http://www.w3.org/2000/svg", "tspan"); + } else { + span = document.createElement("span"); + span.className = className; + } + span.appendChild(document.createTextNode(val.substr(pos, text.length))); + node.parentNode.insertBefore(span, node.parentNode.insertBefore( + document.createTextNode(val.substr(pos + text.length)), + node.nextSibling)); + node.nodeValue = val.substr(0, pos); + if (isInSVG) { + var rect = document.createElementNS("http://www.w3.org/2000/svg", "rect"); + var bbox = node.parentElement.getBBox(); + rect.x.baseVal.value = bbox.x; + rect.y.baseVal.value = bbox.y; + rect.width.baseVal.value = bbox.width; + rect.height.baseVal.value = bbox.height; + rect.setAttribute('class', className); + addItems.push({ + "parent": node.parentNode, + "target": rect}); + } + } + } + else if (!jQuery(node).is("button, select, textarea")) { + jQuery.each(node.childNodes, function() { + highlight(this, addItems); + }); + } + } + var addItems = []; + var result = this.each(function() { + highlight(this, addItems); + }); + for (var i = 0; i < addItems.length; ++i) { + jQuery(addItems[i].parent).before(addItems[i].target); + } + return result; +}; + +/* + * backward compatibility for jQuery.browser + * This will be supported until firefox bug is fixed. + */ +if (!jQuery.browser) { + jQuery.uaMatch = function(ua) { + ua = ua.toLowerCase(); + + var match = /(chrome)[ \/]([\w.]+)/.exec(ua) || + /(webkit)[ \/]([\w.]+)/.exec(ua) || + /(opera)(?:.*version|)[ \/]([\w.]+)/.exec(ua) || + /(msie) ([\w.]+)/.exec(ua) || + ua.indexOf("compatible") < 0 && /(mozilla)(?:.*? rv:([\w.]+)|)/.exec(ua) || + []; + + return { + browser: match[ 1 ] || "", + version: match[ 2 ] || "0" + }; + }; + jQuery.browser = {}; + jQuery.browser[jQuery.uaMatch(navigator.userAgent).browser] = true; +} diff --git a/docs/pages/html/_static/basic.css b/docs/pages/html/_static/basic.css index 7577acb..7ebbd6d 100644 --- a/docs/pages/html/_static/basic.css +++ b/docs/pages/html/_static/basic.css @@ -1,12 +1,5 @@ /* - * basic.css - * ~~~~~~~~~ - * * Sphinx stylesheet -- basic theme. - * - * :copyright: Copyright 2007-2023 by the Sphinx team, see AUTHORS. - * :license: BSD, see LICENSE for details. - * */ /* -- main layout ----------------------------------------------------------- */ @@ -115,15 +108,11 @@ img { /* -- search page ----------------------------------------------------------- */ ul.search { - margin: 10px 0 0 20px; - padding: 0; + margin-top: 10px; } ul.search li { - padding: 5px 0 5px 20px; - background-image: url(file.png); - background-repeat: no-repeat; - background-position: 0 7px; + padding: 5px 0; } ul.search li a { @@ -237,6 +226,10 @@ a.headerlink { visibility: hidden; } +a:visited { + color: #551A8B; +} + h1:hover > a.headerlink, h2:hover > a.headerlink, h3:hover > a.headerlink, @@ -670,6 +663,16 @@ dd { 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video",version:m,shivCSS:n.shivCSS!==!1,supportsUnknownElements:l,shivMethods:n.shivMethods!==!1,type:"default",shivDocument:j,createElement:g,createDocumentFragment:h,addElements:e};a.html5=t,j(b),"object"==typeof module&&module.exports&&(module.exports=t)}("undefined"!=typeof window?window:this,document); \ No newline at end of file diff --git a/docs/pages/html/_static/js/versions.js b/docs/pages/html/_static/js/versions.js new file mode 100644 index 0000000..4958195 --- /dev/null +++ b/docs/pages/html/_static/js/versions.js @@ -0,0 +1,228 @@ +const themeFlyoutDisplay = "hidden"; +const themeVersionSelector = true; +const themeLanguageSelector = true; + +if (themeFlyoutDisplay === "attached") { + function renderLanguages(config) { + if (!config.projects.translations.length) { + return ""; + } + + // Insert the current language to the options on the selector + let languages = config.projects.translations.concat(config.projects.current); + languages = languages.sort((a, b) => 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{ + const config = event.detail.data(); + + const flyout = ` + + + Read the Docs + v: ${config.versions.current.slug} + + + + + ${renderLanguages(config)} + ${renderVersions(config)} + ${renderDownloads(config)} + + On Read the Docs + + Project Home + + + Builds + + + Downloads + + + + Search + + + + + + + + + Hosted by Read the Docs + + + + `; + + // Inject the generated flyout into the body HTML element. + document.body.insertAdjacentHTML("beforeend", flyout); + + // Trigger the Read the Docs Addons Search modal when clicking on the "Search docs" input from inside the flyout. + document + .querySelector("#flyout-search-form") + .addEventListener("focusin", () => { + const event = new CustomEvent("readthedocs-search-show"); + document.dispatchEvent(event); + }); + }) +} + +if (themeLanguageSelector || themeVersionSelector) { + function onSelectorSwitch(event) { + const option = event.target.selectedIndex; + const item = event.target.options[option]; + window.location.href = item.dataset.url; + } + + document.addEventListener("readthedocs-addons-data-ready", function (event) { + const config = event.detail.data(); + + const versionSwitch = document.querySelector( + "div.switch-menus > div.version-switch", + ); + if (themeVersionSelector) { + let versions = config.versions.active; + if (config.versions.current.hidden || config.versions.current.type === "external") { + versions.unshift(config.versions.current); + } + const versionSelect = ` + + ${versions + .map( + (version) => ` + + ${version.slug} + `, + ) + .join("\n")} + + `; + + versionSwitch.innerHTML = versionSelect; + versionSwitch.firstElementChild.addEventListener("change", onSelectorSwitch); + } + + const languageSwitch = document.querySelector( + "div.switch-menus > div.language-switch", + ); + + if (themeLanguageSelector) { + if (config.projects.translations.length) { + // Add the current language to the options on the selector + let languages = config.projects.translations.concat( + config.projects.current, + ); + languages = languages.sort((a, b) => + a.language.name.localeCompare(b.language.name), + ); + + const languageSelect = ` + + ${languages + .map( + (language) => ` + + ${language.language.name} + `, + ) + .join("\n")} + + `; + + languageSwitch.innerHTML = languageSelect; + languageSwitch.firstElementChild.addEventListener("change", onSelectorSwitch); + } + else { + languageSwitch.remove(); + } + } + }); +} + +document.addEventListener("readthedocs-addons-data-ready", function (event) { + // Trigger the Read the Docs Addons Search modal when clicking on "Search docs" input from the topnav. + document + .querySelector("[role='search'] input") + .addEventListener("focusin", () => { + const event = new CustomEvent("readthedocs-search-show"); + document.dispatchEvent(event); + }); +}); \ No newline at end of file diff --git a/docs/pages/html/_static/language_data.js b/docs/pages/html/_static/language_data.js index 250f566..c7fe6c6 100644 --- a/docs/pages/html/_static/language_data.js +++ b/docs/pages/html/_static/language_data.js @@ -1,19 +1,12 @@ /* - * language_data.js - * ~~~~~~~~~~~~~~~~ - * * This script contains the language-specific data used by searchtools.js, * namely the list of stopwords, stemmer, scorer and splitter. - * - * :copyright: Copyright 2007-2023 by the Sphinx team, see AUTHORS. - * :license: BSD, see LICENSE for details. - * */ var stopwords = ["a", "and", "are", "as", "at", "be", "but", "by", "for", "if", "in", "into", "is", "it", "near", "no", "not", "of", "on", "or", "such", "that", "the", "their", "then", "there", "these", "they", "this", "to", "was", "will", "with"]; -/* Non-minified version is copied as a separate JS file, is available */ +/* Non-minified version is copied as a separate JS file, if available */ /** * Porter Stemmer diff --git a/docs/pages/html/_static/notebooks/pca_examples.html b/docs/pages/html/_static/notebooks/pca_examples.html index c9a75dc..7bb55a3 100644 --- a/docs/pages/html/_static/notebooks/pca_examples.html +++ b/docs/pages/html/_static/notebooks/pca_examples.html @@ -1,13 +1,9 @@ - - - + + + pca_examples - - - - - - - - - - - - - - + + + - - - - + void Promise.all([...diagrams].map(renderOneMarmaid)); + }); + + + + + + + - + pca A Python Package for Principal Component Analysis. The core of PCA is build on sklearn functionality to find maximum compatibility when combining with other packages. But this package can do a lot more. Besides the regular pca, it can also perform SparsePCA, and TruncatedSVD. Depending on your input data, the best approach will be choosen. Other functionalities are: @@ -15124,38 +7531,30 @@ github pca - - - + + -In [1]: +In [1]: - -!pip install pca + +!pip install pca - - - + - - - - - - - + + Requirement already satisfied: pca in /usr/local/lib/python3.7/dist-packages (1.7.2) Requirement already satisfied: matplotlib in /usr/local/lib/python3.7/dist-packages (from pca) (3.2.2) Requirement already satisfied: wget in /usr/local/lib/python3.7/dist-packages (from pca) (3.2) @@ -15180,179 +7579,149 @@ - - - - - + + - + Lets check the version - - - + + -In [2]: +In [2]: - -import pca + +import pca print(pca.__version__) - - - + - - - - - - - + + 1.7.2 - - - - - + + - + Import the pca library - - - + + -In [3]: +In [3]: - -from pca import pca + +from pca import pca import numpy as np import pandas as pd - - - - - + + + - + Here we will create a random dataset. - - - + + -In [4]: +In [4]: - -# Dataset + +# Dataset from sklearn.datasets import load_iris X = pd.DataFrame(data=load_iris().data, columns=load_iris().feature_names, index=load_iris().target) - - - - - + + + - + Initialize using specified parameters. The parameters here are the default parameters. - - - + + -In [5]: +In [5]: - -# Initialize + +# Initialize model = pca(n_components=3, normalize=True) - - - - - + + + -In [6]: +In [6]: - -# Fit transform + +# Fit transform out = model.fit_transform(X) - - - + - - - - - - - + + [pca] >Processing dataframe.. [pca] >Normalizing input data per feature (zero mean and unit variance).. [pca] >The PCA reduction is performed on the [4] columns of the input dataframe. @@ -15364,171 +7733,119 @@ - - - - - + + -In [7]: +In [7]: - -# Make plot with only the directions (no scatter) + +# Make plot with only the directions (no scatter) fig, ax = model.biplot(textlabel=True, legend=False, figsize=(10, 6)) - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 with loadings. - - - - - - - - + + + - - - - - - + + -In [8]: +In [8]: - -# Make plot with only the directions (no scatter) + +# Make plot with only the directions (no scatter) fig, ax = model.biplot(cmap=None, textlabel=False, legend=False, figsize=(10, 6)) - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 with loadings. - - - - - - - - + + + - - - - - - + + -In [9]: +In [9]: - -from pca import pca + +from pca import pca # Load example data from sklearn.datasets import load_iris X = pd.DataFrame(data=load_iris().data, columns=load_iris().feature_names, index=load_iris().target) - - - - - + + + -In [10]: +In [10]: - -# Initialize + +# Initialize model = pca(n_components=3) # Fit using PCA results = model.fit_transform(X) - - - + - - - - - - - + + [pca] >Processing dataframe.. [pca] >The PCA reduction is performed on the [4] columns of the input dataframe. [pca] >Fit using PCA. @@ -15539,20 +7856,17 @@ - - - - - + + -In [11]: +In [11]: - -# Make plots + +# Make plots # Scree plot fig, ax = model.plot(figsize=(10, 6)) @@ -15563,190 +7877,117 @@ # Biplot fig, ax = model.biplot(figsize=(10, 6)) - - - + - - - - - - - - - - + + + - - - - - - - - - + + + - - - - - - + + [pca] >Plot PC1 vs PC2 with loadings. - - - - - - - + + <Figure size 432x288 with 0 Axes> - - - - - - - - - + + + - - - - - - + + -In [17]: +In [17]: - -# Coloring on density to focus on the core samples. + +# Coloring on density to focus on the core samples. # Biplot -fig, ax = model.biplot(figsize=(10, 6), gradient='#ffffff') +fig, ax = model.biplot(figsize=(10, 6), gradient='#ffffff') - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 with loadings. - - - - - - - - + + + - - - - - - + + -In [18]: +In [18]: - -# Outliers are stored in results: -results['outliers'] + +# Outliers are stored in results: +results['outliers'] # Outliers based on T2 -print('--------T2------------') -print(results['outliers'].loc[results['outliers']['y_bool'], :]) +print('--------T2------------') +print(results['outliers'].loc[results['outliers']['y_bool'], :]) # Outliers based on SPE -print('--------SPE------------') -print(results['outliers'].loc[results['outliers']['y_bool_spe'], :]) +print('--------SPE------------') +print(results['outliers'].loc[results['outliers']['y_bool_spe'], :]) - - - + - - - - - - - + + --------T2------------ y_proba y_score y_bool y_bool_spe y_score_spe 2 0.040551 13.160880 True True 3.679935 @@ -15771,270 +8012,168 @@ - - - - - + + -In [20]: +In [20]: - -# Outlier detection + +# Outlier detection fig, ax = model.biplot(SPE=True, HT2=True, figsize=(10, 6)) - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 with loadings. - - - - - - - - + + + - - - - - - + + -In [21]: +In [21]: - -# 3D plots + +# 3D plots fig, ax = model.scatter3d(figsize=(10, 6)) fig, ax = model.biplot3d(figsize=(10, 6)) fig, ax = model.biplot3d(SPE=True, HT2=True, figsize=(10, 6)) - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 vs PC3 with loadings. - - - - - - - - + + + - - - - - - - - - + + + - - - - - - + + [pca] >Plot PC1 vs PC2 vs PC3 with loadings. - - - - - - - - + + + - - - - - - + + -In [22]: +In [22]: - -fig, ax = model.biplot3d(SPE=True, HT2=True, visible=False, figsize=(10, 6)) + +fig, ax = model.biplot3d(SPE=True, HT2=True, visible=False, figsize=(10, 6)) # Set the figure again to True and show the figure. fig.set_visible(True) fig - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 vs PC3 with loadings. - - Out[22]: - - - - - - +Out[22]: + + - - - - - - - - - + + + - - - - - - + + -In [23]: +In [23]: - -# Normalize out PCs + +
# List all the active environments. pca should be listed. conda env list -# Remove the pca environment +# Remove the pca environment conda env remove --name pca -# List all the active environments. pca should be absent. +# List all the active environments. pca should be absent. conda env list
To detect outliers across the multidimensional space of PCA, the hotellings T2 test is implemented. It works by computing the chi-square tests across the top n_components: default is PC1 to PC5. The reason for not using more PC’s is that it is expected that the highest variance (and thus the outliers) will be seen in the first few components. Going deeper into PC space may therefore not be required. Nevertheless, the depth is optional.
The hotellings T2 test outputs a P-value matrix (samples x PCs), which are are subsequently combined using fishers method. This allows to determine outliers with its ranking (strongest to weak). The alpha parameter determines the detection of outliers (default: 0.05).
Outlier can be detected using SPE/DmodX (distance to model) based on the mean and covariance of the first 2 dimensions of X. On the model plane (SPE ≈ 0). Note that the SPE or Hotelling’s T2 are complementary to each other.
model.biplot(legend=True, SPE=True, HT2=True) @@ -204,7 +203,7 @@ SPE/Dmodx -Detected outliers +Detected outliers @@ -213,7 +212,7 @@ SPE/Dmodx -Selection of the Outliers +Selection of the Outliers Selecting the outliers can be usefull to remove them from the dataset or for deeper investigation. # Select the outliers Xoutliers = X[results['outliers']['y_bool'],:] @@ -224,7 +223,7 @@ Selection of the Outliers -Detect new unseen outliers +Detect new unseen outliers After fitting a model on the data, you may want to use the model in a later stage to detect outliers on unseen data. Detection of outliers is performed in the transform function and does not require any additional action. An example is shown in the code block below. # Import libraries @@ -252,7 +251,7 @@ Detect new unseen outliers -Detected outliers +Detected outliers @@ -288,7 +287,7 @@ Detect new unseen outliers -Detected outliers +Detected outliers @@ -296,7 +295,7 @@ Detect new unseen outliers -Detection of outliers without PCA +Detection of outliers without PCA If desired, the outliers can also be detected directly using the hotelling T2 and/or SPE/DmodX functionality. For demonstration purposes I use the PCs from the results but any other dataset would also work. import pca diff --git a/docs/pages/html/Plots.html b/docs/pages/html/Plots.html index c1677b6..f054370 100644 --- a/docs/pages/html/Plots.html +++ b/docs/pages/html/Plots.html @@ -1,20 +1,22 @@ + + - + - + Load dataset — pca pca documentation - - - - + + + + - - - + + + + + @@ -33,9 +35,6 @@ pca - - 2.0.1 - @@ -134,7 +133,7 @@ -Load dataset +Load dataset Let’s load the wine dataset to demonstrate the plots. # Load library from sklearn.datasets import load_wine @@ -166,7 +165,7 @@ Load dataset -Scatter plot +Scatter plot # Make scatterplot model.scatter() @@ -187,7 +186,7 @@ Scatter plot -Scatterplots +Scatterplots @@ -204,16 +203,40 @@ Scatter plot -Biplot +Biplot +The biplot draws the loadings (arrows) together with the samples (scatterplot). +The loadings can be colored red and blue which indicates the strength of the particular feature in the PC. +For each principal component (PC), the feature is determined with the largest absolute loading. This indicates which feature contributes the most to each PC and can occur in multiple PCs. +The highest loading values for the features are colored red in the biplot and described as “best” in the output dataframe. +The features that were not seen with highest loadings for any PC are considered weaker features, and are colored blue the biplot. In the output dataframe these features are described as “weak”. # Make biplot model.biplot() # Here again, many other options can be turned on and off model.biplot(SPE=True, HT2=True, legend=1) + +# Show the top features +results['topfeat'] + +# PC feature loading type +# 0 PC1 flavanoids 0.422934 best +# 1 PC2 color_intensity 0.529996 best +# 2 PC3 ash 0.626224 best +# 3 PC4 malic_acid 0.536890 best +# 4 PC5 magnesium 0.727049 best +# 5 PC6 malic_acid 0.536814 best +# 6 PC7 nonflavanoid_phenols 0.595447 best +# 7 PC8 hue 0.436624 best +# 8 PC9 proline 0.575786 best +# 9 PC10 od280/od315_of_diluted_wines 0.523706 best +# 10 PC9 alcohol -0.508619 weak +# 11 PC3 alcalinity_of_ash 0.612080 weak +# 12 PC8 total_phenols -0.405934 weak +# 13 PC6 proanthocyanins -0.533795 weak -Biplots +Biplots @@ -223,28 +246,30 @@ Biplot -Biplot (only arrows) +Biplot (only arrows) # Make plot with parameters: set cmap to None and label and legend to False. Only directions will be plotted. model.biplot(cmap=None, legend=False) - + + -Explained variance plot +Explained variance plot model.plot() - + + -Alpha Transparency +Alpha Transparency fig, ax = model.scatter(alpha=1) -Markers +Markers import numpy as np from sklearn.datasets import make_friedman1 from pca import pca @@ -272,7 +297,7 @@ Markers -Biplots with markers +Biplots with markers @@ -280,7 +305,7 @@ Markers -Control color/marker/size per sample +Control color/marker/size per sample import numpy as np import matplotlib.pyplot as plt import matplotlib.colors as mcolors @@ -329,7 +354,7 @@ Control color/marker/size per sample -Biplot with customized properties per sample. +Biplot with customized properties per sample. @@ -337,15 +362,16 @@ Control color/marker/size per sample -3D plots +3D plots All plots can also be created in 3D by setting the d3=True parameter. model.biplot3d() - + + -Toggle visible status +Toggle visible status The visible status for can be turned on and off. # Make plot but not visible. fig, ax = model.biplot(visible=False) diff --git a/docs/pages/html/_sources/Plots.rst.txt b/docs/pages/html/_sources/Plots.rst.txt index 33319b2..38cd2db 100644 --- a/docs/pages/html/_sources/Plots.rst.txt +++ b/docs/pages/html/_sources/Plots.rst.txt @@ -83,6 +83,14 @@ Scatter plot Biplot ############### +The biplot draws the loadings (arrows) together with the samples (scatterplot). +The loadings can be colored red and blue which indicates the strength of the particular feature in the PC. + +For each principal component (PC), the feature is determined with the largest absolute loading. This indicates which feature contributes the most to each PC and can occur in multiple PCs. +The highest loading values for the features are colored red in the biplot and described as "best" in the output dataframe. +The features that were not seen with highest loadings for any PC are considered weaker features, and are colored blue the biplot. In the output dataframe these features are described as "weak". + + .. code:: python # Make biplot @@ -91,6 +99,24 @@ Biplot # Here again, many other options can be turned on and off model.biplot(SPE=True, HT2=True, legend=1) + # Show the top features + results['topfeat'] + + # PC feature loading type + # 0 PC1 flavanoids 0.422934 best + # 1 PC2 color_intensity 0.529996 best + # 2 PC3 ash 0.626224 best + # 3 PC4 malic_acid 0.536890 best + # 4 PC5 magnesium 0.727049 best + # 5 PC6 malic_acid 0.536814 best + # 6 PC7 nonflavanoid_phenols 0.595447 best + # 7 PC8 hue 0.436624 best + # 8 PC9 proline 0.575786 best + # 9 PC10 od280/od315_of_diluted_wines 0.523706 best + # 10 PC9 alcohol -0.508619 weak + # 11 PC3 alcalinity_of_ash 0.612080 weak + # 12 PC8 total_phenols -0.405934 weak + # 13 PC6 proanthocyanins -0.533795 weak .. |figP5| image:: ../figs/wine_biplot.png .. |figP6| image:: ../figs/wine_biplot_with_outliers.png diff --git a/docs/pages/html/_sources/sponsor.rst.txt b/docs/pages/html/_sources/sponsor.rst.txt index a46c410..f006896 100644 --- a/docs/pages/html/_sources/sponsor.rst.txt +++ b/docs/pages/html/_sources/sponsor.rst.txt @@ -4,8 +4,10 @@ * Become a `Sponsor `_! * `Buy `_ me a coffee! I ❤️ coffee :) * `Donate `_ in Bitcoin. - * Follow me on medium! Go to my `medium profile `_ and press *follow*. + * Follow me on Medium! Go to my `medium profile `_ and press *follow*. + * Subscribe to me on Substack! Go to my `profile `_ where you can *subscribe*. * **Star** this repo at the github page. + * You can also buy a digital educational product over `here `_. * Other contributions can be in the form of feature requests, idea discussions, reporting bugs, opening pull requests. Cheers Mate. diff --git a/docs/pages/html/_static/_sphinx_javascript_frameworks_compat.js b/docs/pages/html/_static/_sphinx_javascript_frameworks_compat.js new file mode 100644 index 0000000..8141580 --- /dev/null +++ b/docs/pages/html/_static/_sphinx_javascript_frameworks_compat.js @@ -0,0 +1,123 @@ +/* Compatability shim for jQuery and underscores.js. + * + * Copyright Sphinx contributors + * Released under the two clause BSD licence + */ + +/** + * small helper function to urldecode strings + * + * See https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/decodeURIComponent#Decoding_query_parameters_from_a_URL + */ +jQuery.urldecode = function(x) { + if (!x) { + return x + } + return decodeURIComponent(x.replace(/\+/g, ' ')); +}; + +/** + * small helper function to urlencode strings + */ +jQuery.urlencode = encodeURIComponent; + +/** + * This function returns the parsed url parameters of the + * current request. Multiple values per key are supported, + * it will always return arrays of strings for the value parts. + */ +jQuery.getQueryParameters = function(s) { + if (typeof s === 'undefined') + s = document.location.search; + var parts = s.substr(s.indexOf('?') + 1).split('&'); + var result = {}; + for (var i = 0; i < parts.length; i++) { + var tmp = parts[i].split('=', 2); + var key = jQuery.urldecode(tmp[0]); + var value = jQuery.urldecode(tmp[1]); + if (key in result) + result[key].push(value); + else + result[key] = [value]; + } + return result; +}; + +/** + * highlight a given string on a jquery object by wrapping it in + * span elements with the given class name. + */ +jQuery.fn.highlightText = function(text, className) { + function highlight(node, addItems) { + if (node.nodeType === 3) { + var val = node.nodeValue; + var pos = val.toLowerCase().indexOf(text); + if (pos >= 0 && + !jQuery(node.parentNode).hasClass(className) && + !jQuery(node.parentNode).hasClass("nohighlight")) { + var span; + var isInSVG = jQuery(node).closest("body, svg, foreignObject").is("svg"); + if (isInSVG) { + span = document.createElementNS("http://www.w3.org/2000/svg", "tspan"); + } else { + span = document.createElement("span"); + span.className = className; + } + span.appendChild(document.createTextNode(val.substr(pos, text.length))); + node.parentNode.insertBefore(span, node.parentNode.insertBefore( + document.createTextNode(val.substr(pos + text.length)), + node.nextSibling)); + node.nodeValue = val.substr(0, pos); + if (isInSVG) { + var rect = document.createElementNS("http://www.w3.org/2000/svg", "rect"); + var bbox = node.parentElement.getBBox(); + rect.x.baseVal.value = bbox.x; + rect.y.baseVal.value = bbox.y; + rect.width.baseVal.value = bbox.width; + rect.height.baseVal.value = bbox.height; + rect.setAttribute('class', className); + addItems.push({ + "parent": node.parentNode, + "target": rect}); + } + } + } + else if (!jQuery(node).is("button, select, textarea")) { + jQuery.each(node.childNodes, function() { + highlight(this, addItems); + }); + } + } + var addItems = []; + var result = this.each(function() { + highlight(this, addItems); + }); + for (var i = 0; i < addItems.length; ++i) { + jQuery(addItems[i].parent).before(addItems[i].target); + } + return result; +}; + +/* + * backward compatibility for jQuery.browser + * This will be supported until firefox bug is fixed. + */ +if (!jQuery.browser) { + jQuery.uaMatch = function(ua) { + ua = ua.toLowerCase(); + + var match = /(chrome)[ \/]([\w.]+)/.exec(ua) || + /(webkit)[ \/]([\w.]+)/.exec(ua) || + /(opera)(?:.*version|)[ \/]([\w.]+)/.exec(ua) || + /(msie) ([\w.]+)/.exec(ua) || + ua.indexOf("compatible") < 0 && /(mozilla)(?:.*? rv:([\w.]+)|)/.exec(ua) || + []; + + return { + browser: match[ 1 ] || "", + version: match[ 2 ] || "0" + }; + }; + jQuery.browser = {}; + jQuery.browser[jQuery.uaMatch(navigator.userAgent).browser] = true; +} diff --git a/docs/pages/html/_static/basic.css b/docs/pages/html/_static/basic.css index 7577acb..7ebbd6d 100644 --- a/docs/pages/html/_static/basic.css +++ b/docs/pages/html/_static/basic.css @@ -1,12 +1,5 @@ /* - * basic.css - * ~~~~~~~~~ - * * Sphinx stylesheet -- basic theme. - * - * :copyright: Copyright 2007-2023 by the Sphinx team, see AUTHORS. - * :license: BSD, see LICENSE for details. - * */ /* -- main layout ----------------------------------------------------------- */ @@ -115,15 +108,11 @@ img { /* -- search page ----------------------------------------------------------- */ ul.search { - margin: 10px 0 0 20px; - padding: 0; + margin-top: 10px; } ul.search li { - padding: 5px 0 5px 20px; - background-image: url(file.png); - background-repeat: no-repeat; - background-position: 0 7px; + padding: 5px 0; } ul.search li a { @@ -237,6 +226,10 @@ a.headerlink { visibility: hidden; } +a:visited { + color: #551A8B; +} + h1:hover > a.headerlink, h2:hover > a.headerlink, h3:hover > a.headerlink, @@ -670,6 +663,16 @@ dd { margin-left: 30px; } +.sig dd { + margin-top: 0px; + margin-bottom: 0px; +} + +.sig dl { + margin-top: 0px; + margin-bottom: 0px; +} + dl > dd:last-child, dl > dd:last-child > :last-child { margin-bottom: 0; @@ -738,6 +741,14 @@ abbr, acronym { cursor: help; } +.translated { + background-color: rgba(207, 255, 207, 0.2) +} + +.untranslated { + background-color: rgba(255, 207, 207, 0.2) +} + /* -- code displays --------------------------------------------------------- */ pre { diff --git a/docs/pages/html/_static/css/badge_only.css b/docs/pages/html/_static/css/badge_only.css index c718cee..88ba55b 100644 --- a/docs/pages/html/_static/css/badge_only.css +++ b/docs/pages/html/_static/css/badge_only.css @@ -1 +1 @@ -.clearfix{*zoom:1}.clearfix:after,.clearfix:before{display:table;content:""}.clearfix:after{clear:both}@font-face{font-family:FontAwesome;font-style:normal;font-weight:400;src:url(fonts/fontawesome-webfont.eot?674f50d287a8c48dc19ba404d20fe713?#iefix) 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{ + const config = event.detail.data(); + + const flyout = ` + + + Read the Docs + v: ${config.versions.current.slug} + + + + + ${renderLanguages(config)} + ${renderVersions(config)} + ${renderDownloads(config)} + + On Read the Docs + + Project Home + + + Builds + + + Downloads + + + + Search + + + + + + + + + Hosted by Read the Docs + + + + `; + + // Inject the generated flyout into the body HTML element. + document.body.insertAdjacentHTML("beforeend", flyout); + + // Trigger the Read the Docs Addons Search modal when clicking on the "Search docs" input from inside the flyout. + document + .querySelector("#flyout-search-form") + .addEventListener("focusin", () => { + const event = new CustomEvent("readthedocs-search-show"); + document.dispatchEvent(event); + }); + }) +} + +if (themeLanguageSelector || themeVersionSelector) { + function onSelectorSwitch(event) { + const option = event.target.selectedIndex; + const item = event.target.options[option]; + window.location.href = 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config.projects.current, + ); + languages = languages.sort((a, b) => + a.language.name.localeCompare(b.language.name), + ); + + const languageSelect = ` + + ${languages + .map( + (language) => ` + + ${language.language.name} + `, + ) + .join("\n")} + + `; + + languageSwitch.innerHTML = languageSelect; + languageSwitch.firstElementChild.addEventListener("change", onSelectorSwitch); + } + else { + languageSwitch.remove(); + } + } + }); +} + +document.addEventListener("readthedocs-addons-data-ready", function (event) { + // Trigger the Read the Docs Addons Search modal when clicking on "Search docs" input from the topnav. + document + .querySelector("[role='search'] input") + .addEventListener("focusin", () => { + const event = new CustomEvent("readthedocs-search-show"); + document.dispatchEvent(event); + }); +}); \ No newline at end of file diff --git a/docs/pages/html/_static/language_data.js b/docs/pages/html/_static/language_data.js index 250f566..c7fe6c6 100644 --- a/docs/pages/html/_static/language_data.js +++ b/docs/pages/html/_static/language_data.js @@ -1,19 +1,12 @@ /* - * language_data.js - * ~~~~~~~~~~~~~~~~ - * * This script contains the language-specific data used by searchtools.js, * namely the list of stopwords, stemmer, scorer and splitter. - * - * :copyright: Copyright 2007-2023 by the Sphinx team, see AUTHORS. - * :license: BSD, see LICENSE for details. - * */ var stopwords = ["a", "and", "are", "as", "at", "be", "but", "by", "for", "if", "in", "into", "is", "it", "near", "no", "not", "of", "on", "or", "such", "that", "the", "their", "then", "there", "these", "they", "this", "to", "was", "will", "with"]; -/* Non-minified version is copied as a separate JS file, is available */ +/* Non-minified version is copied as a separate JS file, if available */ /** * Porter Stemmer diff --git a/docs/pages/html/_static/notebooks/pca_examples.html b/docs/pages/html/_static/notebooks/pca_examples.html index c9a75dc..7bb55a3 100644 --- a/docs/pages/html/_static/notebooks/pca_examples.html +++ b/docs/pages/html/_static/notebooks/pca_examples.html @@ -1,13 +1,9 @@ - - - + + + pca_examples - - - - - - - - - - - - - - + + + - - - - + void Promise.all([...diagrams].map(renderOneMarmaid)); + }); + + + + + + + - + pca A Python Package for Principal Component Analysis. The core of PCA is build on sklearn functionality to find maximum compatibility when combining with other packages. But this package can do a lot more. Besides the regular pca, it can also perform SparsePCA, and TruncatedSVD. Depending on your input data, the best approach will be choosen. Other functionalities are: @@ -15124,38 +7531,30 @@ github pca - - - + + -In [1]: +In [1]: - -!pip install pca + +!pip install pca - - - + - - - - - - - + + Requirement already satisfied: pca in /usr/local/lib/python3.7/dist-packages (1.7.2) Requirement already satisfied: matplotlib in /usr/local/lib/python3.7/dist-packages (from pca) (3.2.2) Requirement already satisfied: wget in /usr/local/lib/python3.7/dist-packages (from pca) (3.2) @@ -15180,179 +7579,149 @@ - - - - - + + - + Lets check the version - - - + + -In [2]: +In [2]: - -import pca + +import pca print(pca.__version__) - - - + - - - - - - - + + 1.7.2 - - - - - + + - + Import the pca library - - - + + -In [3]: +In [3]: - -from pca import pca + +from pca import pca import numpy as np import pandas as pd - - - - - + + + - + Here we will create a random dataset. - - - + + -In [4]: +In [4]: - -# Dataset + +# Dataset from sklearn.datasets import load_iris X = pd.DataFrame(data=load_iris().data, columns=load_iris().feature_names, index=load_iris().target) - - - - - + + + - + Initialize using specified parameters. The parameters here are the default parameters. - - - + + -In [5]: +In [5]: - -# Initialize + +# Initialize model = pca(n_components=3, normalize=True) - - - - - + + + -In [6]: +In [6]: - -# Fit transform + +# Fit transform out = model.fit_transform(X) - - - + - - - - - - - + + [pca] >Processing dataframe.. [pca] >Normalizing input data per feature (zero mean and unit variance).. [pca] >The PCA reduction is performed on the [4] columns of the input dataframe. @@ -15364,171 +7733,119 @@ - - - - - + + -In [7]: +In [7]: - -# Make plot with only the directions (no scatter) + +# Make plot with only the directions (no scatter) fig, ax = model.biplot(textlabel=True, legend=False, figsize=(10, 6)) - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 with loadings. - - - - - - - - + + + - - - - - - + + -In [8]: +In [8]: - -# Make plot with only the directions (no scatter) + +# Make plot with only the directions (no scatter) fig, ax = model.biplot(cmap=None, textlabel=False, legend=False, figsize=(10, 6)) - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 with loadings. - - - - - - - - + + + - - - - - - + + -In [9]: +In [9]: - -from pca import pca + +from pca import pca # Load example data from sklearn.datasets import load_iris X = pd.DataFrame(data=load_iris().data, columns=load_iris().feature_names, index=load_iris().target) - - - - - + + + -In [10]: +In [10]: - -# Initialize + +# Initialize model = pca(n_components=3) # Fit using PCA results = model.fit_transform(X) - - - + - - - - - - - + + [pca] >Processing dataframe.. [pca] >The PCA reduction is performed on the [4] columns of the input dataframe. [pca] >Fit using PCA. @@ -15539,20 +7856,17 @@ - - - - - + + -In [11]: +In [11]: - -# Make plots + +# Make plots # Scree plot fig, ax = model.plot(figsize=(10, 6)) @@ -15563,190 +7877,117 @@ # Biplot fig, ax = model.biplot(figsize=(10, 6)) - - - + - - - - - - - - - - + + + - - - - - - - - - + + + - - - - - - + + [pca] >Plot PC1 vs PC2 with loadings. - - - - - - - + + <Figure size 432x288 with 0 Axes> - - - - - - - - - + + + - - - - - - + + -In [17]: +In [17]: - -# Coloring on density to focus on the core samples. + +# Coloring on density to focus on the core samples. # Biplot -fig, ax = model.biplot(figsize=(10, 6), gradient='#ffffff') +fig, ax = model.biplot(figsize=(10, 6), gradient='#ffffff') - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 with loadings. - - - - - - - - + + + - - - - - - + + -In [18]: +In [18]: - -# Outliers are stored in results: -results['outliers'] + +# Outliers are stored in results: +results['outliers'] # Outliers based on T2 -print('--------T2------------') -print(results['outliers'].loc[results['outliers']['y_bool'], :]) +print('--------T2------------') +print(results['outliers'].loc[results['outliers']['y_bool'], :]) # Outliers based on SPE -print('--------SPE------------') -print(results['outliers'].loc[results['outliers']['y_bool_spe'], :]) +print('--------SPE------------') +print(results['outliers'].loc[results['outliers']['y_bool_spe'], :]) - - - + - - - - - - - + + --------T2------------ y_proba y_score y_bool y_bool_spe y_score_spe 2 0.040551 13.160880 True True 3.679935 @@ -15771,270 +8012,168 @@ - - - - - + + -In [20]: +In [20]: - -# Outlier detection + +# Outlier detection fig, ax = model.biplot(SPE=True, HT2=True, figsize=(10, 6)) - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 with loadings. - - - - - - - - + + + - - - - - - + + -In [21]: +In [21]: - -# 3D plots + +# 3D plots fig, ax = model.scatter3d(figsize=(10, 6)) fig, ax = model.biplot3d(figsize=(10, 6)) fig, ax = model.biplot3d(SPE=True, HT2=True, figsize=(10, 6)) - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 vs PC3 with loadings. - - - - - - - - + + + - - - - - - - - - + + + - - - - - - + + [pca] >Plot PC1 vs PC2 vs PC3 with loadings. - - - - - - - - + + + - - - - - - + + -In [22]: +In [22]: - -fig, ax = model.biplot3d(SPE=True, HT2=True, visible=False, figsize=(10, 6)) + +fig, ax = model.biplot3d(SPE=True, HT2=True, visible=False, figsize=(10, 6)) # Set the figure again to True and show the figure. fig.set_visible(True) fig - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 vs PC3 with loadings. - - Out[22]: - - - - - - +Out[22]: + + - - - - - - - - - + + + - - - - - - + + -In [23]: +In [23]: - -# Normalize out PCs + +
Selecting the outliers can be usefull to remove them from the dataset or for deeper investigation.
# Select the outliers Xoutliers = X[results['outliers']['y_bool'],:] @@ -224,7 +223,7 @@ Selection of the Outliers -Detect new unseen outliers +Detect new unseen outliers After fitting a model on the data, you may want to use the model in a later stage to detect outliers on unseen data. Detection of outliers is performed in the transform function and does not require any additional action. An example is shown in the code block below. # Import libraries @@ -252,7 +251,7 @@ Detect new unseen outliers -Detected outliers +Detected outliers @@ -288,7 +287,7 @@ Detect new unseen outliers -Detected outliers +Detected outliers @@ -296,7 +295,7 @@ Detect new unseen outliers -Detection of outliers without PCA +Detection of outliers without PCA If desired, the outliers can also be detected directly using the hotelling T2 and/or SPE/DmodX functionality. For demonstration purposes I use the PCs from the results but any other dataset would also work. import pca diff --git a/docs/pages/html/Plots.html b/docs/pages/html/Plots.html index c1677b6..f054370 100644 --- a/docs/pages/html/Plots.html +++ b/docs/pages/html/Plots.html @@ -1,20 +1,22 @@ + + - + - + Load dataset — pca pca documentation - - - - + + + + - - - + + + + + @@ -33,9 +35,6 @@ pca - - 2.0.1 - @@ -134,7 +133,7 @@ -Load dataset +Load dataset Let’s load the wine dataset to demonstrate the plots. # Load library from sklearn.datasets import load_wine @@ -166,7 +165,7 @@ Load dataset -Scatter plot +Scatter plot # Make scatterplot model.scatter() @@ -187,7 +186,7 @@ Scatter plot -Scatterplots +Scatterplots @@ -204,16 +203,40 @@ Scatter plot -Biplot +Biplot +The biplot draws the loadings (arrows) together with the samples (scatterplot). +The loadings can be colored red and blue which indicates the strength of the particular feature in the PC. +For each principal component (PC), the feature is determined with the largest absolute loading. This indicates which feature contributes the most to each PC and can occur in multiple PCs. +The highest loading values for the features are colored red in the biplot and described as “best” in the output dataframe. +The features that were not seen with highest loadings for any PC are considered weaker features, and are colored blue the biplot. In the output dataframe these features are described as “weak”. # Make biplot model.biplot() # Here again, many other options can be turned on and off model.biplot(SPE=True, HT2=True, legend=1) + +# Show the top features +results['topfeat'] + +# PC feature loading type +# 0 PC1 flavanoids 0.422934 best +# 1 PC2 color_intensity 0.529996 best +# 2 PC3 ash 0.626224 best +# 3 PC4 malic_acid 0.536890 best +# 4 PC5 magnesium 0.727049 best +# 5 PC6 malic_acid 0.536814 best +# 6 PC7 nonflavanoid_phenols 0.595447 best +# 7 PC8 hue 0.436624 best +# 8 PC9 proline 0.575786 best +# 9 PC10 od280/od315_of_diluted_wines 0.523706 best +# 10 PC9 alcohol -0.508619 weak +# 11 PC3 alcalinity_of_ash 0.612080 weak +# 12 PC8 total_phenols -0.405934 weak +# 13 PC6 proanthocyanins -0.533795 weak -Biplots +Biplots @@ -223,28 +246,30 @@ Biplot -Biplot (only arrows) +Biplot (only arrows) # Make plot with parameters: set cmap to None and label and legend to False. Only directions will be plotted. model.biplot(cmap=None, legend=False) - + + -Explained variance plot +Explained variance plot model.plot() - + + -Alpha Transparency +Alpha Transparency fig, ax = model.scatter(alpha=1) -Markers +Markers import numpy as np from sklearn.datasets import make_friedman1 from pca import pca @@ -272,7 +297,7 @@ Markers -Biplots with markers +Biplots with markers @@ -280,7 +305,7 @@ Markers -Control color/marker/size per sample +Control color/marker/size per sample import numpy as np import matplotlib.pyplot as plt import matplotlib.colors as mcolors @@ -329,7 +354,7 @@ Control color/marker/size per sample -Biplot with customized properties per sample. +Biplot with customized properties per sample. @@ -337,15 +362,16 @@ Control color/marker/size per sample -3D plots +3D plots All plots can also be created in 3D by setting the d3=True parameter. model.biplot3d() - + + -Toggle visible status +Toggle visible status The visible status for can be turned on and off. # Make plot but not visible. fig, ax = model.biplot(visible=False) diff --git a/docs/pages/html/_sources/Plots.rst.txt b/docs/pages/html/_sources/Plots.rst.txt index 33319b2..38cd2db 100644 --- a/docs/pages/html/_sources/Plots.rst.txt +++ b/docs/pages/html/_sources/Plots.rst.txt @@ -83,6 +83,14 @@ Scatter plot Biplot ############### +The biplot draws the loadings (arrows) together with the samples (scatterplot). +The loadings can be colored red and blue which indicates the strength of the particular feature in the PC. + +For each principal component (PC), the feature is determined with the largest absolute loading. This indicates which feature contributes the most to each PC and can occur in multiple PCs. +The highest loading values for the features are colored red in the biplot and described as "best" in the output dataframe. +The features that were not seen with highest loadings for any PC are considered weaker features, and are colored blue the biplot. In the output dataframe these features are described as "weak". + + .. code:: python # Make biplot @@ -91,6 +99,24 @@ Biplot # Here again, many other options can be turned on and off model.biplot(SPE=True, HT2=True, legend=1) + # Show the top features + results['topfeat'] + + # PC feature loading type + # 0 PC1 flavanoids 0.422934 best + # 1 PC2 color_intensity 0.529996 best + # 2 PC3 ash 0.626224 best + # 3 PC4 malic_acid 0.536890 best + # 4 PC5 magnesium 0.727049 best + # 5 PC6 malic_acid 0.536814 best + # 6 PC7 nonflavanoid_phenols 0.595447 best + # 7 PC8 hue 0.436624 best + # 8 PC9 proline 0.575786 best + # 9 PC10 od280/od315_of_diluted_wines 0.523706 best + # 10 PC9 alcohol -0.508619 weak + # 11 PC3 alcalinity_of_ash 0.612080 weak + # 12 PC8 total_phenols -0.405934 weak + # 13 PC6 proanthocyanins -0.533795 weak .. |figP5| image:: ../figs/wine_biplot.png .. |figP6| image:: ../figs/wine_biplot_with_outliers.png diff --git a/docs/pages/html/_sources/sponsor.rst.txt b/docs/pages/html/_sources/sponsor.rst.txt index a46c410..f006896 100644 --- a/docs/pages/html/_sources/sponsor.rst.txt +++ b/docs/pages/html/_sources/sponsor.rst.txt @@ -4,8 +4,10 @@ * Become a `Sponsor `_! * `Buy `_ me a coffee! I ❤️ coffee :) * `Donate `_ in Bitcoin. - * Follow me on medium! Go to my `medium profile `_ and press *follow*. + * Follow me on Medium! Go to my `medium profile `_ and press *follow*. + * Subscribe to me on Substack! Go to my `profile `_ where you can *subscribe*. * **Star** this repo at the github page. + * You can also buy a digital educational product over `here `_. * Other contributions can be in the form of feature requests, idea discussions, reporting bugs, opening pull requests. Cheers Mate. diff --git a/docs/pages/html/_static/_sphinx_javascript_frameworks_compat.js b/docs/pages/html/_static/_sphinx_javascript_frameworks_compat.js new file mode 100644 index 0000000..8141580 --- /dev/null +++ b/docs/pages/html/_static/_sphinx_javascript_frameworks_compat.js @@ -0,0 +1,123 @@ +/* Compatability shim for jQuery and underscores.js. + * + * Copyright Sphinx contributors + * Released under the two clause BSD licence + */ + +/** + * small helper function to urldecode strings + * + * See https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/decodeURIComponent#Decoding_query_parameters_from_a_URL + */ +jQuery.urldecode = function(x) { + if (!x) { + return x + } + return decodeURIComponent(x.replace(/\+/g, ' ')); +}; + +/** + * small helper function to urlencode strings + */ +jQuery.urlencode = encodeURIComponent; + +/** + * This function returns the parsed url parameters of the + * current request. Multiple values per key are supported, + * it will always return arrays of strings for the value parts. + */ +jQuery.getQueryParameters = function(s) { + if (typeof s === 'undefined') + s = document.location.search; + var parts = s.substr(s.indexOf('?') + 1).split('&'); + var result = {}; + for (var i = 0; i < parts.length; i++) { + var tmp = parts[i].split('=', 2); + var key = jQuery.urldecode(tmp[0]); + var value = jQuery.urldecode(tmp[1]); + if (key in result) + result[key].push(value); + else + result[key] = [value]; + } + return result; +}; + +/** + * highlight a given string on a jquery object by wrapping it in + * span elements with the given class name. + */ +jQuery.fn.highlightText = function(text, className) { + function highlight(node, addItems) { + if (node.nodeType === 3) { + var val = node.nodeValue; + var pos = val.toLowerCase().indexOf(text); + if (pos >= 0 && + !jQuery(node.parentNode).hasClass(className) && + !jQuery(node.parentNode).hasClass("nohighlight")) { + var span; + var isInSVG = jQuery(node).closest("body, svg, foreignObject").is("svg"); + if (isInSVG) { + span = document.createElementNS("http://www.w3.org/2000/svg", "tspan"); + } else { + span = document.createElement("span"); + span.className = className; + } + span.appendChild(document.createTextNode(val.substr(pos, text.length))); + node.parentNode.insertBefore(span, node.parentNode.insertBefore( + document.createTextNode(val.substr(pos + text.length)), + node.nextSibling)); + node.nodeValue = val.substr(0, pos); + if (isInSVG) { + var rect = document.createElementNS("http://www.w3.org/2000/svg", "rect"); + var bbox = node.parentElement.getBBox(); + rect.x.baseVal.value = bbox.x; + rect.y.baseVal.value = bbox.y; + rect.width.baseVal.value = bbox.width; + rect.height.baseVal.value = bbox.height; + rect.setAttribute('class', className); + addItems.push({ + "parent": node.parentNode, + "target": rect}); + } + } + } + else if (!jQuery(node).is("button, select, textarea")) { + jQuery.each(node.childNodes, function() { + highlight(this, addItems); + }); + } + } + var addItems = []; + var result = this.each(function() { + highlight(this, addItems); + }); + for (var i = 0; i < addItems.length; ++i) { + jQuery(addItems[i].parent).before(addItems[i].target); + } + return result; +}; + +/* + * backward compatibility for jQuery.browser + * This will be supported until firefox bug is fixed. + */ +if (!jQuery.browser) { + jQuery.uaMatch = function(ua) { + ua = ua.toLowerCase(); + + var match = /(chrome)[ \/]([\w.]+)/.exec(ua) || + /(webkit)[ \/]([\w.]+)/.exec(ua) || + /(opera)(?:.*version|)[ \/]([\w.]+)/.exec(ua) || + /(msie) ([\w.]+)/.exec(ua) || + ua.indexOf("compatible") < 0 && /(mozilla)(?:.*? rv:([\w.]+)|)/.exec(ua) || + []; + + return { + browser: match[ 1 ] || "", + version: match[ 2 ] || "0" + }; + }; + jQuery.browser = {}; + jQuery.browser[jQuery.uaMatch(navigator.userAgent).browser] = true; +} diff --git a/docs/pages/html/_static/basic.css b/docs/pages/html/_static/basic.css index 7577acb..7ebbd6d 100644 --- a/docs/pages/html/_static/basic.css +++ b/docs/pages/html/_static/basic.css @@ -1,12 +1,5 @@ /* - * basic.css - * ~~~~~~~~~ - * * Sphinx stylesheet -- basic theme. - * - * :copyright: Copyright 2007-2023 by the Sphinx team, see AUTHORS. - * :license: BSD, see LICENSE for details. - * */ /* -- main layout ----------------------------------------------------------- */ @@ -115,15 +108,11 @@ img { /* -- search page ----------------------------------------------------------- */ ul.search { - margin: 10px 0 0 20px; - padding: 0; + margin-top: 10px; } ul.search li { - padding: 5px 0 5px 20px; - background-image: url(file.png); - background-repeat: no-repeat; - background-position: 0 7px; + padding: 5px 0; } ul.search li a { @@ -237,6 +226,10 @@ a.headerlink { visibility: hidden; } +a:visited { + color: #551A8B; +} + h1:hover > a.headerlink, h2:hover > a.headerlink, h3:hover > a.headerlink, @@ -670,6 +663,16 @@ dd { 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{ + const config = event.detail.data(); + + const flyout = ` + + + Read the Docs + v: ${config.versions.current.slug} + + + + + ${renderLanguages(config)} + ${renderVersions(config)} + ${renderDownloads(config)} + + On Read the Docs + + Project Home + + + Builds + + + Downloads + + + + Search + + + + + + + + + Hosted by Read the Docs + + + + `; + + // Inject the generated flyout into the body HTML element. + document.body.insertAdjacentHTML("beforeend", flyout); + + // Trigger the Read the Docs Addons Search modal when clicking on the "Search docs" input from inside the flyout. + document + .querySelector("#flyout-search-form") + .addEventListener("focusin", () => { + const event = new CustomEvent("readthedocs-search-show"); + document.dispatchEvent(event); + }); + }) +} + +if (themeLanguageSelector || themeVersionSelector) { + function onSelectorSwitch(event) { + const option = event.target.selectedIndex; + const item = event.target.options[option]; + window.location.href = item.dataset.url; + } + + document.addEventListener("readthedocs-addons-data-ready", function (event) { + const config = event.detail.data(); + + const versionSwitch = document.querySelector( + "div.switch-menus > div.version-switch", + ); + if (themeVersionSelector) { + let versions = config.versions.active; + if (config.versions.current.hidden || config.versions.current.type === "external") { + versions.unshift(config.versions.current); + } + const versionSelect = ` + + ${versions + .map( + (version) => ` + + ${version.slug} + `, + ) + .join("\n")} + + `; + + versionSwitch.innerHTML = versionSelect; + versionSwitch.firstElementChild.addEventListener("change", onSelectorSwitch); + } + + const languageSwitch = document.querySelector( + "div.switch-menus > div.language-switch", + ); + + if (themeLanguageSelector) { + if (config.projects.translations.length) { + // Add the current language to the options on the selector + let languages = config.projects.translations.concat( + config.projects.current, + ); + languages = languages.sort((a, b) => + a.language.name.localeCompare(b.language.name), + ); + + const languageSelect = ` + + ${languages + .map( + (language) => ` + + ${language.language.name} + `, + ) + .join("\n")} + + `; + + languageSwitch.innerHTML = languageSelect; + languageSwitch.firstElementChild.addEventListener("change", onSelectorSwitch); + } + else { + languageSwitch.remove(); + } + } + }); +} + +document.addEventListener("readthedocs-addons-data-ready", function (event) { + // Trigger the Read the Docs Addons Search modal when clicking on "Search docs" input from the topnav. + document + .querySelector("[role='search'] input") + .addEventListener("focusin", () => { + const event = new CustomEvent("readthedocs-search-show"); + document.dispatchEvent(event); + }); +}); \ No newline at end of file diff --git a/docs/pages/html/_static/language_data.js b/docs/pages/html/_static/language_data.js index 250f566..c7fe6c6 100644 --- a/docs/pages/html/_static/language_data.js +++ b/docs/pages/html/_static/language_data.js @@ -1,19 +1,12 @@ /* - * language_data.js - * ~~~~~~~~~~~~~~~~ - * * This script contains the language-specific data used by searchtools.js, * namely the list of stopwords, stemmer, scorer and splitter. - * - * :copyright: Copyright 2007-2023 by the Sphinx team, see AUTHORS. - * :license: BSD, see LICENSE for details. - * */ var stopwords = ["a", "and", "are", "as", "at", "be", "but", "by", "for", "if", "in", "into", "is", "it", "near", "no", "not", "of", "on", "or", "such", "that", "the", "their", "then", "there", "these", "they", "this", "to", "was", "will", "with"]; -/* Non-minified version is copied as a separate JS file, is available */ +/* Non-minified version is copied as a separate JS file, if available */ /** * Porter Stemmer diff --git a/docs/pages/html/_static/notebooks/pca_examples.html b/docs/pages/html/_static/notebooks/pca_examples.html index c9a75dc..7bb55a3 100644 --- a/docs/pages/html/_static/notebooks/pca_examples.html +++ b/docs/pages/html/_static/notebooks/pca_examples.html @@ -1,13 +1,9 @@ - - - + + + pca_examples - - - - - - - - - - - - - - + + + - - - - + void Promise.all([...diagrams].map(renderOneMarmaid)); + }); + + + + + + + - + pca A Python Package for Principal Component Analysis. The core of PCA is build on sklearn functionality to find maximum compatibility when combining with other packages. But this package can do a lot more. Besides the regular pca, it can also perform SparsePCA, and TruncatedSVD. Depending on your input data, the best approach will be choosen. Other functionalities are: @@ -15124,38 +7531,30 @@ github pca - - - + + -In [1]: +In [1]: - -!pip install pca + +!pip install pca - - - + - - - - - - - + + Requirement already satisfied: pca in /usr/local/lib/python3.7/dist-packages (1.7.2) Requirement already satisfied: matplotlib in /usr/local/lib/python3.7/dist-packages (from pca) (3.2.2) Requirement already satisfied: wget in /usr/local/lib/python3.7/dist-packages (from pca) (3.2) @@ -15180,179 +7579,149 @@ - - - - - + + - + Lets check the version - - - + + -In [2]: +In [2]: - -import pca + +import pca print(pca.__version__) - - - + - - - - - - - + + 1.7.2 - - - - - + + - + Import the pca library - - - + + -In [3]: +In [3]: - -from pca import pca + +from pca import pca import numpy as np import pandas as pd - - - - - + + + - + Here we will create a random dataset. - - - + + -In [4]: +In [4]: - -# Dataset + +# Dataset from sklearn.datasets import load_iris X = pd.DataFrame(data=load_iris().data, columns=load_iris().feature_names, index=load_iris().target) - - - - - + + + - + Initialize using specified parameters. The parameters here are the default parameters. - - - + + -In [5]: +In [5]: - -# Initialize + +# Initialize model = pca(n_components=3, normalize=True) - - - - - + + + -In [6]: +In [6]: - -# Fit transform + +# Fit transform out = model.fit_transform(X) - - - + - - - - - - - + + [pca] >Processing dataframe.. [pca] >Normalizing input data per feature (zero mean and unit variance).. [pca] >The PCA reduction is performed on the [4] columns of the input dataframe. @@ -15364,171 +7733,119 @@ - - - - - + + -In [7]: +In [7]: - -# Make plot with only the directions (no scatter) + +# Make plot with only the directions (no scatter) fig, ax = model.biplot(textlabel=True, legend=False, figsize=(10, 6)) - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 with loadings. - - - - - - - - + + + - - - - - - + + -In [8]: +In [8]: - -# Make plot with only the directions (no scatter) + +# Make plot with only the directions (no scatter) fig, ax = model.biplot(cmap=None, textlabel=False, legend=False, figsize=(10, 6)) - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 with loadings. - - - - - - - - + + + - - - - - - + + -In [9]: +In [9]: - -from pca import pca + +from pca import pca # Load example data from sklearn.datasets import load_iris X = pd.DataFrame(data=load_iris().data, columns=load_iris().feature_names, index=load_iris().target) - - - - - + + + -In [10]: +In [10]: - -# Initialize + +# Initialize model = pca(n_components=3) # Fit using PCA results = model.fit_transform(X) - - - + - - - - - - - + + [pca] >Processing dataframe.. [pca] >The PCA reduction is performed on the [4] columns of the input dataframe. [pca] >Fit using PCA. @@ -15539,20 +7856,17 @@ - - - - - + + -In [11]: +In [11]: - -# Make plots + +# Make plots # Scree plot fig, ax = model.plot(figsize=(10, 6)) @@ -15563,190 +7877,117 @@ # Biplot fig, ax = model.biplot(figsize=(10, 6)) - - - + - - - - - - - - - - + + + - - - - - - - - - + + + - - - - - - + + [pca] >Plot PC1 vs PC2 with loadings. - - - - - - - + + <Figure size 432x288 with 0 Axes> - - - - - - - - - + + + - - - - - - + + -In [17]: +In [17]: - -# Coloring on density to focus on the core samples. + +# Coloring on density to focus on the core samples. # Biplot -fig, ax = model.biplot(figsize=(10, 6), gradient='#ffffff') +fig, ax = model.biplot(figsize=(10, 6), gradient='#ffffff') - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 with loadings. - - - - - - - - + + + - - - - - - + + -In [18]: +In [18]: - -# Outliers are stored in results: -results['outliers'] + +# Outliers are stored in results: +results['outliers'] # Outliers based on T2 -print('--------T2------------') -print(results['outliers'].loc[results['outliers']['y_bool'], :]) +print('--------T2------------') +print(results['outliers'].loc[results['outliers']['y_bool'], :]) # Outliers based on SPE -print('--------SPE------------') -print(results['outliers'].loc[results['outliers']['y_bool_spe'], :]) +print('--------SPE------------') +print(results['outliers'].loc[results['outliers']['y_bool_spe'], :]) - - - + - - - - - - - + + --------T2------------ y_proba y_score y_bool y_bool_spe y_score_spe 2 0.040551 13.160880 True True 3.679935 @@ -15771,270 +8012,168 @@ - - - - - + + -In [20]: +In [20]: - -# Outlier detection + +# Outlier detection fig, ax = model.biplot(SPE=True, HT2=True, figsize=(10, 6)) - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 with loadings. - - - - - - - - + + + - - - - - - + + -In [21]: +In [21]: - -# 3D plots + +# 3D plots fig, ax = model.scatter3d(figsize=(10, 6)) fig, ax = model.biplot3d(figsize=(10, 6)) fig, ax = model.biplot3d(SPE=True, HT2=True, figsize=(10, 6)) - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 vs PC3 with loadings. - - - - - - - - + + + - - - - - - - - - + + + - - - - - - + + [pca] >Plot PC1 vs PC2 vs PC3 with loadings. - - - - - - - - + + + - - - - - - + + -In [22]: +In [22]: - -fig, ax = model.biplot3d(SPE=True, HT2=True, visible=False, figsize=(10, 6)) + +fig, ax = model.biplot3d(SPE=True, HT2=True, visible=False, figsize=(10, 6)) # Set the figure again to True and show the figure. fig.set_visible(True) fig - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 vs PC3 with loadings. - - Out[22]: - - - - - - +Out[22]: + + - - - - - - - - - + + + - - - - - - + + -In [23]: +In [23]: - -# Normalize out PCs + +
After fitting a model on the data, you may want to use the model in a later stage to detect outliers on unseen data. Detection of outliers is performed in the transform function and does not require any additional action. An example is shown in the code block below.
# Import libraries @@ -252,7 +251,7 @@ Detect new unseen outliers -Detected outliers +Detected outliers @@ -288,7 +287,7 @@ Detect new unseen outliers -Detected outliers +Detected outliers @@ -296,7 +295,7 @@ Detect new unseen outliers -Detection of outliers without PCA +Detection of outliers without PCA If desired, the outliers can also be detected directly using the hotelling T2 and/or SPE/DmodX functionality. For demonstration purposes I use the PCs from the results but any other dataset would also work. import pca diff --git a/docs/pages/html/Plots.html b/docs/pages/html/Plots.html index c1677b6..f054370 100644 --- a/docs/pages/html/Plots.html +++ b/docs/pages/html/Plots.html @@ -1,20 +1,22 @@ + + - + - + Load dataset — pca pca documentation - - - - + + + + - - - + + + + + @@ -33,9 +35,6 @@ pca - - 2.0.1 - @@ -134,7 +133,7 @@ -Load dataset +Load dataset Let’s load the wine dataset to demonstrate the plots. # Load library from sklearn.datasets import load_wine @@ -166,7 +165,7 @@ Load dataset -Scatter plot +Scatter plot # Make scatterplot model.scatter() @@ -187,7 +186,7 @@ Scatter plot -Scatterplots +Scatterplots @@ -204,16 +203,40 @@ Scatter plot -Biplot +Biplot +The biplot draws the loadings (arrows) together with the samples (scatterplot). +The loadings can be colored red and blue which indicates the strength of the particular feature in the PC. +For each principal component (PC), the feature is determined with the largest absolute loading. This indicates which feature contributes the most to each PC and can occur in multiple PCs. +The highest loading values for the features are colored red in the biplot and described as “best” in the output dataframe. +The features that were not seen with highest loadings for any PC are considered weaker features, and are colored blue the biplot. In the output dataframe these features are described as “weak”. # Make biplot model.biplot() # Here again, many other options can be turned on and off model.biplot(SPE=True, HT2=True, legend=1) + +# Show the top features +results['topfeat'] + +# PC feature loading type +# 0 PC1 flavanoids 0.422934 best +# 1 PC2 color_intensity 0.529996 best +# 2 PC3 ash 0.626224 best +# 3 PC4 malic_acid 0.536890 best +# 4 PC5 magnesium 0.727049 best +# 5 PC6 malic_acid 0.536814 best +# 6 PC7 nonflavanoid_phenols 0.595447 best +# 7 PC8 hue 0.436624 best +# 8 PC9 proline 0.575786 best +# 9 PC10 od280/od315_of_diluted_wines 0.523706 best +# 10 PC9 alcohol -0.508619 weak +# 11 PC3 alcalinity_of_ash 0.612080 weak +# 12 PC8 total_phenols -0.405934 weak +# 13 PC6 proanthocyanins -0.533795 weak -Biplots +Biplots @@ -223,28 +246,30 @@ Biplot -Biplot (only arrows) +Biplot (only arrows) # Make plot with parameters: set cmap to None and label and legend to False. Only directions will be plotted. model.biplot(cmap=None, legend=False) - + + -Explained variance plot +Explained variance plot model.plot() - + + -Alpha Transparency +Alpha Transparency fig, ax = model.scatter(alpha=1) -Markers +Markers import numpy as np from sklearn.datasets import make_friedman1 from pca import pca @@ -272,7 +297,7 @@ Markers -Biplots with markers +Biplots with markers @@ -280,7 +305,7 @@ Markers -Control color/marker/size per sample +Control color/marker/size per sample import numpy as np import matplotlib.pyplot as plt import matplotlib.colors as mcolors @@ -329,7 +354,7 @@ Control color/marker/size per sample -Biplot with customized properties per sample. +Biplot with customized properties per sample. @@ -337,15 +362,16 @@ Control color/marker/size per sample -3D plots +3D plots All plots can also be created in 3D by setting the d3=True parameter. model.biplot3d() - + + -Toggle visible status +Toggle visible status The visible status for can be turned on and off. # Make plot but not visible. fig, ax = model.biplot(visible=False) diff --git a/docs/pages/html/_sources/Plots.rst.txt b/docs/pages/html/_sources/Plots.rst.txt index 33319b2..38cd2db 100644 --- a/docs/pages/html/_sources/Plots.rst.txt +++ b/docs/pages/html/_sources/Plots.rst.txt @@ -83,6 +83,14 @@ Scatter plot Biplot ############### +The biplot draws the loadings (arrows) together with the samples (scatterplot). +The loadings can be colored red and blue which indicates the strength of the particular feature in the PC. + +For each principal component (PC), the feature is determined with the largest absolute loading. This indicates which feature contributes the most to each PC and can occur in multiple PCs. +The highest loading values for the features are colored red in the biplot and described as "best" in the output dataframe. +The features that were not seen with highest loadings for any PC are considered weaker features, and are colored blue the biplot. In the output dataframe these features are described as "weak". + + .. code:: python # Make biplot @@ -91,6 +99,24 @@ Biplot # Here again, many other options can be turned on and off model.biplot(SPE=True, HT2=True, legend=1) + # Show the top features + results['topfeat'] + + # PC feature loading type + # 0 PC1 flavanoids 0.422934 best + # 1 PC2 color_intensity 0.529996 best + # 2 PC3 ash 0.626224 best + # 3 PC4 malic_acid 0.536890 best + # 4 PC5 magnesium 0.727049 best + # 5 PC6 malic_acid 0.536814 best + # 6 PC7 nonflavanoid_phenols 0.595447 best + # 7 PC8 hue 0.436624 best + # 8 PC9 proline 0.575786 best + # 9 PC10 od280/od315_of_diluted_wines 0.523706 best + # 10 PC9 alcohol -0.508619 weak + # 11 PC3 alcalinity_of_ash 0.612080 weak + # 12 PC8 total_phenols -0.405934 weak + # 13 PC6 proanthocyanins -0.533795 weak .. |figP5| image:: ../figs/wine_biplot.png .. |figP6| image:: ../figs/wine_biplot_with_outliers.png diff --git a/docs/pages/html/_sources/sponsor.rst.txt b/docs/pages/html/_sources/sponsor.rst.txt index a46c410..f006896 100644 --- a/docs/pages/html/_sources/sponsor.rst.txt +++ b/docs/pages/html/_sources/sponsor.rst.txt @@ -4,8 +4,10 @@ * Become a `Sponsor `_! * `Buy `_ me a coffee! I ❤️ coffee :) * `Donate `_ in Bitcoin. - * Follow me on medium! Go to my `medium profile `_ and press *follow*. + * Follow me on Medium! Go to my `medium profile `_ and press *follow*. + * Subscribe to me on Substack! Go to my `profile `_ where you can *subscribe*. * **Star** this repo at the github page. + * You can also buy a digital educational product over `here `_. * Other contributions can be in the form of feature requests, idea discussions, reporting bugs, opening pull requests. Cheers Mate. diff --git a/docs/pages/html/_static/_sphinx_javascript_frameworks_compat.js b/docs/pages/html/_static/_sphinx_javascript_frameworks_compat.js new file mode 100644 index 0000000..8141580 --- /dev/null +++ b/docs/pages/html/_static/_sphinx_javascript_frameworks_compat.js @@ -0,0 +1,123 @@ +/* Compatability shim for jQuery and underscores.js. + * + * Copyright Sphinx contributors + * Released under the two clause BSD licence + */ + +/** + * small helper function to urldecode strings + * + * See https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/decodeURIComponent#Decoding_query_parameters_from_a_URL + */ +jQuery.urldecode = function(x) { + if (!x) { + return x + } + return decodeURIComponent(x.replace(/\+/g, ' ')); +}; + +/** + * small helper function to urlencode strings + */ +jQuery.urlencode = encodeURIComponent; + +/** + * This function returns the parsed url parameters of the + * current request. Multiple values per key are supported, + * it will always return arrays of strings for the value parts. + */ +jQuery.getQueryParameters = function(s) { + if (typeof s === 'undefined') + s = document.location.search; + var parts = s.substr(s.indexOf('?') + 1).split('&'); + var result = {}; + for (var i = 0; i < parts.length; i++) { + var tmp = parts[i].split('=', 2); + var key = jQuery.urldecode(tmp[0]); + var value = jQuery.urldecode(tmp[1]); + if (key in result) + result[key].push(value); + else + result[key] = [value]; + } + return result; +}; + +/** + * highlight a given string on a jquery object by wrapping it in + * span elements with the given class name. + */ +jQuery.fn.highlightText = function(text, className) { + function highlight(node, addItems) { + if (node.nodeType === 3) { + var val = node.nodeValue; + var pos = val.toLowerCase().indexOf(text); + if (pos >= 0 && + !jQuery(node.parentNode).hasClass(className) && + !jQuery(node.parentNode).hasClass("nohighlight")) { + var span; + var isInSVG = jQuery(node).closest("body, svg, foreignObject").is("svg"); + if (isInSVG) { + span = document.createElementNS("http://www.w3.org/2000/svg", "tspan"); + } else { + span = document.createElement("span"); + span.className = className; + } + span.appendChild(document.createTextNode(val.substr(pos, text.length))); + node.parentNode.insertBefore(span, node.parentNode.insertBefore( + document.createTextNode(val.substr(pos + text.length)), + node.nextSibling)); + node.nodeValue = val.substr(0, pos); + if (isInSVG) { + var rect = document.createElementNS("http://www.w3.org/2000/svg", "rect"); + var bbox = node.parentElement.getBBox(); + rect.x.baseVal.value = bbox.x; + rect.y.baseVal.value = bbox.y; + rect.width.baseVal.value = bbox.width; + rect.height.baseVal.value = bbox.height; + rect.setAttribute('class', className); + addItems.push({ + "parent": node.parentNode, + "target": rect}); + } + } + } + else if (!jQuery(node).is("button, select, textarea")) { + jQuery.each(node.childNodes, function() { + highlight(this, addItems); + }); + } + } + var addItems = []; + var result = this.each(function() { + highlight(this, addItems); + }); + for (var i = 0; i < addItems.length; ++i) { + jQuery(addItems[i].parent).before(addItems[i].target); + } + return result; +}; + +/* + * backward compatibility for jQuery.browser + * This will be supported until firefox bug is fixed. + */ +if (!jQuery.browser) { + jQuery.uaMatch = function(ua) { + ua = ua.toLowerCase(); + + var match = /(chrome)[ \/]([\w.]+)/.exec(ua) || + /(webkit)[ \/]([\w.]+)/.exec(ua) || + /(opera)(?:.*version|)[ \/]([\w.]+)/.exec(ua) || + /(msie) ([\w.]+)/.exec(ua) || + ua.indexOf("compatible") < 0 && /(mozilla)(?:.*? rv:([\w.]+)|)/.exec(ua) || + []; + + return { + browser: match[ 1 ] || "", + version: match[ 2 ] || "0" + }; + }; + jQuery.browser = {}; + jQuery.browser[jQuery.uaMatch(navigator.userAgent).browser] = true; +} diff --git a/docs/pages/html/_static/basic.css b/docs/pages/html/_static/basic.css index 7577acb..7ebbd6d 100644 --- a/docs/pages/html/_static/basic.css +++ b/docs/pages/html/_static/basic.css @@ -1,12 +1,5 @@ /* - * basic.css - * ~~~~~~~~~ - * * Sphinx stylesheet -- basic theme. - * - * :copyright: Copyright 2007-2023 by the Sphinx team, see AUTHORS. - * :license: BSD, see LICENSE for details. - * */ /* -- main layout ----------------------------------------------------------- */ @@ -115,15 +108,11 @@ img { /* -- search page ----------------------------------------------------------- */ ul.search { - margin: 10px 0 0 20px; - padding: 0; + margin-top: 10px; } ul.search li { - padding: 5px 0 5px 20px; - background-image: url(file.png); - background-repeat: no-repeat; - background-position: 0 7px; + padding: 5px 0; } ul.search li a { @@ -237,6 +226,10 @@ a.headerlink { visibility: hidden; } +a:visited { + color: #551A8B; +} + h1:hover > a.headerlink, h2:hover > a.headerlink, h3:hover > a.headerlink, @@ -670,6 +663,16 @@ dd { 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video",version:m,shivCSS:n.shivCSS!==!1,supportsUnknownElements:l,shivMethods:n.shivMethods!==!1,type:"default",shivDocument:j,createElement:g,createDocumentFragment:h,addElements:e};a.html5=t,j(b),"object"==typeof module&&module.exports&&(module.exports=t)}("undefined"!=typeof window?window:this,document); \ No newline at end of file diff --git a/docs/pages/html/_static/js/versions.js b/docs/pages/html/_static/js/versions.js new file mode 100644 index 0000000..4958195 --- /dev/null +++ b/docs/pages/html/_static/js/versions.js @@ -0,0 +1,228 @@ +const themeFlyoutDisplay = "hidden"; +const themeVersionSelector = true; +const themeLanguageSelector = true; + +if (themeFlyoutDisplay === "attached") { + function renderLanguages(config) { + if (!config.projects.translations.length) { + return ""; + } + + // Insert the current language to the options on the selector + let languages = config.projects.translations.concat(config.projects.current); + languages = languages.sort((a, b) => a.language.name.localeCompare(b.language.name)); + + const languagesHTML = ` + + Languages + ${languages + .map( + (translation) => ` + + ${translation.language.code} + + `, + ) + .join("\n")} + + `; + return languagesHTML; + } + + function renderVersions(config) { + if (!config.versions.active.length) { + return ""; + } + const versionsHTML = ` + + Versions + ${config.versions.active + .map( + (version) => ` + + ${version.slug} + + `, + ) + .join("\n")} + + `; + return versionsHTML; + } + + function renderDownloads(config) { + if (!Object.keys(config.versions.current.downloads).length) { + return ""; + } + const downloadsNameDisplay = { + pdf: "PDF", + epub: "Epub", + htmlzip: "HTML", + }; + + const downloadsHTML = ` + + Downloads + ${Object.entries(config.versions.current.downloads) + .map( + ([name, url]) => ` + + ${downloadsNameDisplay[name]} + + `, + ) + .join("\n")} + + `; + return downloadsHTML; + } + + document.addEventListener("readthedocs-addons-data-ready", function (event) { + const config = event.detail.data(); + + const flyout = ` + + + Read the Docs + v: ${config.versions.current.slug} + + + + + ${renderLanguages(config)} + ${renderVersions(config)} + ${renderDownloads(config)} + + On Read the Docs + + Project Home + + + Builds + + + Downloads + + + + Search + + + + + + + + + Hosted by Read the Docs + + + + `; + + // Inject the generated flyout into the body HTML element. + document.body.insertAdjacentHTML("beforeend", flyout); + + // Trigger the Read the Docs Addons Search modal when clicking on the "Search docs" input from inside the flyout. + document + .querySelector("#flyout-search-form") + .addEventListener("focusin", () => { + const event = new CustomEvent("readthedocs-search-show"); + document.dispatchEvent(event); + }); + }) +} + +if (themeLanguageSelector || themeVersionSelector) { + function onSelectorSwitch(event) { + const option = event.target.selectedIndex; + const item = event.target.options[option]; + window.location.href = item.dataset.url; + } + + document.addEventListener("readthedocs-addons-data-ready", function (event) { + const config = event.detail.data(); + + const versionSwitch = document.querySelector( + "div.switch-menus > div.version-switch", + ); + if (themeVersionSelector) { + let versions = config.versions.active; + if (config.versions.current.hidden || config.versions.current.type === "external") { + versions.unshift(config.versions.current); + } + const versionSelect = ` + + ${versions + .map( + (version) => ` + + ${version.slug} + `, + ) + .join("\n")} + + `; + + versionSwitch.innerHTML = versionSelect; + versionSwitch.firstElementChild.addEventListener("change", onSelectorSwitch); + } + + const languageSwitch = document.querySelector( + "div.switch-menus > div.language-switch", + ); + + if (themeLanguageSelector) { + if (config.projects.translations.length) { + // Add the current language to the options on the selector + let languages = config.projects.translations.concat( + config.projects.current, + ); + languages = languages.sort((a, b) => + a.language.name.localeCompare(b.language.name), + ); + + const languageSelect = ` + + ${languages + .map( + (language) => ` + + ${language.language.name} + `, + ) + .join("\n")} + + `; + + languageSwitch.innerHTML = languageSelect; + languageSwitch.firstElementChild.addEventListener("change", onSelectorSwitch); + } + else { + languageSwitch.remove(); + } + } + }); +} + +document.addEventListener("readthedocs-addons-data-ready", function (event) { + // Trigger the Read the Docs Addons Search modal when clicking on "Search docs" input from the topnav. + document + .querySelector("[role='search'] input") + .addEventListener("focusin", () => { + const event = new CustomEvent("readthedocs-search-show"); + document.dispatchEvent(event); + }); +}); \ No newline at end of file diff --git a/docs/pages/html/_static/language_data.js b/docs/pages/html/_static/language_data.js index 250f566..c7fe6c6 100644 --- a/docs/pages/html/_static/language_data.js +++ b/docs/pages/html/_static/language_data.js @@ -1,19 +1,12 @@ /* - * language_data.js - * ~~~~~~~~~~~~~~~~ - * * This script contains the language-specific data used by searchtools.js, * namely the list of stopwords, stemmer, scorer and splitter. - * - * :copyright: Copyright 2007-2023 by the Sphinx team, see AUTHORS. - * :license: BSD, see LICENSE for details. - * */ var stopwords = ["a", "and", "are", "as", "at", "be", "but", "by", "for", "if", "in", "into", "is", "it", "near", "no", "not", "of", "on", "or", "such", "that", "the", "their", "then", "there", "these", "they", "this", "to", "was", "will", "with"]; -/* Non-minified version is copied as a separate JS file, is available */ +/* Non-minified version is copied as a separate JS file, if available */ /** * Porter Stemmer diff --git a/docs/pages/html/_static/notebooks/pca_examples.html b/docs/pages/html/_static/notebooks/pca_examples.html index c9a75dc..7bb55a3 100644 --- a/docs/pages/html/_static/notebooks/pca_examples.html +++ b/docs/pages/html/_static/notebooks/pca_examples.html @@ -1,13 +1,9 @@ - - - + + + pca_examples - - - - - - - - - - - - - - + + + - - - - + void Promise.all([...diagrams].map(renderOneMarmaid)); + }); + + + + + + + - + pca A Python Package for Principal Component Analysis. The core of PCA is build on sklearn functionality to find maximum compatibility when combining with other packages. But this package can do a lot more. Besides the regular pca, it can also perform SparsePCA, and TruncatedSVD. Depending on your input data, the best approach will be choosen. Other functionalities are: @@ -15124,38 +7531,30 @@ github pca - - - + + -In [1]: +In [1]: - -!pip install pca + +!pip install pca - - - + - - - - - - - + + Requirement already satisfied: pca in /usr/local/lib/python3.7/dist-packages (1.7.2) Requirement already satisfied: matplotlib in /usr/local/lib/python3.7/dist-packages (from pca) (3.2.2) Requirement already satisfied: wget in /usr/local/lib/python3.7/dist-packages (from pca) (3.2) @@ -15180,179 +7579,149 @@ - - - - - + + - + Lets check the version - - - + + -In [2]: +In [2]: - -import pca + +import pca print(pca.__version__) - - - + - - - - - - - + + 1.7.2 - - - - - + + - + Import the pca library - - - + + -In [3]: +In [3]: - -from pca import pca + +from pca import pca import numpy as np import pandas as pd - - - - - + + + - + Here we will create a random dataset. - - - + + -In [4]: +In [4]: - -# Dataset + +# Dataset from sklearn.datasets import load_iris X = pd.DataFrame(data=load_iris().data, columns=load_iris().feature_names, index=load_iris().target) - - - - - + + + - + Initialize using specified parameters. The parameters here are the default parameters. - - - + + -In [5]: +In [5]: - -# Initialize + +# Initialize model = pca(n_components=3, normalize=True) - - - - - + + + -In [6]: +In [6]: - -# Fit transform + +# Fit transform out = model.fit_transform(X) - - - + - - - - - - - + + [pca] >Processing dataframe.. [pca] >Normalizing input data per feature (zero mean and unit variance).. [pca] >The PCA reduction is performed on the [4] columns of the input dataframe. @@ -15364,171 +7733,119 @@ - - - - - + + -In [7]: +In [7]: - -# Make plot with only the directions (no scatter) + +# Make plot with only the directions (no scatter) fig, ax = model.biplot(textlabel=True, legend=False, figsize=(10, 6)) - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 with loadings. - - - - - - - - + + + - - - - - - + + -In [8]: +In [8]: - -# Make plot with only the directions (no scatter) + +# Make plot with only the directions (no scatter) fig, ax = model.biplot(cmap=None, textlabel=False, legend=False, figsize=(10, 6)) - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 with loadings. - - - - - - - - + + + - - - - - - + + -In [9]: +In [9]: - -from pca import pca + +from pca import pca # Load example data from sklearn.datasets import load_iris X = pd.DataFrame(data=load_iris().data, columns=load_iris().feature_names, index=load_iris().target) - - - - - + + + -In [10]: +In [10]: - -# Initialize + +# Initialize model = pca(n_components=3) # Fit using PCA results = model.fit_transform(X) - - - + - - - - - - - + + [pca] >Processing dataframe.. [pca] >The PCA reduction is performed on the [4] columns of the input dataframe. [pca] >Fit using PCA. @@ -15539,20 +7856,17 @@ - - - - - + + -In [11]: +In [11]: - -# Make plots + +# Make plots # Scree plot fig, ax = model.plot(figsize=(10, 6)) @@ -15563,190 +7877,117 @@ # Biplot fig, ax = model.biplot(figsize=(10, 6)) - - - + - - - - - - - - - - + + + - - - - - - - - - + + + - - - - - - + + [pca] >Plot PC1 vs PC2 with loadings. - - - - - - - + + <Figure size 432x288 with 0 Axes> - - - - - - - - - + + + - - - - - - + + -In [17]: +In [17]: - -# Coloring on density to focus on the core samples. + +# Coloring on density to focus on the core samples. # Biplot -fig, ax = model.biplot(figsize=(10, 6), gradient='#ffffff') +fig, ax = model.biplot(figsize=(10, 6), gradient='#ffffff') - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 with loadings. - - - - - - - - + + + - - - - - - + + -In [18]: +In [18]: - -# Outliers are stored in results: -results['outliers'] + +# Outliers are stored in results: +results['outliers'] # Outliers based on T2 -print('--------T2------------') -print(results['outliers'].loc[results['outliers']['y_bool'], :]) +print('--------T2------------') +print(results['outliers'].loc[results['outliers']['y_bool'], :]) # Outliers based on SPE -print('--------SPE------------') -print(results['outliers'].loc[results['outliers']['y_bool_spe'], :]) +print('--------SPE------------') +print(results['outliers'].loc[results['outliers']['y_bool_spe'], :]) - - - + - - - - - - - + + --------T2------------ y_proba y_score y_bool y_bool_spe y_score_spe 2 0.040551 13.160880 True True 3.679935 @@ -15771,270 +8012,168 @@ - - - - - + + -In [20]: +In [20]: - -# Outlier detection + +# Outlier detection fig, ax = model.biplot(SPE=True, HT2=True, figsize=(10, 6)) - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 with loadings. - - - - - - - - + + + - - - - - - + + -In [21]: +In [21]: - -# 3D plots + +# 3D plots fig, ax = model.scatter3d(figsize=(10, 6)) fig, ax = model.biplot3d(figsize=(10, 6)) fig, ax = model.biplot3d(SPE=True, HT2=True, figsize=(10, 6)) - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 vs PC3 with loadings. - - - - - - - - + + + - - - - - - - - - + + + - - - - - - + + [pca] >Plot PC1 vs PC2 vs PC3 with loadings. - - - - - - - - + + + - - - - - - + + -In [22]: +In [22]: - -fig, ax = model.biplot3d(SPE=True, HT2=True, visible=False, figsize=(10, 6)) + +fig, ax = model.biplot3d(SPE=True, HT2=True, visible=False, figsize=(10, 6)) # Set the figure again to True and show the figure. fig.set_visible(True) fig - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 vs PC3 with loadings. - - Out[22]: - - - - - - +Out[22]: + + - - - - - - - - - + + + - - - - - - + + -In [23]: +In [23]: - -# Normalize out PCs + +
If desired, the outliers can also be detected directly using the hotelling T2 and/or SPE/DmodX functionality. For demonstration purposes I use the PCs from the results but any other dataset would also work.
import pca diff --git a/docs/pages/html/Plots.html b/docs/pages/html/Plots.html index c1677b6..f054370 100644 --- a/docs/pages/html/Plots.html +++ b/docs/pages/html/Plots.html @@ -1,20 +1,22 @@ + + - + - + Load dataset — pca pca documentation - - - - + + + + - - - + + + + + @@ -33,9 +35,6 @@ pca - - 2.0.1 - @@ -134,7 +133,7 @@ -Load dataset +Load dataset Let’s load the wine dataset to demonstrate the plots. # Load library from sklearn.datasets import load_wine @@ -166,7 +165,7 @@ Load dataset -Scatter plot +Scatter plot # Make scatterplot model.scatter() @@ -187,7 +186,7 @@ Scatter plot -Scatterplots +Scatterplots @@ -204,16 +203,40 @@ Scatter plot -Biplot +Biplot +The biplot draws the loadings (arrows) together with the samples (scatterplot). +The loadings can be colored red and blue which indicates the strength of the particular feature in the PC. +For each principal component (PC), the feature is determined with the largest absolute loading. This indicates which feature contributes the most to each PC and can occur in multiple PCs. +The highest loading values for the features are colored red in the biplot and described as “best” in the output dataframe. +The features that were not seen with highest loadings for any PC are considered weaker features, and are colored blue the biplot. In the output dataframe these features are described as “weak”. # Make biplot model.biplot() # Here again, many other options can be turned on and off model.biplot(SPE=True, HT2=True, legend=1) + +# Show the top features +results['topfeat'] + +# PC feature loading type +# 0 PC1 flavanoids 0.422934 best +# 1 PC2 color_intensity 0.529996 best +# 2 PC3 ash 0.626224 best +# 3 PC4 malic_acid 0.536890 best +# 4 PC5 magnesium 0.727049 best +# 5 PC6 malic_acid 0.536814 best +# 6 PC7 nonflavanoid_phenols 0.595447 best +# 7 PC8 hue 0.436624 best +# 8 PC9 proline 0.575786 best +# 9 PC10 od280/od315_of_diluted_wines 0.523706 best +# 10 PC9 alcohol -0.508619 weak +# 11 PC3 alcalinity_of_ash 0.612080 weak +# 12 PC8 total_phenols -0.405934 weak +# 13 PC6 proanthocyanins -0.533795 weak -Biplots +Biplots @@ -223,28 +246,30 @@ Biplot -Biplot (only arrows) +Biplot (only arrows) # Make plot with parameters: set cmap to None and label and legend to False. Only directions will be plotted. model.biplot(cmap=None, legend=False) - + + -Explained variance plot +Explained variance plot model.plot() - + + -Alpha Transparency +Alpha Transparency fig, ax = model.scatter(alpha=1) -Markers +Markers import numpy as np from sklearn.datasets import make_friedman1 from pca import pca @@ -272,7 +297,7 @@ Markers -Biplots with markers +Biplots with markers @@ -280,7 +305,7 @@ Markers -Control color/marker/size per sample +Control color/marker/size per sample import numpy as np import matplotlib.pyplot as plt import matplotlib.colors as mcolors @@ -329,7 +354,7 @@ Control color/marker/size per sample -Biplot with customized properties per sample. +Biplot with customized properties per sample. @@ -337,15 +362,16 @@ Control color/marker/size per sample -3D plots +3D plots All plots can also be created in 3D by setting the d3=True parameter. model.biplot3d() - + + -Toggle visible status +Toggle visible status The visible status for can be turned on and off. # Make plot but not visible. fig, ax = model.biplot(visible=False) diff --git a/docs/pages/html/_sources/Plots.rst.txt b/docs/pages/html/_sources/Plots.rst.txt index 33319b2..38cd2db 100644 --- a/docs/pages/html/_sources/Plots.rst.txt +++ b/docs/pages/html/_sources/Plots.rst.txt @@ -83,6 +83,14 @@ Scatter plot Biplot ############### +The biplot draws the loadings (arrows) together with the samples (scatterplot). +The loadings can be colored red and blue which indicates the strength of the particular feature in the PC. + +For each principal component (PC), the feature is determined with the largest absolute loading. This indicates which feature contributes the most to each PC and can occur in multiple PCs. +The highest loading values for the features are colored red in the biplot and described as "best" in the output dataframe. +The features that were not seen with highest loadings for any PC are considered weaker features, and are colored blue the biplot. In the output dataframe these features are described as "weak". + + .. code:: python # Make biplot @@ -91,6 +99,24 @@ Biplot # Here again, many other options can be turned on and off model.biplot(SPE=True, HT2=True, legend=1) + # Show the top features + results['topfeat'] + + # PC feature loading type + # 0 PC1 flavanoids 0.422934 best + # 1 PC2 color_intensity 0.529996 best + # 2 PC3 ash 0.626224 best + # 3 PC4 malic_acid 0.536890 best + # 4 PC5 magnesium 0.727049 best + # 5 PC6 malic_acid 0.536814 best + # 6 PC7 nonflavanoid_phenols 0.595447 best + # 7 PC8 hue 0.436624 best + # 8 PC9 proline 0.575786 best + # 9 PC10 od280/od315_of_diluted_wines 0.523706 best + # 10 PC9 alcohol -0.508619 weak + # 11 PC3 alcalinity_of_ash 0.612080 weak + # 12 PC8 total_phenols -0.405934 weak + # 13 PC6 proanthocyanins -0.533795 weak .. |figP5| image:: ../figs/wine_biplot.png .. |figP6| image:: ../figs/wine_biplot_with_outliers.png diff --git a/docs/pages/html/_sources/sponsor.rst.txt b/docs/pages/html/_sources/sponsor.rst.txt index a46c410..f006896 100644 --- a/docs/pages/html/_sources/sponsor.rst.txt +++ b/docs/pages/html/_sources/sponsor.rst.txt @@ -4,8 +4,10 @@ * Become a `Sponsor `_! * `Buy `_ me a coffee! I ❤️ coffee :) * `Donate `_ in Bitcoin. - * Follow me on medium! Go to my `medium profile `_ and press *follow*. + * Follow me on Medium! Go to my `medium profile `_ and press *follow*. + * Subscribe to me on Substack! Go to my `profile `_ where you can *subscribe*. * **Star** this repo at the github page. + * You can also buy a digital educational product over `here `_. * Other contributions can be in the form of feature requests, idea discussions, reporting bugs, opening pull requests. Cheers Mate. diff --git a/docs/pages/html/_static/_sphinx_javascript_frameworks_compat.js b/docs/pages/html/_static/_sphinx_javascript_frameworks_compat.js new file mode 100644 index 0000000..8141580 --- /dev/null +++ b/docs/pages/html/_static/_sphinx_javascript_frameworks_compat.js @@ -0,0 +1,123 @@ +/* Compatability shim for jQuery and underscores.js. + * + * Copyright Sphinx contributors + * Released under the two clause BSD licence + */ + +/** + * small helper function to urldecode strings + * + * See https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/decodeURIComponent#Decoding_query_parameters_from_a_URL + */ +jQuery.urldecode = function(x) { + if (!x) { + return x + } + return decodeURIComponent(x.replace(/\+/g, ' ')); +}; + +/** + * small helper function to urlencode strings + */ +jQuery.urlencode = encodeURIComponent; + +/** + * This function returns the parsed url parameters of the + * current request. Multiple values per key are supported, + * it will always return arrays of strings for the value parts. + */ +jQuery.getQueryParameters = function(s) { + if (typeof s === 'undefined') + s = document.location.search; + var parts = s.substr(s.indexOf('?') + 1).split('&'); + var result = {}; + for (var i = 0; i < parts.length; i++) { + var tmp = parts[i].split('=', 2); + var key = jQuery.urldecode(tmp[0]); + var value = jQuery.urldecode(tmp[1]); + if (key in result) + result[key].push(value); + else + result[key] = [value]; + } + return result; +}; + +/** + * highlight a given string on a jquery object by wrapping it in + * span elements with the given class name. + */ +jQuery.fn.highlightText = function(text, className) { + function highlight(node, addItems) { + if (node.nodeType === 3) { + var val = node.nodeValue; + var pos = val.toLowerCase().indexOf(text); + if (pos >= 0 && + !jQuery(node.parentNode).hasClass(className) && + !jQuery(node.parentNode).hasClass("nohighlight")) { + var span; + var isInSVG = jQuery(node).closest("body, svg, foreignObject").is("svg"); + if (isInSVG) { + span = document.createElementNS("http://www.w3.org/2000/svg", "tspan"); + } else { + span = document.createElement("span"); + span.className = className; + } + span.appendChild(document.createTextNode(val.substr(pos, text.length))); + node.parentNode.insertBefore(span, node.parentNode.insertBefore( + document.createTextNode(val.substr(pos + text.length)), + node.nextSibling)); + node.nodeValue = val.substr(0, pos); + if (isInSVG) { + var rect = document.createElementNS("http://www.w3.org/2000/svg", "rect"); + var bbox = node.parentElement.getBBox(); + rect.x.baseVal.value = bbox.x; + rect.y.baseVal.value = bbox.y; + rect.width.baseVal.value = bbox.width; + rect.height.baseVal.value = bbox.height; + rect.setAttribute('class', className); + addItems.push({ + "parent": node.parentNode, + "target": rect}); + } + } + } + else if (!jQuery(node).is("button, select, textarea")) { + jQuery.each(node.childNodes, function() { + highlight(this, addItems); + }); + } + } + var addItems = []; + var result = this.each(function() { + highlight(this, addItems); + }); + for (var i = 0; i < addItems.length; ++i) { + jQuery(addItems[i].parent).before(addItems[i].target); + } + return result; +}; + +/* + * backward compatibility for jQuery.browser + * This will be supported until firefox bug is fixed. + */ +if (!jQuery.browser) { + jQuery.uaMatch = function(ua) { + ua = ua.toLowerCase(); + + var match = /(chrome)[ \/]([\w.]+)/.exec(ua) || + /(webkit)[ \/]([\w.]+)/.exec(ua) || + /(opera)(?:.*version|)[ \/]([\w.]+)/.exec(ua) || + /(msie) ([\w.]+)/.exec(ua) || + ua.indexOf("compatible") < 0 && /(mozilla)(?:.*? rv:([\w.]+)|)/.exec(ua) || + []; + + return { + browser: match[ 1 ] || "", + version: match[ 2 ] || "0" + }; + }; + jQuery.browser = {}; + jQuery.browser[jQuery.uaMatch(navigator.userAgent).browser] = true; +} diff --git a/docs/pages/html/_static/basic.css b/docs/pages/html/_static/basic.css index 7577acb..7ebbd6d 100644 --- a/docs/pages/html/_static/basic.css +++ b/docs/pages/html/_static/basic.css @@ -1,12 +1,5 @@ /* - * basic.css - * ~~~~~~~~~ - * * Sphinx stylesheet -- basic theme. - * - * :copyright: Copyright 2007-2023 by the Sphinx team, see AUTHORS. - * :license: BSD, see LICENSE for details. - * */ /* -- main layout ----------------------------------------------------------- */ @@ -115,15 +108,11 @@ img { /* -- search page ----------------------------------------------------------- */ ul.search { - margin: 10px 0 0 20px; - padding: 0; + margin-top: 10px; } ul.search li { - padding: 5px 0 5px 20px; - background-image: url(file.png); - background-repeat: no-repeat; - background-position: 0 7px; + padding: 5px 0; } ul.search li a { @@ -237,6 +226,10 @@ a.headerlink { visibility: hidden; } +a:visited { + color: #551A8B; +} + h1:hover > a.headerlink, h2:hover > a.headerlink, h3:hover > a.headerlink, @@ -670,6 +663,16 @@ dd { margin-left: 30px; } +.sig dd { + margin-top: 0px; + margin-bottom: 0px; +} + +.sig dl { + margin-top: 0px; + margin-bottom: 0px; +} + dl > dd:last-child, dl > dd:last-child > :last-child { margin-bottom: 0; @@ -738,6 +741,14 @@ abbr, acronym { cursor: help; } +.translated { + background-color: rgba(207, 255, 207, 0.2) +} + +.untranslated { + background-color: rgba(255, 207, 207, 0.2) +} + /* -- code displays --------------------------------------------------------- */ pre { diff --git a/docs/pages/html/_static/css/badge_only.css b/docs/pages/html/_static/css/badge_only.css index c718cee..88ba55b 100644 --- a/docs/pages/html/_static/css/badge_only.css +++ b/docs/pages/html/_static/css/badge_only.css @@ -1 +1 @@ -.clearfix{*zoom:1}.clearfix:after,.clearfix:before{display:table;content:""}.clearfix:after{clear:both}@font-face{font-family:FontAwesome;font-style:normal;font-weight:400;src:url(fonts/fontawesome-webfont.eot?674f50d287a8c48dc19ba404d20fe713?#iefix) 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config.projects.current, + ); + languages = languages.sort((a, b) => + a.language.name.localeCompare(b.language.name), + ); + + const languageSelect = ` + + ${languages + .map( + (language) => ` + + ${language.language.name} + `, + ) + .join("\n")} + + `; + + languageSwitch.innerHTML = languageSelect; + languageSwitch.firstElementChild.addEventListener("change", onSelectorSwitch); + } + else { + languageSwitch.remove(); + } + } + }); +} + +document.addEventListener("readthedocs-addons-data-ready", function (event) { + // Trigger the Read the Docs Addons Search modal when clicking on "Search docs" input from the topnav. + document + .querySelector("[role='search'] input") + .addEventListener("focusin", () => { + const event = new CustomEvent("readthedocs-search-show"); + document.dispatchEvent(event); + }); +}); \ No newline at end of file diff --git a/docs/pages/html/_static/language_data.js b/docs/pages/html/_static/language_data.js index 250f566..c7fe6c6 100644 --- a/docs/pages/html/_static/language_data.js +++ b/docs/pages/html/_static/language_data.js @@ -1,19 +1,12 @@ /* - * language_data.js - * ~~~~~~~~~~~~~~~~ - * * This script contains the language-specific data used by searchtools.js, * namely the list of stopwords, stemmer, scorer and splitter. - * - * :copyright: Copyright 2007-2023 by the Sphinx team, see AUTHORS. - * :license: BSD, see LICENSE for details. - * */ var stopwords = ["a", "and", "are", "as", "at", "be", "but", "by", "for", "if", "in", "into", "is", "it", "near", "no", "not", "of", "on", "or", "such", "that", "the", "their", "then", "there", "these", "they", "this", "to", "was", "will", "with"]; -/* Non-minified version is copied as a separate JS file, is available */ +/* Non-minified version is copied as a separate JS file, if available */ /** * Porter Stemmer diff --git a/docs/pages/html/_static/notebooks/pca_examples.html b/docs/pages/html/_static/notebooks/pca_examples.html index c9a75dc..7bb55a3 100644 --- a/docs/pages/html/_static/notebooks/pca_examples.html +++ b/docs/pages/html/_static/notebooks/pca_examples.html @@ -1,13 +1,9 @@ - - - + + + pca_examples - - - - - - - - - - - - - - + + + - - - - + void Promise.all([...diagrams].map(renderOneMarmaid)); + }); + + + + + + + - + pca A Python Package for Principal Component Analysis. The core of PCA is build on sklearn functionality to find maximum compatibility when combining with other packages. But this package can do a lot more. Besides the regular pca, it can also perform SparsePCA, and TruncatedSVD. Depending on your input data, the best approach will be choosen. Other functionalities are: @@ -15124,38 +7531,30 @@ github pca - - - + + -In [1]: +In [1]: - -!pip install pca + +!pip install pca - - - + - - - - - - - + + Requirement already satisfied: pca in /usr/local/lib/python3.7/dist-packages (1.7.2) Requirement already satisfied: matplotlib in /usr/local/lib/python3.7/dist-packages (from pca) (3.2.2) Requirement already satisfied: wget in /usr/local/lib/python3.7/dist-packages (from pca) (3.2) @@ -15180,179 +7579,149 @@ - - - - - + + - + Lets check the version - - - + + -In [2]: +In [2]: - -import pca + +import pca print(pca.__version__) - - - + - - - - - - - + + 1.7.2 - - - - - + + - + Import the pca library - - - + + -In [3]: +In [3]: - -from pca import pca + +from pca import pca import numpy as np import pandas as pd - - - - - + + + - + Here we will create a random dataset. - - - + + -In [4]: +In [4]: - -# Dataset + +# Dataset from sklearn.datasets import load_iris X = pd.DataFrame(data=load_iris().data, columns=load_iris().feature_names, index=load_iris().target) - - - - - + + + - + Initialize using specified parameters. The parameters here are the default parameters. - - - + + -In [5]: +In [5]: - -# Initialize + +# Initialize model = pca(n_components=3, normalize=True) - - - - - + + + -In [6]: +In [6]: - -# Fit transform + +# Fit transform out = model.fit_transform(X) - - - + - - - - - - - + + [pca] >Processing dataframe.. [pca] >Normalizing input data per feature (zero mean and unit variance).. [pca] >The PCA reduction is performed on the [4] columns of the input dataframe. @@ -15364,171 +7733,119 @@ - - - - - + + -In [7]: +In [7]: - -# Make plot with only the directions (no scatter) + +# Make plot with only the directions (no scatter) fig, ax = model.biplot(textlabel=True, legend=False, figsize=(10, 6)) - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 with loadings. - - - - - - - - + + + - - - - - - + + -In [8]: +In [8]: - -# Make plot with only the directions (no scatter) + +# Make plot with only the directions (no scatter) fig, ax = model.biplot(cmap=None, textlabel=False, legend=False, figsize=(10, 6)) - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 with loadings. - - - - - - - - + + + - - - - - - + + -In [9]: +In [9]: - -from pca import pca + +from pca import pca # Load example data from sklearn.datasets import load_iris X = pd.DataFrame(data=load_iris().data, columns=load_iris().feature_names, index=load_iris().target) - - - - - + + + -In [10]: +In [10]: - -# Initialize + +# Initialize model = pca(n_components=3) # Fit using PCA results = model.fit_transform(X) - - - + - - - - - - - + + [pca] >Processing dataframe.. [pca] >The PCA reduction is performed on the [4] columns of the input dataframe. [pca] >Fit using PCA. @@ -15539,20 +7856,17 @@ - - - - - + + -In [11]: +In [11]: - -# Make plots + +# Make plots # Scree plot fig, ax = model.plot(figsize=(10, 6)) @@ -15563,190 +7877,117 @@ # Biplot fig, ax = model.biplot(figsize=(10, 6)) - - - + - - - - - - - - - - + + + - - - - - - - - - + + + - - - - - - + + [pca] >Plot PC1 vs PC2 with loadings. - - - - - - - + + <Figure size 432x288 with 0 Axes> - - - - - - - - - + + + - - - - - - + + -In [17]: +In [17]: - -# Coloring on density to focus on the core samples. + +# Coloring on density to focus on the core samples. # Biplot -fig, ax = model.biplot(figsize=(10, 6), gradient='#ffffff') +fig, ax = model.biplot(figsize=(10, 6), gradient='#ffffff') - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 with loadings. - - - - - - - - + + + - - - - - - + + -In [18]: +In [18]: - -# Outliers are stored in results: -results['outliers'] + +# Outliers are stored in results: +results['outliers'] # Outliers based on T2 -print('--------T2------------') -print(results['outliers'].loc[results['outliers']['y_bool'], :]) +print('--------T2------------') +print(results['outliers'].loc[results['outliers']['y_bool'], :]) # Outliers based on SPE -print('--------SPE------------') -print(results['outliers'].loc[results['outliers']['y_bool_spe'], :]) +print('--------SPE------------') +print(results['outliers'].loc[results['outliers']['y_bool_spe'], :]) - - - + - - - - - - - + + --------T2------------ y_proba y_score y_bool y_bool_spe y_score_spe 2 0.040551 13.160880 True True 3.679935 @@ -15771,270 +8012,168 @@ - - - - - + + -In [20]: +In [20]: - -# Outlier detection + +# Outlier detection fig, ax = model.biplot(SPE=True, HT2=True, figsize=(10, 6)) - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 with loadings. - - - - - - - - + + + - - - - - - + + -In [21]: +In [21]: - -# 3D plots + +# 3D plots fig, ax = model.scatter3d(figsize=(10, 6)) fig, ax = model.biplot3d(figsize=(10, 6)) fig, ax = model.biplot3d(SPE=True, HT2=True, figsize=(10, 6)) - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 vs PC3 with loadings. - - - - - - - - + + + - - - - - - - - - + + + - - - - - - + + [pca] >Plot PC1 vs PC2 vs PC3 with loadings. - - - - - - - - + + + - - - - - - + + -In [22]: +In [22]: - -fig, ax = model.biplot3d(SPE=True, HT2=True, visible=False, figsize=(10, 6)) + +fig, ax = model.biplot3d(SPE=True, HT2=True, visible=False, figsize=(10, 6)) # Set the figure again to True and show the figure. fig.set_visible(True) fig - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 vs PC3 with loadings. - - Out[22]: - - - - - - +Out[22]: + + - - - - - - - - - + + + - - - - - - + + -In [23]: +In [23]: - -# Normalize out PCs + +
Let’s load the wine dataset to demonstrate the plots.
# Load library from sklearn.datasets import load_wine @@ -166,7 +165,7 @@ Load dataset -Scatter plot +Scatter plot # Make scatterplot model.scatter() @@ -187,7 +186,7 @@ Scatter plot -Scatterplots +Scatterplots @@ -204,16 +203,40 @@ Scatter plot -Biplot +Biplot +The biplot draws the loadings (arrows) together with the samples (scatterplot). +The loadings can be colored red and blue which indicates the strength of the particular feature in the PC. +For each principal component (PC), the feature is determined with the largest absolute loading. This indicates which feature contributes the most to each PC and can occur in multiple PCs. +The highest loading values for the features are colored red in the biplot and described as “best” in the output dataframe. +The features that were not seen with highest loadings for any PC are considered weaker features, and are colored blue the biplot. In the output dataframe these features are described as “weak”. # Make biplot model.biplot() # Here again, many other options can be turned on and off model.biplot(SPE=True, HT2=True, legend=1) + +# Show the top features +results['topfeat'] + +# PC feature loading type +# 0 PC1 flavanoids 0.422934 best +# 1 PC2 color_intensity 0.529996 best +# 2 PC3 ash 0.626224 best +# 3 PC4 malic_acid 0.536890 best +# 4 PC5 magnesium 0.727049 best +# 5 PC6 malic_acid 0.536814 best +# 6 PC7 nonflavanoid_phenols 0.595447 best +# 7 PC8 hue 0.436624 best +# 8 PC9 proline 0.575786 best +# 9 PC10 od280/od315_of_diluted_wines 0.523706 best +# 10 PC9 alcohol -0.508619 weak +# 11 PC3 alcalinity_of_ash 0.612080 weak +# 12 PC8 total_phenols -0.405934 weak +# 13 PC6 proanthocyanins -0.533795 weak -Biplots +Biplots @@ -223,28 +246,30 @@ Biplot -Biplot (only arrows) +Biplot (only arrows) # Make plot with parameters: set cmap to None and label and legend to False. Only directions will be plotted. model.biplot(cmap=None, legend=False) - + + -Explained variance plot +Explained variance plot model.plot() - + + -Alpha Transparency +Alpha Transparency fig, ax = model.scatter(alpha=1) -Markers +Markers import numpy as np from sklearn.datasets import make_friedman1 from pca import pca @@ -272,7 +297,7 @@ Markers -Biplots with markers +Biplots with markers @@ -280,7 +305,7 @@ Markers -Control color/marker/size per sample +Control color/marker/size per sample import numpy as np import matplotlib.pyplot as plt import matplotlib.colors as mcolors @@ -329,7 +354,7 @@ Control color/marker/size per sample -Biplot with customized properties per sample. +Biplot with customized properties per sample. @@ -337,15 +362,16 @@ Control color/marker/size per sample -3D plots +3D plots All plots can also be created in 3D by setting the d3=True parameter. model.biplot3d() - + + -Toggle visible status +Toggle visible status The visible status for can be turned on and off. # Make plot but not visible. fig, ax = model.biplot(visible=False) diff --git a/docs/pages/html/_sources/Plots.rst.txt b/docs/pages/html/_sources/Plots.rst.txt index 33319b2..38cd2db 100644 --- a/docs/pages/html/_sources/Plots.rst.txt +++ b/docs/pages/html/_sources/Plots.rst.txt @@ -83,6 +83,14 @@ Scatter plot Biplot ############### +The biplot draws the loadings (arrows) together with the samples (scatterplot). +The loadings can be colored red and blue which indicates the strength of the particular feature in the PC. + +For each principal component (PC), the feature is determined with the largest absolute loading. This indicates which feature contributes the most to each PC and can occur in multiple PCs. +The highest loading values for the features are colored red in the biplot and described as "best" in the output dataframe. +The features that were not seen with highest loadings for any PC are considered weaker features, and are colored blue the biplot. In the output dataframe these features are described as "weak". + + .. code:: python # Make biplot @@ -91,6 +99,24 @@ Biplot # Here again, many other options can be turned on and off model.biplot(SPE=True, HT2=True, legend=1) + # Show the top features + results['topfeat'] + + # PC feature loading type + # 0 PC1 flavanoids 0.422934 best + # 1 PC2 color_intensity 0.529996 best + # 2 PC3 ash 0.626224 best + # 3 PC4 malic_acid 0.536890 best + # 4 PC5 magnesium 0.727049 best + # 5 PC6 malic_acid 0.536814 best + # 6 PC7 nonflavanoid_phenols 0.595447 best + # 7 PC8 hue 0.436624 best + # 8 PC9 proline 0.575786 best + # 9 PC10 od280/od315_of_diluted_wines 0.523706 best + # 10 PC9 alcohol -0.508619 weak + # 11 PC3 alcalinity_of_ash 0.612080 weak + # 12 PC8 total_phenols -0.405934 weak + # 13 PC6 proanthocyanins -0.533795 weak .. |figP5| image:: ../figs/wine_biplot.png .. |figP6| image:: ../figs/wine_biplot_with_outliers.png diff --git a/docs/pages/html/_sources/sponsor.rst.txt b/docs/pages/html/_sources/sponsor.rst.txt index a46c410..f006896 100644 --- a/docs/pages/html/_sources/sponsor.rst.txt +++ b/docs/pages/html/_sources/sponsor.rst.txt @@ -4,8 +4,10 @@ * Become a `Sponsor `_! * `Buy `_ me a coffee! I ❤️ coffee :) * `Donate `_ in Bitcoin. - * Follow me on medium! Go to my `medium profile `_ and press *follow*. + * Follow me on Medium! Go to my `medium profile `_ and press *follow*. + * Subscribe to me on Substack! Go to my `profile `_ where you can *subscribe*. * **Star** this repo at the github page. + * You can also buy a digital educational product over `here `_. * Other contributions can be in the form of feature requests, idea discussions, reporting bugs, opening pull requests. Cheers Mate. diff --git a/docs/pages/html/_static/_sphinx_javascript_frameworks_compat.js b/docs/pages/html/_static/_sphinx_javascript_frameworks_compat.js new file mode 100644 index 0000000..8141580 --- /dev/null +++ b/docs/pages/html/_static/_sphinx_javascript_frameworks_compat.js @@ -0,0 +1,123 @@ +/* Compatability shim for jQuery and underscores.js. + * + * Copyright Sphinx contributors + * Released under the two clause BSD licence + */ + +/** + * small helper function to urldecode strings + * + * See https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/decodeURIComponent#Decoding_query_parameters_from_a_URL + */ +jQuery.urldecode = function(x) { + if (!x) { + return x + } + return decodeURIComponent(x.replace(/\+/g, ' ')); +}; + +/** + * small helper function to urlencode strings + */ +jQuery.urlencode = encodeURIComponent; + +/** + * This function returns the parsed url parameters of the + * current request. Multiple values per key are supported, + * it will always return arrays of strings for the value parts. + */ +jQuery.getQueryParameters = function(s) { + if (typeof s === 'undefined') + s = document.location.search; + var parts = s.substr(s.indexOf('?') + 1).split('&'); + var result = {}; + for (var i = 0; i < parts.length; i++) { + var tmp = parts[i].split('=', 2); + var key = jQuery.urldecode(tmp[0]); + var value = jQuery.urldecode(tmp[1]); + if (key in result) + result[key].push(value); + else + result[key] = [value]; + } + return result; +}; + +/** + * highlight a given string on a jquery object by wrapping it in + * span elements with the given class name. + */ +jQuery.fn.highlightText = function(text, className) { + function highlight(node, addItems) { + if (node.nodeType === 3) { + var val = node.nodeValue; + var pos = val.toLowerCase().indexOf(text); + if (pos >= 0 && + !jQuery(node.parentNode).hasClass(className) && + !jQuery(node.parentNode).hasClass("nohighlight")) { + var span; + var isInSVG = jQuery(node).closest("body, svg, foreignObject").is("svg"); + if (isInSVG) { + span = document.createElementNS("http://www.w3.org/2000/svg", "tspan"); + } else { + span = document.createElement("span"); + span.className = className; + } + span.appendChild(document.createTextNode(val.substr(pos, text.length))); + node.parentNode.insertBefore(span, node.parentNode.insertBefore( + document.createTextNode(val.substr(pos + text.length)), + node.nextSibling)); + node.nodeValue = val.substr(0, pos); + if (isInSVG) { + var rect = document.createElementNS("http://www.w3.org/2000/svg", "rect"); + var bbox = node.parentElement.getBBox(); + rect.x.baseVal.value = bbox.x; + rect.y.baseVal.value = bbox.y; + rect.width.baseVal.value = bbox.width; + rect.height.baseVal.value = bbox.height; + rect.setAttribute('class', className); + addItems.push({ + "parent": node.parentNode, + "target": rect}); + } + } + } + else if (!jQuery(node).is("button, select, textarea")) { + jQuery.each(node.childNodes, function() { + highlight(this, addItems); + }); + } + } + var addItems = []; + var result = this.each(function() { + highlight(this, addItems); + }); + for (var i = 0; i < addItems.length; ++i) { + jQuery(addItems[i].parent).before(addItems[i].target); + } + return result; +}; + +/* + * backward compatibility for jQuery.browser + * This will be supported until firefox bug is fixed. + */ +if (!jQuery.browser) { + jQuery.uaMatch = function(ua) { + ua = ua.toLowerCase(); + + var match = /(chrome)[ \/]([\w.]+)/.exec(ua) || + /(webkit)[ \/]([\w.]+)/.exec(ua) || + /(opera)(?:.*version|)[ \/]([\w.]+)/.exec(ua) || + /(msie) ([\w.]+)/.exec(ua) || + ua.indexOf("compatible") < 0 && /(mozilla)(?:.*? rv:([\w.]+)|)/.exec(ua) || + []; + + return { + browser: match[ 1 ] || "", + version: match[ 2 ] || "0" + }; + }; + jQuery.browser = {}; + jQuery.browser[jQuery.uaMatch(navigator.userAgent).browser] = true; +} diff --git a/docs/pages/html/_static/basic.css b/docs/pages/html/_static/basic.css index 7577acb..7ebbd6d 100644 --- a/docs/pages/html/_static/basic.css +++ b/docs/pages/html/_static/basic.css @@ -1,12 +1,5 @@ /* - * basic.css - * ~~~~~~~~~ - * * Sphinx stylesheet -- basic theme. - * - * :copyright: Copyright 2007-2023 by the Sphinx team, see AUTHORS. - * :license: BSD, see LICENSE for details. - * */ /* -- main layout ----------------------------------------------------------- */ @@ -115,15 +108,11 @@ img { /* -- search page ----------------------------------------------------------- */ ul.search { - margin: 10px 0 0 20px; - padding: 0; + margin-top: 10px; } ul.search li { - padding: 5px 0 5px 20px; - background-image: url(file.png); - background-repeat: no-repeat; - background-position: 0 7px; + padding: 5px 0; } ul.search li a { @@ -237,6 +226,10 @@ a.headerlink { visibility: hidden; } +a:visited { + color: #551A8B; +} + h1:hover > a.headerlink, h2:hover > a.headerlink, h3:hover > a.headerlink, @@ -670,6 +663,16 @@ dd { 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{ + const config = event.detail.data(); + + const flyout = ` + + + Read the Docs + v: ${config.versions.current.slug} + + + + + ${renderLanguages(config)} + ${renderVersions(config)} + ${renderDownloads(config)} + + On Read the Docs + + Project Home + + + Builds + + + Downloads + + + + Search + + + + + + + + + Hosted by Read the Docs + + + + `; + + // Inject the generated flyout into the body HTML element. + document.body.insertAdjacentHTML("beforeend", flyout); + + // Trigger the Read the Docs Addons Search modal when clicking on the "Search docs" input from inside the flyout. + document + .querySelector("#flyout-search-form") + .addEventListener("focusin", () => { + const event = new CustomEvent("readthedocs-search-show"); + document.dispatchEvent(event); + }); + }) +} + +if (themeLanguageSelector || themeVersionSelector) { + function onSelectorSwitch(event) { + const option = event.target.selectedIndex; + const item = event.target.options[option]; + window.location.href = item.dataset.url; + } + + document.addEventListener("readthedocs-addons-data-ready", function (event) { + const config = event.detail.data(); + + const versionSwitch = document.querySelector( + "div.switch-menus > div.version-switch", + ); + if (themeVersionSelector) { + let versions = config.versions.active; + if (config.versions.current.hidden || config.versions.current.type === "external") { + versions.unshift(config.versions.current); + } + const versionSelect = ` + + ${versions + .map( + (version) => ` + + ${version.slug} + `, + ) + .join("\n")} + + `; + + versionSwitch.innerHTML = versionSelect; + versionSwitch.firstElementChild.addEventListener("change", onSelectorSwitch); + } + + const languageSwitch = document.querySelector( + "div.switch-menus > div.language-switch", + ); + + if (themeLanguageSelector) { + if (config.projects.translations.length) { + // Add the current language to the options on the selector + let languages = config.projects.translations.concat( + config.projects.current, + ); + languages = languages.sort((a, b) => + a.language.name.localeCompare(b.language.name), + ); + + const languageSelect = ` + + ${languages + .map( + (language) => ` + + ${language.language.name} + `, + ) + .join("\n")} + + `; + + languageSwitch.innerHTML = languageSelect; + languageSwitch.firstElementChild.addEventListener("change", onSelectorSwitch); + } + else { + languageSwitch.remove(); + } + } + }); +} + +document.addEventListener("readthedocs-addons-data-ready", function (event) { + // Trigger the Read the Docs Addons Search modal when clicking on "Search docs" input from the topnav. + document + .querySelector("[role='search'] input") + .addEventListener("focusin", () => { + const event = new CustomEvent("readthedocs-search-show"); + document.dispatchEvent(event); + }); +}); \ No newline at end of file diff --git a/docs/pages/html/_static/language_data.js b/docs/pages/html/_static/language_data.js index 250f566..c7fe6c6 100644 --- a/docs/pages/html/_static/language_data.js +++ b/docs/pages/html/_static/language_data.js @@ -1,19 +1,12 @@ /* - * language_data.js - * ~~~~~~~~~~~~~~~~ - * * This script contains the language-specific data used by searchtools.js, * namely the list of stopwords, stemmer, scorer and splitter. - * - * :copyright: Copyright 2007-2023 by the Sphinx team, see AUTHORS. - * :license: BSD, see LICENSE for details. - * */ var stopwords = ["a", "and", "are", "as", "at", "be", "but", "by", "for", "if", "in", "into", "is", "it", "near", "no", "not", "of", "on", "or", "such", "that", "the", "their", "then", "there", "these", "they", "this", "to", "was", "will", "with"]; -/* Non-minified version is copied as a separate JS file, is available */ +/* Non-minified version is copied as a separate JS file, if available */ /** * Porter Stemmer diff --git a/docs/pages/html/_static/notebooks/pca_examples.html b/docs/pages/html/_static/notebooks/pca_examples.html index c9a75dc..7bb55a3 100644 --- a/docs/pages/html/_static/notebooks/pca_examples.html +++ b/docs/pages/html/_static/notebooks/pca_examples.html @@ -1,13 +1,9 @@ - - - + + + pca_examples - - - - - - - - - - - - - - + + + - - - - + void Promise.all([...diagrams].map(renderOneMarmaid)); + }); + + + + + + + - + pca A Python Package for Principal Component Analysis. The core of PCA is build on sklearn functionality to find maximum compatibility when combining with other packages. But this package can do a lot more. Besides the regular pca, it can also perform SparsePCA, and TruncatedSVD. Depending on your input data, the best approach will be choosen. Other functionalities are: @@ -15124,38 +7531,30 @@ github pca - - - + + -In [1]: +In [1]: - -!pip install pca + +!pip install pca - - - + - - - - - - - + + Requirement already satisfied: pca in /usr/local/lib/python3.7/dist-packages (1.7.2) Requirement already satisfied: matplotlib in /usr/local/lib/python3.7/dist-packages (from pca) (3.2.2) Requirement already satisfied: wget in /usr/local/lib/python3.7/dist-packages (from pca) (3.2) @@ -15180,179 +7579,149 @@ - - - - - + + - + Lets check the version - - - + + -In [2]: +In [2]: - -import pca + +import pca print(pca.__version__) - - - + - - - - - - - + + 1.7.2 - - - - - + + - + Import the pca library - - - + + -In [3]: +In [3]: - -from pca import pca + +from pca import pca import numpy as np import pandas as pd - - - - - + + + - + Here we will create a random dataset. - - - + + -In [4]: +In [4]: - -# Dataset + +# Dataset from sklearn.datasets import load_iris X = pd.DataFrame(data=load_iris().data, columns=load_iris().feature_names, index=load_iris().target) - - - - - + + + - + Initialize using specified parameters. The parameters here are the default parameters. - - - + + -In [5]: +In [5]: - -# Initialize + +# Initialize model = pca(n_components=3, normalize=True) - - - - - + + + -In [6]: +In [6]: - -# Fit transform + +# Fit transform out = model.fit_transform(X) - - - + - - - - - - - + + [pca] >Processing dataframe.. [pca] >Normalizing input data per feature (zero mean and unit variance).. [pca] >The PCA reduction is performed on the [4] columns of the input dataframe. @@ -15364,171 +7733,119 @@ - - - - - + + -In [7]: +In [7]: - -# Make plot with only the directions (no scatter) + +# Make plot with only the directions (no scatter) fig, ax = model.biplot(textlabel=True, legend=False, figsize=(10, 6)) - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 with loadings. - - - - - - - - + + + - - - - - - + + -In [8]: +In [8]: - -# Make plot with only the directions (no scatter) + +# Make plot with only the directions (no scatter) fig, ax = model.biplot(cmap=None, textlabel=False, legend=False, figsize=(10, 6)) - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 with loadings. - - - - - - - - + + + - - - - - - + + -In [9]: +In [9]: - -from pca import pca + +from pca import pca # Load example data from sklearn.datasets import load_iris X = pd.DataFrame(data=load_iris().data, columns=load_iris().feature_names, index=load_iris().target) - - - - - + + + -In [10]: +In [10]: - -# Initialize + +# Initialize model = pca(n_components=3) # Fit using PCA results = model.fit_transform(X) - - - + - - - - - - - + + [pca] >Processing dataframe.. [pca] >The PCA reduction is performed on the [4] columns of the input dataframe. [pca] >Fit using PCA. @@ -15539,20 +7856,17 @@ - - - - - + + -In [11]: +In [11]: - -# Make plots + +# Make plots # Scree plot fig, ax = model.plot(figsize=(10, 6)) @@ -15563,190 +7877,117 @@ # Biplot fig, ax = model.biplot(figsize=(10, 6)) - - - + - - - - - - - - - - + + + - - - - - - - - - + + + - - - - - - + + [pca] >Plot PC1 vs PC2 with loadings. - - - - - - - + + <Figure size 432x288 with 0 Axes> - - - - - - - - - + + + - - - - - - + + -In [17]: +In [17]: - -# Coloring on density to focus on the core samples. + +# Coloring on density to focus on the core samples. # Biplot -fig, ax = model.biplot(figsize=(10, 6), gradient='#ffffff') +fig, ax = model.biplot(figsize=(10, 6), gradient='#ffffff') - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 with loadings. - - - - - - - - + + + - - - - - - + + -In [18]: +In [18]: - -# Outliers are stored in results: -results['outliers'] + +# Outliers are stored in results: +results['outliers'] # Outliers based on T2 -print('--------T2------------') -print(results['outliers'].loc[results['outliers']['y_bool'], :]) +print('--------T2------------') +print(results['outliers'].loc[results['outliers']['y_bool'], :]) # Outliers based on SPE -print('--------SPE------------') -print(results['outliers'].loc[results['outliers']['y_bool_spe'], :]) +print('--------SPE------------') +print(results['outliers'].loc[results['outliers']['y_bool_spe'], :]) - - - + - - - - - - - + + --------T2------------ y_proba y_score y_bool y_bool_spe y_score_spe 2 0.040551 13.160880 True True 3.679935 @@ -15771,270 +8012,168 @@ - - - - - + + -In [20]: +In [20]: - -# Outlier detection + +# Outlier detection fig, ax = model.biplot(SPE=True, HT2=True, figsize=(10, 6)) - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 with loadings. - - - - - - - - + + + - - - - - - + + -In [21]: +In [21]: - -# 3D plots + +# 3D plots fig, ax = model.scatter3d(figsize=(10, 6)) fig, ax = model.biplot3d(figsize=(10, 6)) fig, ax = model.biplot3d(SPE=True, HT2=True, figsize=(10, 6)) - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 vs PC3 with loadings. - - - - - - - - + + + - - - - - - - - - + + + - - - - - - + + [pca] >Plot PC1 vs PC2 vs PC3 with loadings. - - - - - - - - + + + - - - - - - + + -In [22]: +In [22]: - -fig, ax = model.biplot3d(SPE=True, HT2=True, visible=False, figsize=(10, 6)) + +fig, ax = model.biplot3d(SPE=True, HT2=True, visible=False, figsize=(10, 6)) # Set the figure again to True and show the figure. fig.set_visible(True) fig - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 vs PC3 with loadings. - - Out[22]: - - - - - - +Out[22]: + + - - - - - - - - - + + + - - - - - - + + -In [23]: +In [23]: - -# Normalize out PCs + +
# Make scatterplot model.scatter() @@ -187,7 +186,7 @@ Scatter plot -Scatterplots +Scatterplots @@ -204,16 +203,40 @@ Scatter plot -Biplot +Biplot +The biplot draws the loadings (arrows) together with the samples (scatterplot). +The loadings can be colored red and blue which indicates the strength of the particular feature in the PC. +For each principal component (PC), the feature is determined with the largest absolute loading. This indicates which feature contributes the most to each PC and can occur in multiple PCs. +The highest loading values for the features are colored red in the biplot and described as “best” in the output dataframe. +The features that were not seen with highest loadings for any PC are considered weaker features, and are colored blue the biplot. In the output dataframe these features are described as “weak”. # Make biplot model.biplot() # Here again, many other options can be turned on and off model.biplot(SPE=True, HT2=True, legend=1) + +# Show the top features +results['topfeat'] + +# PC feature loading type +# 0 PC1 flavanoids 0.422934 best +# 1 PC2 color_intensity 0.529996 best +# 2 PC3 ash 0.626224 best +# 3 PC4 malic_acid 0.536890 best +# 4 PC5 magnesium 0.727049 best +# 5 PC6 malic_acid 0.536814 best +# 6 PC7 nonflavanoid_phenols 0.595447 best +# 7 PC8 hue 0.436624 best +# 8 PC9 proline 0.575786 best +# 9 PC10 od280/od315_of_diluted_wines 0.523706 best +# 10 PC9 alcohol -0.508619 weak +# 11 PC3 alcalinity_of_ash 0.612080 weak +# 12 PC8 total_phenols -0.405934 weak +# 13 PC6 proanthocyanins -0.533795 weak -Biplots +Biplots @@ -223,28 +246,30 @@ Biplot -Biplot (only arrows) +Biplot (only arrows) # Make plot with parameters: set cmap to None and label and legend to False. Only directions will be plotted. model.biplot(cmap=None, legend=False) - + + -Explained variance plot +Explained variance plot model.plot() - + + -Alpha Transparency +Alpha Transparency fig, ax = model.scatter(alpha=1) -Markers +Markers import numpy as np from sklearn.datasets import make_friedman1 from pca import pca @@ -272,7 +297,7 @@ Markers -Biplots with markers +Biplots with markers @@ -280,7 +305,7 @@ Markers -Control color/marker/size per sample +Control color/marker/size per sample import numpy as np import matplotlib.pyplot as plt import matplotlib.colors as mcolors @@ -329,7 +354,7 @@ Control color/marker/size per sample -Biplot with customized properties per sample. +Biplot with customized properties per sample. @@ -337,15 +362,16 @@ Control color/marker/size per sample -3D plots +3D plots All plots can also be created in 3D by setting the d3=True parameter. model.biplot3d() - + + -Toggle visible status +Toggle visible status The visible status for can be turned on and off. # Make plot but not visible. fig, ax = model.biplot(visible=False) diff --git a/docs/pages/html/_sources/Plots.rst.txt b/docs/pages/html/_sources/Plots.rst.txt index 33319b2..38cd2db 100644 --- a/docs/pages/html/_sources/Plots.rst.txt +++ b/docs/pages/html/_sources/Plots.rst.txt @@ -83,6 +83,14 @@ Scatter plot Biplot ############### +The biplot draws the loadings (arrows) together with the samples (scatterplot). +The loadings can be colored red and blue which indicates the strength of the particular feature in the PC. + +For each principal component (PC), the feature is determined with the largest absolute loading. This indicates which feature contributes the most to each PC and can occur in multiple PCs. +The highest loading values for the features are colored red in the biplot and described as "best" in the output dataframe. +The features that were not seen with highest loadings for any PC are considered weaker features, and are colored blue the biplot. In the output dataframe these features are described as "weak". + + .. code:: python # Make biplot @@ -91,6 +99,24 @@ Biplot # Here again, many other options can be turned on and off model.biplot(SPE=True, HT2=True, legend=1) + # Show the top features + results['topfeat'] + + # PC feature loading type + # 0 PC1 flavanoids 0.422934 best + # 1 PC2 color_intensity 0.529996 best + # 2 PC3 ash 0.626224 best + # 3 PC4 malic_acid 0.536890 best + # 4 PC5 magnesium 0.727049 best + # 5 PC6 malic_acid 0.536814 best + # 6 PC7 nonflavanoid_phenols 0.595447 best + # 7 PC8 hue 0.436624 best + # 8 PC9 proline 0.575786 best + # 9 PC10 od280/od315_of_diluted_wines 0.523706 best + # 10 PC9 alcohol -0.508619 weak + # 11 PC3 alcalinity_of_ash 0.612080 weak + # 12 PC8 total_phenols -0.405934 weak + # 13 PC6 proanthocyanins -0.533795 weak .. |figP5| image:: ../figs/wine_biplot.png .. |figP6| image:: ../figs/wine_biplot_with_outliers.png diff --git a/docs/pages/html/_sources/sponsor.rst.txt b/docs/pages/html/_sources/sponsor.rst.txt index a46c410..f006896 100644 --- a/docs/pages/html/_sources/sponsor.rst.txt +++ b/docs/pages/html/_sources/sponsor.rst.txt @@ -4,8 +4,10 @@ * Become a `Sponsor `_! * `Buy `_ me a coffee! I ❤️ coffee :) * `Donate `_ in Bitcoin. - * Follow me on medium! Go to my `medium profile `_ and press *follow*. + * Follow me on Medium! Go to my `medium profile `_ and press *follow*. + * Subscribe to me on Substack! Go to my `profile `_ where you can *subscribe*. * **Star** this repo at the github page. + * You can also buy a digital educational product over `here `_. * Other contributions can be in the form of feature requests, idea discussions, reporting bugs, opening pull requests. Cheers Mate. diff --git a/docs/pages/html/_static/_sphinx_javascript_frameworks_compat.js b/docs/pages/html/_static/_sphinx_javascript_frameworks_compat.js new file mode 100644 index 0000000..8141580 --- /dev/null +++ b/docs/pages/html/_static/_sphinx_javascript_frameworks_compat.js @@ -0,0 +1,123 @@ +/* Compatability shim for jQuery and underscores.js. + * + * Copyright Sphinx contributors + * Released under the two clause BSD licence + */ + +/** + * small helper function to urldecode strings + * + * See https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/decodeURIComponent#Decoding_query_parameters_from_a_URL + */ +jQuery.urldecode = function(x) { + if (!x) { + return x + } + return decodeURIComponent(x.replace(/\+/g, ' ')); +}; + +/** + * small helper function to urlencode strings + */ +jQuery.urlencode = encodeURIComponent; + +/** + * This function returns the parsed url parameters of the + * current request. Multiple values per key are supported, + * it will always return arrays of strings for the value parts. + */ +jQuery.getQueryParameters = function(s) { + if (typeof s === 'undefined') + s = document.location.search; + var parts = s.substr(s.indexOf('?') + 1).split('&'); + var result = {}; + for (var i = 0; i < parts.length; i++) { + var tmp = parts[i].split('=', 2); + var key = jQuery.urldecode(tmp[0]); + var value = jQuery.urldecode(tmp[1]); + if (key in result) + result[key].push(value); + else + result[key] = [value]; + } + return result; +}; + +/** + * highlight a given string on a jquery object by wrapping it in + * span elements with the given class name. + */ +jQuery.fn.highlightText = function(text, className) { + function highlight(node, addItems) { + if (node.nodeType === 3) { + var val = node.nodeValue; + var pos = val.toLowerCase().indexOf(text); + if (pos >= 0 && + !jQuery(node.parentNode).hasClass(className) && + !jQuery(node.parentNode).hasClass("nohighlight")) { + var span; + var isInSVG = jQuery(node).closest("body, svg, foreignObject").is("svg"); + if (isInSVG) { + span = document.createElementNS("http://www.w3.org/2000/svg", "tspan"); + } else { + span = document.createElement("span"); + span.className = className; + } + span.appendChild(document.createTextNode(val.substr(pos, text.length))); + node.parentNode.insertBefore(span, node.parentNode.insertBefore( + document.createTextNode(val.substr(pos + text.length)), + node.nextSibling)); + node.nodeValue = val.substr(0, pos); + if (isInSVG) { + var rect = document.createElementNS("http://www.w3.org/2000/svg", "rect"); + var bbox = node.parentElement.getBBox(); + rect.x.baseVal.value = bbox.x; + rect.y.baseVal.value = bbox.y; + rect.width.baseVal.value = bbox.width; + rect.height.baseVal.value = bbox.height; + rect.setAttribute('class', className); + addItems.push({ + "parent": node.parentNode, + "target": rect}); + } + } + } + else if (!jQuery(node).is("button, select, textarea")) { + jQuery.each(node.childNodes, function() { + highlight(this, addItems); + }); + } + } + var addItems = []; + var result = this.each(function() { + highlight(this, addItems); + }); + for (var i = 0; i < addItems.length; ++i) { + jQuery(addItems[i].parent).before(addItems[i].target); + } + return result; +}; + +/* + * backward compatibility for jQuery.browser + * This will be supported until firefox bug is fixed. + */ +if (!jQuery.browser) { + jQuery.uaMatch = function(ua) { + ua = ua.toLowerCase(); + + var match = /(chrome)[ \/]([\w.]+)/.exec(ua) || + /(webkit)[ \/]([\w.]+)/.exec(ua) || + /(opera)(?:.*version|)[ \/]([\w.]+)/.exec(ua) || + /(msie) ([\w.]+)/.exec(ua) || + ua.indexOf("compatible") < 0 && /(mozilla)(?:.*? rv:([\w.]+)|)/.exec(ua) || + []; + + return { + browser: match[ 1 ] || "", + version: match[ 2 ] || "0" + }; + }; + jQuery.browser = {}; + jQuery.browser[jQuery.uaMatch(navigator.userAgent).browser] = true; +} diff --git a/docs/pages/html/_static/basic.css b/docs/pages/html/_static/basic.css index 7577acb..7ebbd6d 100644 --- a/docs/pages/html/_static/basic.css +++ b/docs/pages/html/_static/basic.css @@ -1,12 +1,5 @@ /* - * basic.css - * ~~~~~~~~~ - * * Sphinx stylesheet -- basic theme. - * - * :copyright: Copyright 2007-2023 by the Sphinx team, see AUTHORS. - * :license: BSD, see LICENSE for details. - * */ /* -- main layout ----------------------------------------------------------- */ @@ -115,15 +108,11 @@ img { /* -- search page ----------------------------------------------------------- */ ul.search { - margin: 10px 0 0 20px; - padding: 0; + margin-top: 10px; } ul.search li { - padding: 5px 0 5px 20px; - background-image: url(file.png); - background-repeat: no-repeat; - background-position: 0 7px; + padding: 5px 0; } ul.search li a { @@ -237,6 +226,10 @@ a.headerlink { visibility: hidden; } +a:visited { + color: #551A8B; +} + h1:hover > a.headerlink, h2:hover > a.headerlink, h3:hover > a.headerlink, @@ -670,6 +663,16 @@ dd { 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video",version:m,shivCSS:n.shivCSS!==!1,supportsUnknownElements:l,shivMethods:n.shivMethods!==!1,type:"default",shivDocument:j,createElement:g,createDocumentFragment:h,addElements:e};a.html5=t,j(b),"object"==typeof module&&module.exports&&(module.exports=t)}("undefined"!=typeof window?window:this,document); \ No newline at end of file diff --git a/docs/pages/html/_static/js/versions.js b/docs/pages/html/_static/js/versions.js new file mode 100644 index 0000000..4958195 --- /dev/null +++ b/docs/pages/html/_static/js/versions.js @@ -0,0 +1,228 @@ +const themeFlyoutDisplay = "hidden"; +const themeVersionSelector = true; +const themeLanguageSelector = true; + +if (themeFlyoutDisplay === "attached") { + function renderLanguages(config) { + if (!config.projects.translations.length) { + return ""; + } + + // Insert the current language to the options on the selector + let languages = config.projects.translations.concat(config.projects.current); + languages = languages.sort((a, b) => a.language.name.localeCompare(b.language.name)); + + const languagesHTML = ` + + Languages + ${languages + .map( + (translation) => ` + + ${translation.language.code} + + `, + ) + .join("\n")} + + `; + return languagesHTML; + } + + function renderVersions(config) { + if (!config.versions.active.length) { + return ""; + } + const versionsHTML = ` + + Versions + ${config.versions.active + .map( + (version) => ` + + ${version.slug} + + `, + ) + .join("\n")} + + `; + return versionsHTML; + } + + function renderDownloads(config) { + if (!Object.keys(config.versions.current.downloads).length) { + return ""; + } + const downloadsNameDisplay = { + pdf: "PDF", + epub: "Epub", + htmlzip: "HTML", + }; + + const downloadsHTML = ` + + Downloads + ${Object.entries(config.versions.current.downloads) + .map( + ([name, url]) => ` + + ${downloadsNameDisplay[name]} + + `, + ) + .join("\n")} + + `; + return downloadsHTML; + } + + document.addEventListener("readthedocs-addons-data-ready", function (event) { + const config = event.detail.data(); + + const flyout = ` + + + Read the Docs + v: ${config.versions.current.slug} + + + + + ${renderLanguages(config)} + ${renderVersions(config)} + ${renderDownloads(config)} + + On Read the Docs + + Project Home + + + Builds + + + Downloads + + + + Search + + + + + + + + + Hosted by Read the Docs + + + + `; + + // Inject the generated flyout into the body HTML element. + document.body.insertAdjacentHTML("beforeend", flyout); + + // Trigger the Read the Docs Addons Search modal when clicking on the "Search docs" input from inside the flyout. + document + .querySelector("#flyout-search-form") + .addEventListener("focusin", () => { + const event = new CustomEvent("readthedocs-search-show"); + document.dispatchEvent(event); + }); + }) +} + +if (themeLanguageSelector || themeVersionSelector) { + function onSelectorSwitch(event) { + const option = event.target.selectedIndex; + const item = event.target.options[option]; + window.location.href = item.dataset.url; + } + + document.addEventListener("readthedocs-addons-data-ready", function (event) { + const config = event.detail.data(); + + const versionSwitch = document.querySelector( + "div.switch-menus > div.version-switch", + ); + if (themeVersionSelector) { + let versions = config.versions.active; + if (config.versions.current.hidden || config.versions.current.type === "external") { + versions.unshift(config.versions.current); + } + const versionSelect = ` + + ${versions + .map( + (version) => ` + + ${version.slug} + `, + ) + .join("\n")} + + `; + + versionSwitch.innerHTML = versionSelect; + versionSwitch.firstElementChild.addEventListener("change", onSelectorSwitch); + } + + const languageSwitch = document.querySelector( + "div.switch-menus > div.language-switch", + ); + + if (themeLanguageSelector) { + if (config.projects.translations.length) { + // Add the current language to the options on the selector + let languages = config.projects.translations.concat( + config.projects.current, + ); + languages = languages.sort((a, b) => + a.language.name.localeCompare(b.language.name), + ); + + const languageSelect = ` + + ${languages + .map( + (language) => ` + + ${language.language.name} + `, + ) + .join("\n")} + + `; + + languageSwitch.innerHTML = languageSelect; + languageSwitch.firstElementChild.addEventListener("change", onSelectorSwitch); + } + else { + languageSwitch.remove(); + } + } + }); +} + +document.addEventListener("readthedocs-addons-data-ready", function (event) { + // Trigger the Read the Docs Addons Search modal when clicking on "Search docs" input from the topnav. + document + .querySelector("[role='search'] input") + .addEventListener("focusin", () => { + const event = new CustomEvent("readthedocs-search-show"); + document.dispatchEvent(event); + }); +}); \ No newline at end of file diff --git a/docs/pages/html/_static/language_data.js b/docs/pages/html/_static/language_data.js index 250f566..c7fe6c6 100644 --- a/docs/pages/html/_static/language_data.js +++ b/docs/pages/html/_static/language_data.js @@ -1,19 +1,12 @@ /* - * language_data.js - * ~~~~~~~~~~~~~~~~ - * * This script contains the language-specific data used by searchtools.js, * namely the list of stopwords, stemmer, scorer and splitter. - * - * :copyright: Copyright 2007-2023 by the Sphinx team, see AUTHORS. - * :license: BSD, see LICENSE for details. - * */ var stopwords = ["a", "and", "are", "as", "at", "be", "but", "by", "for", "if", "in", "into", "is", "it", "near", "no", "not", "of", "on", "or", "such", "that", "the", "their", "then", "there", "these", "they", "this", "to", "was", "will", "with"]; -/* Non-minified version is copied as a separate JS file, is available */ +/* Non-minified version is copied as a separate JS file, if available */ /** * Porter Stemmer diff --git a/docs/pages/html/_static/notebooks/pca_examples.html b/docs/pages/html/_static/notebooks/pca_examples.html index c9a75dc..7bb55a3 100644 --- a/docs/pages/html/_static/notebooks/pca_examples.html +++ b/docs/pages/html/_static/notebooks/pca_examples.html @@ -1,13 +1,9 @@ - - - + + + pca_examples - - - - - - - - - - - - - - + + + - - - - + void Promise.all([...diagrams].map(renderOneMarmaid)); + }); + + + + + + + - + pca A Python Package for Principal Component Analysis. The core of PCA is build on sklearn functionality to find maximum compatibility when combining with other packages. But this package can do a lot more. Besides the regular pca, it can also perform SparsePCA, and TruncatedSVD. Depending on your input data, the best approach will be choosen. Other functionalities are: @@ -15124,38 +7531,30 @@ github pca - - - + + -In [1]: +In [1]: - -!pip install pca + +!pip install pca - - - + - - - - - - - + + Requirement already satisfied: pca in /usr/local/lib/python3.7/dist-packages (1.7.2) Requirement already satisfied: matplotlib in /usr/local/lib/python3.7/dist-packages (from pca) (3.2.2) Requirement already satisfied: wget in /usr/local/lib/python3.7/dist-packages (from pca) (3.2) @@ -15180,179 +7579,149 @@ - - - - - + + - + Lets check the version - - - + + -In [2]: +In [2]: - -import pca + +import pca print(pca.__version__) - - - + - - - - - - - + + 1.7.2 - - - - - + + - + Import the pca library - - - + + -In [3]: +In [3]: - -from pca import pca + +from pca import pca import numpy as np import pandas as pd - - - - - + + + - + Here we will create a random dataset. - - - + + -In [4]: +In [4]: - -# Dataset + +# Dataset from sklearn.datasets import load_iris X = pd.DataFrame(data=load_iris().data, columns=load_iris().feature_names, index=load_iris().target) - - - - - + + + - + Initialize using specified parameters. The parameters here are the default parameters. - - - + + -In [5]: +In [5]: - -# Initialize + +# Initialize model = pca(n_components=3, normalize=True) - - - - - + + + -In [6]: +In [6]: - -# Fit transform + +# Fit transform out = model.fit_transform(X) - - - + - - - - - - - + + [pca] >Processing dataframe.. [pca] >Normalizing input data per feature (zero mean and unit variance).. [pca] >The PCA reduction is performed on the [4] columns of the input dataframe. @@ -15364,171 +7733,119 @@ - - - - - + + -In [7]: +In [7]: - -# Make plot with only the directions (no scatter) + +# Make plot with only the directions (no scatter) fig, ax = model.biplot(textlabel=True, legend=False, figsize=(10, 6)) - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 with loadings. - - - - - - - - + + + - - - - - - + + -In [8]: +In [8]: - -# Make plot with only the directions (no scatter) + +# Make plot with only the directions (no scatter) fig, ax = model.biplot(cmap=None, textlabel=False, legend=False, figsize=(10, 6)) - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 with loadings. - - - - - - - - + + + - - - - - - + + -In [9]: +In [9]: - -from pca import pca + +from pca import pca # Load example data from sklearn.datasets import load_iris X = pd.DataFrame(data=load_iris().data, columns=load_iris().feature_names, index=load_iris().target) - - - - - + + + -In [10]: +In [10]: - -# Initialize + +# Initialize model = pca(n_components=3) # Fit using PCA results = model.fit_transform(X) - - - + - - - - - - - + + [pca] >Processing dataframe.. [pca] >The PCA reduction is performed on the [4] columns of the input dataframe. [pca] >Fit using PCA. @@ -15539,20 +7856,17 @@ - - - - - + + -In [11]: +In [11]: - -# Make plots + +# Make plots # Scree plot fig, ax = model.plot(figsize=(10, 6)) @@ -15563,190 +7877,117 @@ # Biplot fig, ax = model.biplot(figsize=(10, 6)) - - - + - - - - - - - - - - + + + - - - - - - - - - + + + - - - - - - + + [pca] >Plot PC1 vs PC2 with loadings. - - - - - - - + + <Figure size 432x288 with 0 Axes> - - - - - - - - - + + + - - - - - - + + -In [17]: +In [17]: - -# Coloring on density to focus on the core samples. + +# Coloring on density to focus on the core samples. # Biplot -fig, ax = model.biplot(figsize=(10, 6), gradient='#ffffff') +fig, ax = model.biplot(figsize=(10, 6), gradient='#ffffff') - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 with loadings. - - - - - - - - + + + - - - - - - + + -In [18]: +In [18]: - -# Outliers are stored in results: -results['outliers'] + +# Outliers are stored in results: +results['outliers'] # Outliers based on T2 -print('--------T2------------') -print(results['outliers'].loc[results['outliers']['y_bool'], :]) +print('--------T2------------') +print(results['outliers'].loc[results['outliers']['y_bool'], :]) # Outliers based on SPE -print('--------SPE------------') -print(results['outliers'].loc[results['outliers']['y_bool_spe'], :]) +print('--------SPE------------') +print(results['outliers'].loc[results['outliers']['y_bool_spe'], :]) - - - + - - - - - - - + + --------T2------------ y_proba y_score y_bool y_bool_spe y_score_spe 2 0.040551 13.160880 True True 3.679935 @@ -15771,270 +8012,168 @@ - - - - - + + -In [20]: +In [20]: - -# Outlier detection + +# Outlier detection fig, ax = model.biplot(SPE=True, HT2=True, figsize=(10, 6)) - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 with loadings. - - - - - - - - + + + - - - - - - + + -In [21]: +In [21]: - -# 3D plots + +# 3D plots fig, ax = model.scatter3d(figsize=(10, 6)) fig, ax = model.biplot3d(figsize=(10, 6)) fig, ax = model.biplot3d(SPE=True, HT2=True, figsize=(10, 6)) - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 vs PC3 with loadings. - - - - - - - - + + + - - - - - - - - - + + + - - - - - - + + [pca] >Plot PC1 vs PC2 vs PC3 with loadings. - - - - - - - - + + + - - - - - - + + -In [22]: +In [22]: - -fig, ax = model.biplot3d(SPE=True, HT2=True, visible=False, figsize=(10, 6)) + +fig, ax = model.biplot3d(SPE=True, HT2=True, visible=False, figsize=(10, 6)) # Set the figure again to True and show the figure. fig.set_visible(True) fig - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 vs PC3 with loadings. - - Out[22]: - - - - - - +Out[22]: + + - - - - - - - - - + + + - - - - - - + + -In [23]: +In [23]: - -# Normalize out PCs + +
The biplot draws the loadings (arrows) together with the samples (scatterplot). +The loadings can be colored red and blue which indicates the strength of the particular feature in the PC.
For each principal component (PC), the feature is determined with the largest absolute loading. This indicates which feature contributes the most to each PC and can occur in multiple PCs. +The highest loading values for the features are colored red in the biplot and described as “best” in the output dataframe. +The features that were not seen with highest loadings for any PC are considered weaker features, and are colored blue the biplot. In the output dataframe these features are described as “weak”.
# Make biplot model.biplot() # Here again, many other options can be turned on and off model.biplot(SPE=True, HT2=True, legend=1) + +# Show the top features +results['topfeat'] + +# PC feature loading type +# 0 PC1 flavanoids 0.422934 best +# 1 PC2 color_intensity 0.529996 best +# 2 PC3 ash 0.626224 best +# 3 PC4 malic_acid 0.536890 best +# 4 PC5 magnesium 0.727049 best +# 5 PC6 malic_acid 0.536814 best +# 6 PC7 nonflavanoid_phenols 0.595447 best +# 7 PC8 hue 0.436624 best +# 8 PC9 proline 0.575786 best +# 9 PC10 od280/od315_of_diluted_wines 0.523706 best +# 10 PC9 alcohol -0.508619 weak +# 11 PC3 alcalinity_of_ash 0.612080 weak +# 12 PC8 total_phenols -0.405934 weak +# 13 PC6 proanthocyanins -0.533795 weak
# Make plot with parameters: set cmap to None and label and legend to False. Only directions will be plotted. model.biplot(cmap=None, legend=False)
fig, ax = model.scatter(alpha=1)
import numpy as np from sklearn.datasets import make_friedman1 from pca import pca @@ -272,7 +297,7 @@ Markers -Biplots with markers +Biplots with markers @@ -280,7 +305,7 @@ Markers -Control color/marker/size per sample +Control color/marker/size per sample import numpy as np import matplotlib.pyplot as plt import matplotlib.colors as mcolors @@ -329,7 +354,7 @@ Control color/marker/size per sample -Biplot with customized properties per sample. +Biplot with customized properties per sample. @@ -337,15 +362,16 @@ Control color/marker/size per sample -3D plots +3D plots All plots can also be created in 3D by setting the d3=True parameter. model.biplot3d() - + + -Toggle visible status +Toggle visible status The visible status for can be turned on and off. # Make plot but not visible. fig, ax = model.biplot(visible=False) diff --git a/docs/pages/html/_sources/Plots.rst.txt b/docs/pages/html/_sources/Plots.rst.txt index 33319b2..38cd2db 100644 --- a/docs/pages/html/_sources/Plots.rst.txt +++ b/docs/pages/html/_sources/Plots.rst.txt @@ -83,6 +83,14 @@ Scatter plot Biplot ############### +The biplot draws the loadings (arrows) together with the samples (scatterplot). +The loadings can be colored red and blue which indicates the strength of the particular feature in the PC. + +For each principal component (PC), the feature is determined with the largest absolute loading. This indicates which feature contributes the most to each PC and can occur in multiple PCs. +The highest loading values for the features are colored red in the biplot and described as "best" in the output dataframe. +The features that were not seen with highest loadings for any PC are considered weaker features, and are colored blue the biplot. In the output dataframe these features are described as "weak". + + .. code:: python # Make biplot @@ -91,6 +99,24 @@ Biplot # Here again, many other options can be turned on and off model.biplot(SPE=True, HT2=True, legend=1) + # Show the top features + results['topfeat'] + + # PC feature loading type + # 0 PC1 flavanoids 0.422934 best + # 1 PC2 color_intensity 0.529996 best + # 2 PC3 ash 0.626224 best + # 3 PC4 malic_acid 0.536890 best + # 4 PC5 magnesium 0.727049 best + # 5 PC6 malic_acid 0.536814 best + # 6 PC7 nonflavanoid_phenols 0.595447 best + # 7 PC8 hue 0.436624 best + # 8 PC9 proline 0.575786 best + # 9 PC10 od280/od315_of_diluted_wines 0.523706 best + # 10 PC9 alcohol -0.508619 weak + # 11 PC3 alcalinity_of_ash 0.612080 weak + # 12 PC8 total_phenols -0.405934 weak + # 13 PC6 proanthocyanins -0.533795 weak .. |figP5| image:: ../figs/wine_biplot.png .. |figP6| image:: ../figs/wine_biplot_with_outliers.png diff --git a/docs/pages/html/_sources/sponsor.rst.txt b/docs/pages/html/_sources/sponsor.rst.txt index a46c410..f006896 100644 --- a/docs/pages/html/_sources/sponsor.rst.txt +++ b/docs/pages/html/_sources/sponsor.rst.txt @@ -4,8 +4,10 @@ * Become a `Sponsor `_! * `Buy `_ me a coffee! I ❤️ coffee :) * `Donate `_ in Bitcoin. - * Follow me on medium! Go to my `medium profile `_ and press *follow*. + * Follow me on Medium! Go to my `medium profile `_ and press *follow*. + * Subscribe to me on Substack! Go to my `profile `_ where you can *subscribe*. * **Star** this repo at the github page. + * You can also buy a digital educational product over `here `_. * Other contributions can be in the form of feature requests, idea discussions, reporting bugs, opening pull requests. Cheers Mate. diff --git a/docs/pages/html/_static/_sphinx_javascript_frameworks_compat.js b/docs/pages/html/_static/_sphinx_javascript_frameworks_compat.js new file mode 100644 index 0000000..8141580 --- /dev/null +++ b/docs/pages/html/_static/_sphinx_javascript_frameworks_compat.js @@ -0,0 +1,123 @@ +/* Compatability shim for jQuery and underscores.js. + * + * Copyright Sphinx contributors + * Released under the two clause BSD licence + */ + +/** + * small helper function to urldecode strings + * + * See https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/decodeURIComponent#Decoding_query_parameters_from_a_URL + */ +jQuery.urldecode = function(x) { + if (!x) { + return x + } + return decodeURIComponent(x.replace(/\+/g, ' ')); +}; + +/** + * small helper function to urlencode strings + */ +jQuery.urlencode = encodeURIComponent; + +/** + * This function returns the parsed url parameters of the + * current request. Multiple values per key are supported, + * it will always return arrays of strings for the value parts. + */ +jQuery.getQueryParameters = function(s) { + if (typeof s === 'undefined') + s = document.location.search; + var parts = s.substr(s.indexOf('?') + 1).split('&'); + var result = {}; + for (var i = 0; i < parts.length; i++) { + var tmp = parts[i].split('=', 2); + var key = jQuery.urldecode(tmp[0]); + var value = jQuery.urldecode(tmp[1]); + if (key in result) + result[key].push(value); + else + result[key] = [value]; + } + return result; +}; + +/** + * highlight a given string on a jquery object by wrapping it in + * span elements with the given class name. + */ +jQuery.fn.highlightText = function(text, className) { + function highlight(node, addItems) { + if (node.nodeType === 3) { + var val = node.nodeValue; + var pos = val.toLowerCase().indexOf(text); + if (pos >= 0 && + !jQuery(node.parentNode).hasClass(className) && + !jQuery(node.parentNode).hasClass("nohighlight")) { + var span; + var isInSVG = jQuery(node).closest("body, svg, foreignObject").is("svg"); + if (isInSVG) { + span = document.createElementNS("http://www.w3.org/2000/svg", "tspan"); + } else { + span = document.createElement("span"); + span.className = className; + } + span.appendChild(document.createTextNode(val.substr(pos, text.length))); + node.parentNode.insertBefore(span, node.parentNode.insertBefore( + document.createTextNode(val.substr(pos + text.length)), + node.nextSibling)); + node.nodeValue = val.substr(0, pos); + if (isInSVG) { + var rect = document.createElementNS("http://www.w3.org/2000/svg", "rect"); + var bbox = node.parentElement.getBBox(); + rect.x.baseVal.value = bbox.x; + rect.y.baseVal.value = bbox.y; + rect.width.baseVal.value = bbox.width; + rect.height.baseVal.value = bbox.height; + rect.setAttribute('class', className); + addItems.push({ + "parent": node.parentNode, + "target": rect}); + } + } + } + else if (!jQuery(node).is("button, select, textarea")) { + jQuery.each(node.childNodes, function() { + highlight(this, addItems); + }); + } + } + var addItems = []; + var result = this.each(function() { + highlight(this, addItems); + }); + for (var i = 0; i < addItems.length; ++i) { + jQuery(addItems[i].parent).before(addItems[i].target); + } + return result; +}; + +/* + * backward compatibility for jQuery.browser + * This will be supported until firefox bug is fixed. + */ +if (!jQuery.browser) { + jQuery.uaMatch = function(ua) { + ua = ua.toLowerCase(); + + var match = /(chrome)[ \/]([\w.]+)/.exec(ua) || + /(webkit)[ \/]([\w.]+)/.exec(ua) || + /(opera)(?:.*version|)[ \/]([\w.]+)/.exec(ua) || + /(msie) ([\w.]+)/.exec(ua) || + ua.indexOf("compatible") < 0 && /(mozilla)(?:.*? rv:([\w.]+)|)/.exec(ua) || + []; + + return { + browser: match[ 1 ] || "", + version: match[ 2 ] || "0" + }; + }; + jQuery.browser = {}; + jQuery.browser[jQuery.uaMatch(navigator.userAgent).browser] = true; +} diff --git a/docs/pages/html/_static/basic.css b/docs/pages/html/_static/basic.css index 7577acb..7ebbd6d 100644 --- a/docs/pages/html/_static/basic.css +++ b/docs/pages/html/_static/basic.css @@ -1,12 +1,5 @@ /* - * basic.css - * ~~~~~~~~~ - * * Sphinx stylesheet -- basic theme. - * - * :copyright: Copyright 2007-2023 by the Sphinx team, see AUTHORS. - * :license: BSD, see LICENSE for details. - * */ /* -- main layout ----------------------------------------------------------- */ @@ -115,15 +108,11 @@ img { /* -- search page ----------------------------------------------------------- */ ul.search { - margin: 10px 0 0 20px; - padding: 0; + margin-top: 10px; } ul.search li { - padding: 5px 0 5px 20px; - background-image: url(file.png); - background-repeat: no-repeat; - background-position: 0 7px; + padding: 5px 0; } ul.search li a { @@ -237,6 +226,10 @@ a.headerlink { visibility: hidden; } +a:visited { + color: #551A8B; +} + h1:hover > a.headerlink, h2:hover > a.headerlink, h3:hover > a.headerlink, @@ -670,6 +663,16 @@ dd { margin-left: 30px; } +.sig dd { + margin-top: 0px; + margin-bottom: 0px; +} + +.sig dl { + margin-top: 0px; + margin-bottom: 0px; +} + dl > dd:last-child, dl > dd:last-child > :last-child { margin-bottom: 0; @@ -738,6 +741,14 @@ abbr, acronym { cursor: help; } +.translated { + background-color: rgba(207, 255, 207, 0.2) +} + +.untranslated { + background-color: rgba(255, 207, 207, 0.2) +} + /* -- code displays --------------------------------------------------------- */ pre { diff --git a/docs/pages/html/_static/css/badge_only.css b/docs/pages/html/_static/css/badge_only.css index c718cee..88ba55b 100644 --- a/docs/pages/html/_static/css/badge_only.css +++ b/docs/pages/html/_static/css/badge_only.css @@ -1 +1 @@ -.clearfix{*zoom:1}.clearfix:after,.clearfix:before{display:table;content:""}.clearfix:after{clear:both}@font-face{font-family:FontAwesome;font-style:normal;font-weight:400;src:url(fonts/fontawesome-webfont.eot?674f50d287a8c48dc19ba404d20fe713?#iefix) 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{ + const config = event.detail.data(); + + const flyout = ` + + + Read the Docs + v: ${config.versions.current.slug} + + + + + ${renderLanguages(config)} + ${renderVersions(config)} + ${renderDownloads(config)} + + On Read the Docs + + Project Home + + + Builds + + + Downloads + + + + Search + + + + + + + + + Hosted by Read the Docs + + + + `; + + // Inject the generated flyout into the body HTML element. + document.body.insertAdjacentHTML("beforeend", flyout); + + // Trigger the Read the Docs Addons Search modal when clicking on the "Search docs" input from inside the flyout. + document + .querySelector("#flyout-search-form") + .addEventListener("focusin", () => { + const event = new CustomEvent("readthedocs-search-show"); + document.dispatchEvent(event); + }); + }) +} + +if (themeLanguageSelector || themeVersionSelector) { + function onSelectorSwitch(event) { + const option = event.target.selectedIndex; + const item = event.target.options[option]; + window.location.href = 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config.projects.current, + ); + languages = languages.sort((a, b) => + a.language.name.localeCompare(b.language.name), + ); + + const languageSelect = ` + + ${languages + .map( + (language) => ` + + ${language.language.name} + `, + ) + .join("\n")} + + `; + + languageSwitch.innerHTML = languageSelect; + languageSwitch.firstElementChild.addEventListener("change", onSelectorSwitch); + } + else { + languageSwitch.remove(); + } + } + }); +} + +document.addEventListener("readthedocs-addons-data-ready", function (event) { + // Trigger the Read the Docs Addons Search modal when clicking on "Search docs" input from the topnav. + document + .querySelector("[role='search'] input") + .addEventListener("focusin", () => { + const event = new CustomEvent("readthedocs-search-show"); + document.dispatchEvent(event); + }); +}); \ No newline at end of file diff --git a/docs/pages/html/_static/language_data.js b/docs/pages/html/_static/language_data.js index 250f566..c7fe6c6 100644 --- a/docs/pages/html/_static/language_data.js +++ b/docs/pages/html/_static/language_data.js @@ -1,19 +1,12 @@ /* - * language_data.js - * ~~~~~~~~~~~~~~~~ - * * This script contains the language-specific data used by searchtools.js, * namely the list of stopwords, stemmer, scorer and splitter. - * - * :copyright: Copyright 2007-2023 by the Sphinx team, see AUTHORS. - * :license: BSD, see LICENSE for details. - * */ var stopwords = ["a", "and", "are", "as", "at", "be", "but", "by", "for", "if", "in", "into", "is", "it", "near", "no", "not", "of", "on", "or", "such", "that", "the", "their", "then", "there", "these", "they", "this", "to", "was", "will", "with"]; -/* Non-minified version is copied as a separate JS file, is available */ +/* Non-minified version is copied as a separate JS file, if available */ /** * Porter Stemmer diff --git a/docs/pages/html/_static/notebooks/pca_examples.html b/docs/pages/html/_static/notebooks/pca_examples.html index c9a75dc..7bb55a3 100644 --- a/docs/pages/html/_static/notebooks/pca_examples.html +++ b/docs/pages/html/_static/notebooks/pca_examples.html @@ -1,13 +1,9 @@ - - - + + + pca_examples - - - - - - - - - - - - - - + + + - - - - + void Promise.all([...diagrams].map(renderOneMarmaid)); + }); + + + + + + + - + pca A Python Package for Principal Component Analysis. The core of PCA is build on sklearn functionality to find maximum compatibility when combining with other packages. But this package can do a lot more. Besides the regular pca, it can also perform SparsePCA, and TruncatedSVD. Depending on your input data, the best approach will be choosen. Other functionalities are: @@ -15124,38 +7531,30 @@ github pca - - - + + -In [1]: +In [1]: - -!pip install pca + +!pip install pca - - - + - - - - - - - + + Requirement already satisfied: pca in /usr/local/lib/python3.7/dist-packages (1.7.2) Requirement already satisfied: matplotlib in /usr/local/lib/python3.7/dist-packages (from pca) (3.2.2) Requirement already satisfied: wget in /usr/local/lib/python3.7/dist-packages (from pca) (3.2) @@ -15180,179 +7579,149 @@ - - - - - + + - + Lets check the version - - - + + -In [2]: +In [2]: - -import pca + +import pca print(pca.__version__) - - - + - - - - - - - + + 1.7.2 - - - - - + + - + Import the pca library - - - + + -In [3]: +In [3]: - -from pca import pca + +from pca import pca import numpy as np import pandas as pd - - - - - + + + - + Here we will create a random dataset. - - - + + -In [4]: +In [4]: - -# Dataset + +# Dataset from sklearn.datasets import load_iris X = pd.DataFrame(data=load_iris().data, columns=load_iris().feature_names, index=load_iris().target) - - - - - + + + - + Initialize using specified parameters. The parameters here are the default parameters. - - - + + -In [5]: +In [5]: - -# Initialize + +# Initialize model = pca(n_components=3, normalize=True) - - - - - + + + -In [6]: +In [6]: - -# Fit transform + +# Fit transform out = model.fit_transform(X) - - - + - - - - - - - + + [pca] >Processing dataframe.. [pca] >Normalizing input data per feature (zero mean and unit variance).. [pca] >The PCA reduction is performed on the [4] columns of the input dataframe. @@ -15364,171 +7733,119 @@ - - - - - + + -In [7]: +In [7]: - -# Make plot with only the directions (no scatter) + +# Make plot with only the directions (no scatter) fig, ax = model.biplot(textlabel=True, legend=False, figsize=(10, 6)) - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 with loadings. - - - - - - - - + + + - - - - - - + + -In [8]: +In [8]: - -# Make plot with only the directions (no scatter) + +# Make plot with only the directions (no scatter) fig, ax = model.biplot(cmap=None, textlabel=False, legend=False, figsize=(10, 6)) - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 with loadings. - - - - - - - - + + + - - - - - - + + -In [9]: +In [9]: - -from pca import pca + +from pca import pca # Load example data from sklearn.datasets import load_iris X = pd.DataFrame(data=load_iris().data, columns=load_iris().feature_names, index=load_iris().target) - - - - - + + + -In [10]: +In [10]: - -# Initialize + +# Initialize model = pca(n_components=3) # Fit using PCA results = model.fit_transform(X) - - - + - - - - - - - + + [pca] >Processing dataframe.. [pca] >The PCA reduction is performed on the [4] columns of the input dataframe. [pca] >Fit using PCA. @@ -15539,20 +7856,17 @@ - - - - - + + -In [11]: +In [11]: - -# Make plots + +# Make plots # Scree plot fig, ax = model.plot(figsize=(10, 6)) @@ -15563,190 +7877,117 @@ # Biplot fig, ax = model.biplot(figsize=(10, 6)) - - - + - - - - - - - - - - + + + - - - - - - - - - + + + - - - - - - + + [pca] >Plot PC1 vs PC2 with loadings. - - - - - - - + + <Figure size 432x288 with 0 Axes> - - - - - - - - - + + + - - - - - - + + -In [17]: +In [17]: - -# Coloring on density to focus on the core samples. + +# Coloring on density to focus on the core samples. # Biplot -fig, ax = model.biplot(figsize=(10, 6), gradient='#ffffff') +fig, ax = model.biplot(figsize=(10, 6), gradient='#ffffff') - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 with loadings. - - - - - - - - + + + - - - - - - + + -In [18]: +In [18]: - -# Outliers are stored in results: -results['outliers'] + +# Outliers are stored in results: +results['outliers'] # Outliers based on T2 -print('--------T2------------') -print(results['outliers'].loc[results['outliers']['y_bool'], :]) +print('--------T2------------') +print(results['outliers'].loc[results['outliers']['y_bool'], :]) # Outliers based on SPE -print('--------SPE------------') -print(results['outliers'].loc[results['outliers']['y_bool_spe'], :]) +print('--------SPE------------') +print(results['outliers'].loc[results['outliers']['y_bool_spe'], :]) - - - + - - - - - - - + + --------T2------------ y_proba y_score y_bool y_bool_spe y_score_spe 2 0.040551 13.160880 True True 3.679935 @@ -15771,270 +8012,168 @@ - - - - - + + -In [20]: +In [20]: - -# Outlier detection + +# Outlier detection fig, ax = model.biplot(SPE=True, HT2=True, figsize=(10, 6)) - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 with loadings. - - - - - - - - + + + - - - - - - + + -In [21]: +In [21]: - -# 3D plots + +# 3D plots fig, ax = model.scatter3d(figsize=(10, 6)) fig, ax = model.biplot3d(figsize=(10, 6)) fig, ax = model.biplot3d(SPE=True, HT2=True, figsize=(10, 6)) - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 vs PC3 with loadings. - - - - - - - - + + + - - - - - - - - - + + + - - - - - - + + [pca] >Plot PC1 vs PC2 vs PC3 with loadings. - - - - - - - - + + + - - - - - - + + -In [22]: +In [22]: - -fig, ax = model.biplot3d(SPE=True, HT2=True, visible=False, figsize=(10, 6)) + +fig, ax = model.biplot3d(SPE=True, HT2=True, visible=False, figsize=(10, 6)) # Set the figure again to True and show the figure. fig.set_visible(True) fig - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 vs PC3 with loadings. - - Out[22]: - - - - - - +Out[22]: + + - - - - - - - - - + + + - - - - - - + + -In [23]: +In [23]: - -# Normalize out PCs + +
import numpy as np import matplotlib.pyplot as plt import matplotlib.colors as mcolors @@ -329,7 +354,7 @@ Control color/marker/size per sample -Biplot with customized properties per sample. +Biplot with customized properties per sample. @@ -337,15 +362,16 @@ Control color/marker/size per sample -3D plots +3D plots All plots can also be created in 3D by setting the d3=True parameter. model.biplot3d() - + + -Toggle visible status +Toggle visible status The visible status for can be turned on and off. # Make plot but not visible. fig, ax = model.biplot(visible=False) diff --git a/docs/pages/html/_sources/Plots.rst.txt b/docs/pages/html/_sources/Plots.rst.txt index 33319b2..38cd2db 100644 --- a/docs/pages/html/_sources/Plots.rst.txt +++ b/docs/pages/html/_sources/Plots.rst.txt @@ -83,6 +83,14 @@ Scatter plot Biplot ############### +The biplot draws the loadings (arrows) together with the samples (scatterplot). +The loadings can be colored red and blue which indicates the strength of the particular feature in the PC. + +For each principal component (PC), the feature is determined with the largest absolute loading. This indicates which feature contributes the most to each PC and can occur in multiple PCs. +The highest loading values for the features are colored red in the biplot and described as "best" in the output dataframe. +The features that were not seen with highest loadings for any PC are considered weaker features, and are colored blue the biplot. In the output dataframe these features are described as "weak". + + .. code:: python # Make biplot @@ -91,6 +99,24 @@ Biplot # Here again, many other options can be turned on and off model.biplot(SPE=True, HT2=True, legend=1) + # Show the top features + results['topfeat'] + + # PC feature loading type + # 0 PC1 flavanoids 0.422934 best + # 1 PC2 color_intensity 0.529996 best + # 2 PC3 ash 0.626224 best + # 3 PC4 malic_acid 0.536890 best + # 4 PC5 magnesium 0.727049 best + # 5 PC6 malic_acid 0.536814 best + # 6 PC7 nonflavanoid_phenols 0.595447 best + # 7 PC8 hue 0.436624 best + # 8 PC9 proline 0.575786 best + # 9 PC10 od280/od315_of_diluted_wines 0.523706 best + # 10 PC9 alcohol -0.508619 weak + # 11 PC3 alcalinity_of_ash 0.612080 weak + # 12 PC8 total_phenols -0.405934 weak + # 13 PC6 proanthocyanins -0.533795 weak .. |figP5| image:: ../figs/wine_biplot.png .. |figP6| image:: ../figs/wine_biplot_with_outliers.png diff --git a/docs/pages/html/_sources/sponsor.rst.txt b/docs/pages/html/_sources/sponsor.rst.txt index a46c410..f006896 100644 --- a/docs/pages/html/_sources/sponsor.rst.txt +++ b/docs/pages/html/_sources/sponsor.rst.txt @@ -4,8 +4,10 @@ * Become a `Sponsor `_! * `Buy `_ me a coffee! I ❤️ coffee :) * `Donate `_ in Bitcoin. - * Follow me on medium! Go to my `medium profile `_ and press *follow*. + * Follow me on Medium! Go to my `medium profile `_ and press *follow*. + * Subscribe to me on Substack! Go to my `profile `_ where you can *subscribe*. * **Star** this repo at the github page. + * You can also buy a digital educational product over `here `_. * Other contributions can be in the form of feature requests, idea discussions, reporting bugs, opening pull requests. Cheers Mate. diff --git a/docs/pages/html/_static/_sphinx_javascript_frameworks_compat.js b/docs/pages/html/_static/_sphinx_javascript_frameworks_compat.js new file mode 100644 index 0000000..8141580 --- /dev/null +++ b/docs/pages/html/_static/_sphinx_javascript_frameworks_compat.js @@ -0,0 +1,123 @@ +/* Compatability shim for jQuery and underscores.js. + * + * Copyright Sphinx contributors + * Released under the two clause BSD licence + */ + +/** + * small helper function to urldecode strings + * + * See https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/decodeURIComponent#Decoding_query_parameters_from_a_URL + */ +jQuery.urldecode = function(x) { + if (!x) { + return x + } + return decodeURIComponent(x.replace(/\+/g, ' ')); +}; + +/** + * small helper function to urlencode strings + */ +jQuery.urlencode = encodeURIComponent; + +/** + * This function returns the parsed url parameters of the + * current request. Multiple values per key are supported, + * it will always return arrays of strings for the value parts. + */ +jQuery.getQueryParameters = function(s) { + if (typeof s === 'undefined') + s = document.location.search; + var parts = s.substr(s.indexOf('?') + 1).split('&'); + var result = {}; + for (var i = 0; i < parts.length; i++) { + var tmp = parts[i].split('=', 2); + var key = jQuery.urldecode(tmp[0]); + var value = jQuery.urldecode(tmp[1]); + if (key in result) + result[key].push(value); + else + result[key] = [value]; + } + return result; +}; + +/** + * highlight a given string on a jquery object by wrapping it in + * span elements with the given class name. + */ +jQuery.fn.highlightText = function(text, className) { + function highlight(node, addItems) { + if (node.nodeType === 3) { + var val = node.nodeValue; + var pos = val.toLowerCase().indexOf(text); + if (pos >= 0 && + !jQuery(node.parentNode).hasClass(className) && + !jQuery(node.parentNode).hasClass("nohighlight")) { + var span; + var isInSVG = jQuery(node).closest("body, svg, foreignObject").is("svg"); + if (isInSVG) { + span = document.createElementNS("http://www.w3.org/2000/svg", "tspan"); + } else { + span = document.createElement("span"); + span.className = className; + } + span.appendChild(document.createTextNode(val.substr(pos, text.length))); + node.parentNode.insertBefore(span, node.parentNode.insertBefore( + document.createTextNode(val.substr(pos + text.length)), + node.nextSibling)); + node.nodeValue = val.substr(0, pos); + if (isInSVG) { + var rect = document.createElementNS("http://www.w3.org/2000/svg", "rect"); + var bbox = node.parentElement.getBBox(); + rect.x.baseVal.value = bbox.x; + rect.y.baseVal.value = bbox.y; + rect.width.baseVal.value = bbox.width; + rect.height.baseVal.value = bbox.height; + rect.setAttribute('class', className); + addItems.push({ + "parent": node.parentNode, + "target": rect}); + } + } + } + else if (!jQuery(node).is("button, select, textarea")) { + jQuery.each(node.childNodes, function() { + highlight(this, addItems); + }); + } + } + var addItems = []; + var result = this.each(function() { + highlight(this, addItems); + }); + for (var i = 0; i < addItems.length; ++i) { + jQuery(addItems[i].parent).before(addItems[i].target); + } + return result; +}; + +/* + * backward compatibility for jQuery.browser + * This will be supported until firefox bug is fixed. + */ +if (!jQuery.browser) { + jQuery.uaMatch = function(ua) { + ua = ua.toLowerCase(); + + var match = /(chrome)[ \/]([\w.]+)/.exec(ua) || + /(webkit)[ \/]([\w.]+)/.exec(ua) || + /(opera)(?:.*version|)[ \/]([\w.]+)/.exec(ua) || + /(msie) ([\w.]+)/.exec(ua) || + ua.indexOf("compatible") < 0 && /(mozilla)(?:.*? rv:([\w.]+)|)/.exec(ua) || + []; + + return { + browser: match[ 1 ] || "", + version: match[ 2 ] || "0" + }; + }; + jQuery.browser = {}; + jQuery.browser[jQuery.uaMatch(navigator.userAgent).browser] = true; +} diff --git a/docs/pages/html/_static/basic.css b/docs/pages/html/_static/basic.css index 7577acb..7ebbd6d 100644 --- a/docs/pages/html/_static/basic.css +++ b/docs/pages/html/_static/basic.css @@ -1,12 +1,5 @@ /* - * basic.css - * ~~~~~~~~~ - * * Sphinx stylesheet -- basic theme. - * - * :copyright: Copyright 2007-2023 by the Sphinx team, see AUTHORS. - * :license: BSD, see LICENSE for details. - * */ /* -- main layout ----------------------------------------------------------- */ @@ -115,15 +108,11 @@ img { /* -- search page ----------------------------------------------------------- */ ul.search { - margin: 10px 0 0 20px; - padding: 0; + margin-top: 10px; } ul.search li { - padding: 5px 0 5px 20px; - background-image: url(file.png); - background-repeat: no-repeat; - background-position: 0 7px; + padding: 5px 0; } ul.search li a { @@ -237,6 +226,10 @@ a.headerlink { visibility: hidden; } +a:visited { + color: #551A8B; +} + h1:hover > a.headerlink, h2:hover > a.headerlink, h3:hover > a.headerlink, @@ -670,6 +663,16 @@ dd { 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{ + const config = event.detail.data(); + + const flyout = ` + + + Read the Docs + v: ${config.versions.current.slug} + + + + + ${renderLanguages(config)} + ${renderVersions(config)} + ${renderDownloads(config)} + + On Read the Docs + + Project Home + + + Builds + + + Downloads + + + + Search + + + + + + + + + Hosted by Read the Docs + + + + `; + + // Inject the generated flyout into the body HTML element. + document.body.insertAdjacentHTML("beforeend", flyout); + + // Trigger the Read the Docs Addons Search modal when clicking on the "Search docs" input from inside the flyout. + document + .querySelector("#flyout-search-form") + .addEventListener("focusin", () => { + const event = new CustomEvent("readthedocs-search-show"); + document.dispatchEvent(event); + }); + }) +} + +if (themeLanguageSelector || themeVersionSelector) { + function onSelectorSwitch(event) { + const option = event.target.selectedIndex; + const item = event.target.options[option]; + window.location.href = item.dataset.url; + } + + document.addEventListener("readthedocs-addons-data-ready", function (event) { + const config = event.detail.data(); + + const versionSwitch = document.querySelector( + "div.switch-menus > div.version-switch", + ); + if (themeVersionSelector) { + let versions = config.versions.active; + if (config.versions.current.hidden || config.versions.current.type === "external") { + versions.unshift(config.versions.current); + } + const versionSelect = ` + + ${versions + .map( + (version) => ` + + ${version.slug} + `, + ) + .join("\n")} + + `; + + versionSwitch.innerHTML = versionSelect; + versionSwitch.firstElementChild.addEventListener("change", onSelectorSwitch); + } + + const languageSwitch = document.querySelector( + "div.switch-menus > div.language-switch", + ); + + if (themeLanguageSelector) { + if (config.projects.translations.length) { + // Add the current language to the options on the selector + let languages = config.projects.translations.concat( + config.projects.current, + ); + languages = languages.sort((a, b) => + a.language.name.localeCompare(b.language.name), + ); + + const languageSelect = ` + + ${languages + .map( + (language) => ` + + ${language.language.name} + `, + ) + .join("\n")} + + `; + + languageSwitch.innerHTML = languageSelect; + languageSwitch.firstElementChild.addEventListener("change", onSelectorSwitch); + } + else { + languageSwitch.remove(); + } + } + }); +} + +document.addEventListener("readthedocs-addons-data-ready", function (event) { + // Trigger the Read the Docs Addons Search modal when clicking on "Search docs" input from the topnav. + document + .querySelector("[role='search'] input") + .addEventListener("focusin", () => { + const event = new CustomEvent("readthedocs-search-show"); + document.dispatchEvent(event); + }); +}); \ No newline at end of file diff --git a/docs/pages/html/_static/language_data.js b/docs/pages/html/_static/language_data.js index 250f566..c7fe6c6 100644 --- a/docs/pages/html/_static/language_data.js +++ b/docs/pages/html/_static/language_data.js @@ -1,19 +1,12 @@ /* - * language_data.js - * ~~~~~~~~~~~~~~~~ - * * This script contains the language-specific data used by searchtools.js, * namely the list of stopwords, stemmer, scorer and splitter. - * - * :copyright: Copyright 2007-2023 by the Sphinx team, see AUTHORS. - * :license: BSD, see LICENSE for details. - * */ var stopwords = ["a", "and", "are", "as", "at", "be", "but", "by", "for", "if", "in", "into", "is", "it", "near", "no", "not", "of", "on", "or", "such", "that", "the", "their", "then", "there", "these", "they", "this", "to", "was", "will", "with"]; -/* Non-minified version is copied as a separate JS file, is available */ +/* Non-minified version is copied as a separate JS file, if available */ /** * Porter Stemmer diff --git a/docs/pages/html/_static/notebooks/pca_examples.html b/docs/pages/html/_static/notebooks/pca_examples.html index c9a75dc..7bb55a3 100644 --- a/docs/pages/html/_static/notebooks/pca_examples.html +++ b/docs/pages/html/_static/notebooks/pca_examples.html @@ -1,13 +1,9 @@ - - - + + + pca_examples - - - - - - - - - - - - - - + + + - - - - + void Promise.all([...diagrams].map(renderOneMarmaid)); + }); + + + + + + + - + pca A Python Package for Principal Component Analysis. The core of PCA is build on sklearn functionality to find maximum compatibility when combining with other packages. But this package can do a lot more. Besides the regular pca, it can also perform SparsePCA, and TruncatedSVD. Depending on your input data, the best approach will be choosen. Other functionalities are: @@ -15124,38 +7531,30 @@ github pca - - - + + -In [1]: +In [1]: - -!pip install pca + +!pip install pca - - - + - - - - - - - + + Requirement already satisfied: pca in /usr/local/lib/python3.7/dist-packages (1.7.2) Requirement already satisfied: matplotlib in /usr/local/lib/python3.7/dist-packages (from pca) (3.2.2) Requirement already satisfied: wget in /usr/local/lib/python3.7/dist-packages (from pca) (3.2) @@ -15180,179 +7579,149 @@ - - - - - + + - + Lets check the version - - - + + -In [2]: +In [2]: - -import pca + +import pca print(pca.__version__) - - - + - - - - - - - + + 1.7.2 - - - - - + + - + Import the pca library - - - + + -In [3]: +In [3]: - -from pca import pca + +from pca import pca import numpy as np import pandas as pd - - - - - + + + - + Here we will create a random dataset. - - - + + -In [4]: +In [4]: - -# Dataset + +# Dataset from sklearn.datasets import load_iris X = pd.DataFrame(data=load_iris().data, columns=load_iris().feature_names, index=load_iris().target) - - - - - + + + - + Initialize using specified parameters. The parameters here are the default parameters. - - - + + -In [5]: +In [5]: - -# Initialize + +# Initialize model = pca(n_components=3, normalize=True) - - - - - + + + -In [6]: +In [6]: - -# Fit transform + +# Fit transform out = model.fit_transform(X) - - - + - - - - - - - + + [pca] >Processing dataframe.. [pca] >Normalizing input data per feature (zero mean and unit variance).. [pca] >The PCA reduction is performed on the [4] columns of the input dataframe. @@ -15364,171 +7733,119 @@ - - - - - + + -In [7]: +In [7]: - -# Make plot with only the directions (no scatter) + +# Make plot with only the directions (no scatter) fig, ax = model.biplot(textlabel=True, legend=False, figsize=(10, 6)) - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 with loadings. - - - - - - - - + + + - - - - - - + + -In [8]: +In [8]: - -# Make plot with only the directions (no scatter) + +# Make plot with only the directions (no scatter) fig, ax = model.biplot(cmap=None, textlabel=False, legend=False, figsize=(10, 6)) - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 with loadings. - - - - - - - - + + + - - - - - - + + -In [9]: +In [9]: - -from pca import pca + +from pca import pca # Load example data from sklearn.datasets import load_iris X = pd.DataFrame(data=load_iris().data, columns=load_iris().feature_names, index=load_iris().target) - - - - - + + + -In [10]: +In [10]: - -# Initialize + +# Initialize model = pca(n_components=3) # Fit using PCA results = model.fit_transform(X) - - - + - - - - - - - + + [pca] >Processing dataframe.. [pca] >The PCA reduction is performed on the [4] columns of the input dataframe. [pca] >Fit using PCA. @@ -15539,20 +7856,17 @@ - - - - - + + -In [11]: +In [11]: - -# Make plots + +# Make plots # Scree plot fig, ax = model.plot(figsize=(10, 6)) @@ -15563,190 +7877,117 @@ # Biplot fig, ax = model.biplot(figsize=(10, 6)) - - - + - - - - - - - - - - + + + - - - - - - - - - + + + - - - - - - + + [pca] >Plot PC1 vs PC2 with loadings. - - - - - - - + + <Figure size 432x288 with 0 Axes> - - - - - - - - - + + + - - - - - - + + -In [17]: +In [17]: - -# Coloring on density to focus on the core samples. + +# Coloring on density to focus on the core samples. # Biplot -fig, ax = model.biplot(figsize=(10, 6), gradient='#ffffff') +fig, ax = model.biplot(figsize=(10, 6), gradient='#ffffff') - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 with loadings. - - - - - - - - + + + - - - - - - + + -In [18]: +In [18]: - -# Outliers are stored in results: -results['outliers'] + +# Outliers are stored in results: +results['outliers'] # Outliers based on T2 -print('--------T2------------') -print(results['outliers'].loc[results['outliers']['y_bool'], :]) +print('--------T2------------') +print(results['outliers'].loc[results['outliers']['y_bool'], :]) # Outliers based on SPE -print('--------SPE------------') -print(results['outliers'].loc[results['outliers']['y_bool_spe'], :]) +print('--------SPE------------') +print(results['outliers'].loc[results['outliers']['y_bool_spe'], :]) - - - + - - - - - - - + + --------T2------------ y_proba y_score y_bool y_bool_spe y_score_spe 2 0.040551 13.160880 True True 3.679935 @@ -15771,270 +8012,168 @@ - - - - - + + -In [20]: +In [20]: - -# Outlier detection + +# Outlier detection fig, ax = model.biplot(SPE=True, HT2=True, figsize=(10, 6)) - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 with loadings. - - - - - - - - + + + - - - - - - + + -In [21]: +In [21]: - -# 3D plots + +# 3D plots fig, ax = model.scatter3d(figsize=(10, 6)) fig, ax = model.biplot3d(figsize=(10, 6)) fig, ax = model.biplot3d(SPE=True, HT2=True, figsize=(10, 6)) - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 vs PC3 with loadings. - - - - - - - - + + + - - - - - - - - - + + + - - - - - - + + [pca] >Plot PC1 vs PC2 vs PC3 with loadings. - - - - - - - - + + + - - - - - - + + -In [22]: +In [22]: - -fig, ax = model.biplot3d(SPE=True, HT2=True, visible=False, figsize=(10, 6)) + +fig, ax = model.biplot3d(SPE=True, HT2=True, visible=False, figsize=(10, 6)) # Set the figure again to True and show the figure. fig.set_visible(True) fig - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 vs PC3 with loadings. - - Out[22]: - - - - - - +Out[22]: + + - - - - - - - - - + + + - - - - - - + + -In [23]: +In [23]: - -# Normalize out PCs + +
All plots can also be created in 3D by setting the d3=True parameter.
d3=True
model.biplot3d()
The visible status for can be turned on and off.
# Make plot but not visible. fig, ax = model.biplot(visible=False) diff --git a/docs/pages/html/_sources/Plots.rst.txt b/docs/pages/html/_sources/Plots.rst.txt index 33319b2..38cd2db 100644 --- a/docs/pages/html/_sources/Plots.rst.txt +++ b/docs/pages/html/_sources/Plots.rst.txt @@ -83,6 +83,14 @@ Scatter plot Biplot ############### +The biplot draws the loadings (arrows) together with the samples (scatterplot). +The loadings can be colored red and blue which indicates the strength of the particular feature in the PC. + +For each principal component (PC), the feature is determined with the largest absolute loading. This indicates which feature contributes the most to each PC and can occur in multiple PCs. +The highest loading values for the features are colored red in the biplot and described as "best" in the output dataframe. +The features that were not seen with highest loadings for any PC are considered weaker features, and are colored blue the biplot. In the output dataframe these features are described as "weak". + + .. code:: python # Make biplot @@ -91,6 +99,24 @@ Biplot # Here again, many other options can be turned on and off model.biplot(SPE=True, HT2=True, legend=1) + # Show the top features + results['topfeat'] + + # PC feature loading type + # 0 PC1 flavanoids 0.422934 best + # 1 PC2 color_intensity 0.529996 best + # 2 PC3 ash 0.626224 best + # 3 PC4 malic_acid 0.536890 best + # 4 PC5 magnesium 0.727049 best + # 5 PC6 malic_acid 0.536814 best + # 6 PC7 nonflavanoid_phenols 0.595447 best + # 7 PC8 hue 0.436624 best + # 8 PC9 proline 0.575786 best + # 9 PC10 od280/od315_of_diluted_wines 0.523706 best + # 10 PC9 alcohol -0.508619 weak + # 11 PC3 alcalinity_of_ash 0.612080 weak + # 12 PC8 total_phenols -0.405934 weak + # 13 PC6 proanthocyanins -0.533795 weak .. |figP5| image:: ../figs/wine_biplot.png .. |figP6| image:: ../figs/wine_biplot_with_outliers.png diff --git a/docs/pages/html/_sources/sponsor.rst.txt b/docs/pages/html/_sources/sponsor.rst.txt index a46c410..f006896 100644 --- a/docs/pages/html/_sources/sponsor.rst.txt +++ b/docs/pages/html/_sources/sponsor.rst.txt @@ -4,8 +4,10 @@ * Become a `Sponsor `_! * `Buy `_ me a coffee! I ❤️ coffee :) * `Donate `_ in Bitcoin. - * Follow me on medium! Go to my `medium profile `_ and press *follow*. + * Follow me on Medium! Go to my `medium profile `_ and press *follow*. + * Subscribe to me on Substack! Go to my `profile `_ where you can *subscribe*. * **Star** this repo at the github page. + * You can also buy a digital educational product over `here `_. * Other contributions can be in the form of feature requests, idea discussions, reporting bugs, opening pull requests. Cheers Mate. diff --git a/docs/pages/html/_static/_sphinx_javascript_frameworks_compat.js b/docs/pages/html/_static/_sphinx_javascript_frameworks_compat.js new file mode 100644 index 0000000..8141580 --- /dev/null +++ b/docs/pages/html/_static/_sphinx_javascript_frameworks_compat.js @@ -0,0 +1,123 @@ +/* Compatability shim for jQuery and underscores.js. + * + * Copyright Sphinx contributors + * Released under the two clause BSD licence + */ + +/** + * small helper function to urldecode strings + * + * See https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/decodeURIComponent#Decoding_query_parameters_from_a_URL + */ +jQuery.urldecode = function(x) { + if (!x) { + return x + } + return decodeURIComponent(x.replace(/\+/g, ' ')); +}; + +/** + * small helper function to urlencode strings + */ +jQuery.urlencode = encodeURIComponent; + +/** + * This function returns the parsed url parameters of the + * current request. Multiple values per key are supported, + * it will always return arrays of strings for the value parts. + */ +jQuery.getQueryParameters = function(s) { + if (typeof s === 'undefined') + s = document.location.search; + var parts = s.substr(s.indexOf('?') + 1).split('&'); + var result = {}; + for (var i = 0; i < parts.length; i++) { + var tmp = parts[i].split('=', 2); + var key = jQuery.urldecode(tmp[0]); + var value = jQuery.urldecode(tmp[1]); + if (key in result) + result[key].push(value); + else + result[key] = [value]; + } + return result; +}; + +/** + * highlight a given string on a jquery object by wrapping it in + * span elements with the given class name. + */ +jQuery.fn.highlightText = function(text, className) { + function highlight(node, addItems) { + if (node.nodeType === 3) { + var val = node.nodeValue; + var pos = val.toLowerCase().indexOf(text); + if (pos >= 0 && + !jQuery(node.parentNode).hasClass(className) && + !jQuery(node.parentNode).hasClass("nohighlight")) { + var span; + var isInSVG = jQuery(node).closest("body, svg, foreignObject").is("svg"); + if (isInSVG) { + span = document.createElementNS("http://www.w3.org/2000/svg", "tspan"); + } else { + span = document.createElement("span"); + span.className = className; + } + span.appendChild(document.createTextNode(val.substr(pos, text.length))); + node.parentNode.insertBefore(span, node.parentNode.insertBefore( + document.createTextNode(val.substr(pos + text.length)), + node.nextSibling)); + node.nodeValue = val.substr(0, pos); + if (isInSVG) { + var rect = document.createElementNS("http://www.w3.org/2000/svg", "rect"); + var bbox = node.parentElement.getBBox(); + rect.x.baseVal.value = bbox.x; + rect.y.baseVal.value = bbox.y; + rect.width.baseVal.value = bbox.width; + rect.height.baseVal.value = bbox.height; + rect.setAttribute('class', className); + addItems.push({ + "parent": node.parentNode, + "target": rect}); + } + } + } + else if (!jQuery(node).is("button, select, textarea")) { + jQuery.each(node.childNodes, function() { + highlight(this, addItems); + }); + } + } + var addItems = []; + var result = this.each(function() { + highlight(this, addItems); + }); + for (var i = 0; i < addItems.length; ++i) { + jQuery(addItems[i].parent).before(addItems[i].target); + } + return result; +}; + +/* + * backward compatibility for jQuery.browser + * This will be supported until firefox bug is fixed. + */ +if (!jQuery.browser) { + jQuery.uaMatch = function(ua) { + ua = ua.toLowerCase(); + + var match = /(chrome)[ \/]([\w.]+)/.exec(ua) || + /(webkit)[ \/]([\w.]+)/.exec(ua) || + /(opera)(?:.*version|)[ \/]([\w.]+)/.exec(ua) || + /(msie) ([\w.]+)/.exec(ua) || + ua.indexOf("compatible") < 0 && /(mozilla)(?:.*? rv:([\w.]+)|)/.exec(ua) || + []; + + return { + browser: match[ 1 ] || "", + version: match[ 2 ] || "0" + }; + }; + jQuery.browser = {}; + jQuery.browser[jQuery.uaMatch(navigator.userAgent).browser] = true; +} diff --git a/docs/pages/html/_static/basic.css b/docs/pages/html/_static/basic.css index 7577acb..7ebbd6d 100644 --- a/docs/pages/html/_static/basic.css +++ b/docs/pages/html/_static/basic.css @@ -1,12 +1,5 @@ /* - * basic.css - * ~~~~~~~~~ - * * Sphinx stylesheet -- basic theme. - * - * :copyright: Copyright 2007-2023 by the Sphinx team, see AUTHORS. - * :license: BSD, see LICENSE for details. - * */ /* -- main layout ----------------------------------------------------------- */ @@ -115,15 +108,11 @@ img { /* -- search page ----------------------------------------------------------- */ ul.search { - margin: 10px 0 0 20px; - padding: 0; + margin-top: 10px; } ul.search li { - padding: 5px 0 5px 20px; - background-image: url(file.png); - background-repeat: no-repeat; - background-position: 0 7px; + padding: 5px 0; } ul.search li a { @@ -237,6 +226,10 @@ a.headerlink { visibility: hidden; } +a:visited { + color: #551A8B; +} + h1:hover > a.headerlink, h2:hover > a.headerlink, h3:hover > a.headerlink, @@ -670,6 +663,16 @@ dd { 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{ + const config = event.detail.data(); + + const flyout = ` + + + Read the Docs + v: ${config.versions.current.slug} + + + + + ${renderLanguages(config)} + ${renderVersions(config)} + ${renderDownloads(config)} + + On Read the Docs + + Project Home + + + Builds + + + Downloads + + + + Search + + + + + + + + + Hosted by Read the Docs + + + + `; + + // Inject the generated flyout into the body HTML element. + document.body.insertAdjacentHTML("beforeend", flyout); + + // Trigger the Read the Docs Addons Search modal when clicking on the "Search docs" input from inside the flyout. + document + .querySelector("#flyout-search-form") + .addEventListener("focusin", () => { + const event = new CustomEvent("readthedocs-search-show"); + document.dispatchEvent(event); + }); + }) +} + +if (themeLanguageSelector || themeVersionSelector) { + function onSelectorSwitch(event) { + const option = event.target.selectedIndex; + const item = event.target.options[option]; + window.location.href = item.dataset.url; + } + + document.addEventListener("readthedocs-addons-data-ready", function (event) { + const config = event.detail.data(); + + const versionSwitch = document.querySelector( + "div.switch-menus > div.version-switch", + ); + if (themeVersionSelector) { + let versions = config.versions.active; + if (config.versions.current.hidden || config.versions.current.type === "external") { + versions.unshift(config.versions.current); + } + const versionSelect = ` + + ${versions + .map( + (version) => ` + + ${version.slug} + `, + ) + .join("\n")} + + `; + + versionSwitch.innerHTML = versionSelect; + versionSwitch.firstElementChild.addEventListener("change", onSelectorSwitch); + } + + const languageSwitch = document.querySelector( + "div.switch-menus > div.language-switch", + ); + + if (themeLanguageSelector) { + if (config.projects.translations.length) { + // Add the current language to the options on the selector + let languages = config.projects.translations.concat( + config.projects.current, + ); + languages = languages.sort((a, b) => + a.language.name.localeCompare(b.language.name), + ); + + const languageSelect = ` + + ${languages + .map( + (language) => ` + + ${language.language.name} + `, + ) + .join("\n")} + + `; + + languageSwitch.innerHTML = languageSelect; + languageSwitch.firstElementChild.addEventListener("change", onSelectorSwitch); + } + else { + languageSwitch.remove(); + } + } + }); +} + +document.addEventListener("readthedocs-addons-data-ready", function (event) { + // Trigger the Read the Docs Addons Search modal when clicking on "Search docs" input from the topnav. + document + .querySelector("[role='search'] input") + .addEventListener("focusin", () => { + const event = new CustomEvent("readthedocs-search-show"); + document.dispatchEvent(event); + }); +}); \ No newline at end of file diff --git a/docs/pages/html/_static/language_data.js b/docs/pages/html/_static/language_data.js index 250f566..c7fe6c6 100644 --- a/docs/pages/html/_static/language_data.js +++ b/docs/pages/html/_static/language_data.js @@ -1,19 +1,12 @@ /* - * language_data.js - * ~~~~~~~~~~~~~~~~ - * * This script contains the language-specific data used by searchtools.js, * namely the list of stopwords, stemmer, scorer and splitter. - * - * :copyright: Copyright 2007-2023 by the Sphinx team, see AUTHORS. - * :license: BSD, see LICENSE for details. - * */ var stopwords = ["a", "and", "are", "as", "at", "be", "but", "by", "for", "if", "in", "into", "is", "it", "near", "no", "not", "of", "on", "or", "such", "that", "the", "their", "then", "there", "these", "they", "this", "to", "was", "will", "with"]; -/* Non-minified version is copied as a separate JS file, is available */ +/* Non-minified version is copied as a separate JS file, if available */ /** * Porter Stemmer diff --git a/docs/pages/html/_static/notebooks/pca_examples.html b/docs/pages/html/_static/notebooks/pca_examples.html index c9a75dc..7bb55a3 100644 --- a/docs/pages/html/_static/notebooks/pca_examples.html +++ b/docs/pages/html/_static/notebooks/pca_examples.html @@ -1,13 +1,9 @@ - - - + + + pca_examples - - - - - - - - - - - - - - + + + - - - - + void Promise.all([...diagrams].map(renderOneMarmaid)); + }); + + + + + + + - + pca A Python Package for Principal Component Analysis. The core of PCA is build on sklearn functionality to find maximum compatibility when combining with other packages. But this package can do a lot more. Besides the regular pca, it can also perform SparsePCA, and TruncatedSVD. Depending on your input data, the best approach will be choosen. Other functionalities are: @@ -15124,38 +7531,30 @@ github pca - - - + + -In [1]: +In [1]: - -!pip install pca + +!pip install pca - - - + - - - - - - - + + Requirement already satisfied: pca in /usr/local/lib/python3.7/dist-packages (1.7.2) Requirement already satisfied: matplotlib in /usr/local/lib/python3.7/dist-packages (from pca) (3.2.2) Requirement already satisfied: wget in /usr/local/lib/python3.7/dist-packages (from pca) (3.2) @@ -15180,179 +7579,149 @@ - - - - - + + - + Lets check the version - - - + + -In [2]: +In [2]: - -import pca + +import pca print(pca.__version__) - - - + - - - - - - - + + 1.7.2 - - - - - + + - + Import the pca library - - - + + -In [3]: +In [3]: - -from pca import pca + +from pca import pca import numpy as np import pandas as pd - - - - - + + + - + Here we will create a random dataset. - - - + + -In [4]: +In [4]: - -# Dataset + +# Dataset from sklearn.datasets import load_iris X = pd.DataFrame(data=load_iris().data, columns=load_iris().feature_names, index=load_iris().target) - - - - - + + + - + Initialize using specified parameters. The parameters here are the default parameters. - - - + + -In [5]: +In [5]: - -# Initialize + +# Initialize model = pca(n_components=3, normalize=True) - - - - - + + + -In [6]: +In [6]: - -# Fit transform + +# Fit transform out = model.fit_transform(X) - - - + - - - - - - - + + [pca] >Processing dataframe.. [pca] >Normalizing input data per feature (zero mean and unit variance).. [pca] >The PCA reduction is performed on the [4] columns of the input dataframe. @@ -15364,171 +7733,119 @@ - - - - - + + -In [7]: +In [7]: - -# Make plot with only the directions (no scatter) + +# Make plot with only the directions (no scatter) fig, ax = model.biplot(textlabel=True, legend=False, figsize=(10, 6)) - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 with loadings. - - - - - - - - + + + - - - - - - + + -In [8]: +In [8]: - -# Make plot with only the directions (no scatter) + +# Make plot with only the directions (no scatter) fig, ax = model.biplot(cmap=None, textlabel=False, legend=False, figsize=(10, 6)) - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 with loadings. - - - - - - - - + + + - - - - - - + + -In [9]: +In [9]: - -from pca import pca + +from pca import pca # Load example data from sklearn.datasets import load_iris X = pd.DataFrame(data=load_iris().data, columns=load_iris().feature_names, index=load_iris().target) - - - - - + + + -In [10]: +In [10]: - -# Initialize + +# Initialize model = pca(n_components=3) # Fit using PCA results = model.fit_transform(X) - - - + - - - - - - - + + [pca] >Processing dataframe.. [pca] >The PCA reduction is performed on the [4] columns of the input dataframe. [pca] >Fit using PCA. @@ -15539,20 +7856,17 @@ - - - - - + + -In [11]: +In [11]: - -# Make plots + +# Make plots # Scree plot fig, ax = model.plot(figsize=(10, 6)) @@ -15563,190 +7877,117 @@ # Biplot fig, ax = model.biplot(figsize=(10, 6)) - - - + - - - - - - - - - - + + + - - - - - - - - - + + + - - - - - - + + [pca] >Plot PC1 vs PC2 with loadings. - - - - - - - + + <Figure size 432x288 with 0 Axes> - - - - - - - - - + + + - - - - - - + + -In [17]: +In [17]: - -# Coloring on density to focus on the core samples. + +# Coloring on density to focus on the core samples. # Biplot -fig, ax = model.biplot(figsize=(10, 6), gradient='#ffffff') +fig, ax = model.biplot(figsize=(10, 6), gradient='#ffffff') - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 with loadings. - - - - - - - - + + + - - - - - - + + -In [18]: +In [18]: - -# Outliers are stored in results: -results['outliers'] + +# Outliers are stored in results: +results['outliers'] # Outliers based on T2 -print('--------T2------------') -print(results['outliers'].loc[results['outliers']['y_bool'], :]) +print('--------T2------------') +print(results['outliers'].loc[results['outliers']['y_bool'], :]) # Outliers based on SPE -print('--------SPE------------') -print(results['outliers'].loc[results['outliers']['y_bool_spe'], :]) +print('--------SPE------------') +print(results['outliers'].loc[results['outliers']['y_bool_spe'], :]) - - - + - - - - - - - + + --------T2------------ y_proba y_score y_bool y_bool_spe y_score_spe 2 0.040551 13.160880 True True 3.679935 @@ -15771,270 +8012,168 @@ - - - - - + + -In [20]: +In [20]: - -# Outlier detection + +# Outlier detection fig, ax = model.biplot(SPE=True, HT2=True, figsize=(10, 6)) - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 with loadings. - - - - - - - - + + + - - - - - - + + -In [21]: +In [21]: - -# 3D plots + +# 3D plots fig, ax = model.scatter3d(figsize=(10, 6)) fig, ax = model.biplot3d(figsize=(10, 6)) fig, ax = model.biplot3d(SPE=True, HT2=True, figsize=(10, 6)) - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 vs PC3 with loadings. - - - - - - - - + + + - - - - - - - - - + + + - - - - - - + + [pca] >Plot PC1 vs PC2 vs PC3 with loadings. - - - - - - - - + + + - - - - - - + + -In [22]: +In [22]: - -fig, ax = model.biplot3d(SPE=True, HT2=True, visible=False, figsize=(10, 6)) + +fig, ax = model.biplot3d(SPE=True, HT2=True, visible=False, figsize=(10, 6)) # Set the figure again to True and show the figure. fig.set_visible(True) fig - - - + - - - - - - - + + [pca] >Plot PC1 vs PC2 vs PC3 with loadings. - - Out[22]: - - - - - - +Out[22]: + + - - - - - - - - - + + + - - - - - - + + -In [23]: +In [23]: - -# Normalize out PCs + +
pca A Python Package for Principal Component Analysis. The core of PCA is build on sklearn functionality to find maximum compatibility when combining with other packages.
But this package can do a lot more. Besides the regular pca, it can also perform SparsePCA, and TruncatedSVD. Depending on your input data, the best approach will be choosen.
Other functionalities are:
!pip install pca + +!pip install pca - -
!pip install pca
Requirement already satisfied: pca in /usr/local/lib/python3.7/dist-packages (1.7.2) Requirement already satisfied: matplotlib in /usr/local/lib/python3.7/dist-packages (from pca) (3.2.2) Requirement already satisfied: wget in /usr/local/lib/python3.7/dist-packages (from pca) (3.2) @@ -15180,179 +7579,149 @@
Lets check the version
import pca + +import pca print(pca.__version__) - -
import pca print(pca.__version__)
1.7.2
Import the pca library
from pca import pca + +from pca import pca import numpy as np import pandas as pd - -
from pca import pca import numpy as np import pandas as pd
Here we will create a random dataset.
# Dataset + +# Dataset from sklearn.datasets import load_iris X = pd.DataFrame(data=load_iris().data, columns=load_iris().feature_names, index=load_iris().target) - -
# Dataset from sklearn.datasets import load_iris X = pd.DataFrame(data=load_iris().data, columns=load_iris().feature_names, index=load_iris().target)
Initialize using specified parameters. The parameters here are the default parameters.
# Initialize + +# Initialize model = pca(n_components=3, normalize=True) - -
# Initialize model = pca(n_components=3, normalize=True)
# Fit transform + +# Fit transform out = model.fit_transform(X) - -
# Fit transform out = model.fit_transform(X)
[pca] >Processing dataframe.. [pca] >Normalizing input data per feature (zero mean and unit variance).. [pca] >The PCA reduction is performed on the [4] columns of the input dataframe. @@ -15364,171 +7733,119 @@
# Make plot with only the directions (no scatter) + +# Make plot with only the directions (no scatter) fig, ax = model.biplot(textlabel=True, legend=False, figsize=(10, 6)) - -
# Make plot with only the directions (no scatter) fig, ax = model.biplot(textlabel=True, legend=False, figsize=(10, 6))
[pca] >Plot PC1 vs PC2 with loadings.
# Make plot with only the directions (no scatter) + +# Make plot with only the directions (no scatter) fig, ax = model.biplot(cmap=None, textlabel=False, legend=False, figsize=(10, 6)) - -
# Make plot with only the directions (no scatter) fig, ax = model.biplot(cmap=None, textlabel=False, legend=False, figsize=(10, 6))
from pca import pca + +from pca import pca # Load example data from sklearn.datasets import load_iris X = pd.DataFrame(data=load_iris().data, columns=load_iris().feature_names, index=load_iris().target) - -
from pca import pca # Load example data from sklearn.datasets import load_iris X = pd.DataFrame(data=load_iris().data, columns=load_iris().feature_names, index=load_iris().target)
# Initialize + +# Initialize model = pca(n_components=3) # Fit using PCA results = model.fit_transform(X) - -
# Initialize model = pca(n_components=3) # Fit using PCA results = model.fit_transform(X)
[pca] >Processing dataframe.. [pca] >The PCA reduction is performed on the [4] columns of the input dataframe. [pca] >Fit using PCA. @@ -15539,20 +7856,17 @@
# Make plots + +# Make plots # Scree plot fig, ax = model.plot(figsize=(10, 6)) @@ -15563,190 +7877,117 @@ # Biplot fig, ax = model.biplot(figsize=(10, 6)) - -
# Make plots # Scree plot fig, ax = model.plot(figsize=(10, 6)) @@ -15563,190 +7877,117 @@ # Biplot fig, ax = model.biplot(figsize=(10, 6))
<Figure size 432x288 with 0 Axes>
# Coloring on density to focus on the core samples. + +# Coloring on density to focus on the core samples. # Biplot -fig, ax = model.biplot(figsize=(10, 6), gradient='#ffffff') +fig, ax = model.biplot(figsize=(10, 6), gradient='#ffffff') - -
# Coloring on density to focus on the core samples. # Biplot -fig, ax = model.biplot(figsize=(10, 6), gradient='#ffffff') +fig, ax = model.biplot(figsize=(10, 6), gradient='#ffffff')
# Outliers are stored in results: -results['outliers'] + +# Outliers are stored in results: +results['outliers'] # Outliers based on T2 -print('--------T2------------') -print(results['outliers'].loc[results['outliers']['y_bool'], :]) +print('--------T2------------') +print(results['outliers'].loc[results['outliers']['y_bool'], :]) # Outliers based on SPE -print('--------SPE------------') -print(results['outliers'].loc[results['outliers']['y_bool_spe'], :]) +print('--------SPE------------') +print(results['outliers'].loc[results['outliers']['y_bool_spe'], :]) - -
# Outliers are stored in results: +results['outliers'] # Outliers based on T2 -print('--------T2------------') -print(results['outliers'].loc[results['outliers']['y_bool'], :]) +print('--------T2------------') +print(results['outliers'].loc[results['outliers']['y_bool'], :]) # Outliers based on SPE -print('--------SPE------------') -print(results['outliers'].loc[results['outliers']['y_bool_spe'], :]) +print('--------SPE------------') +print(results['outliers'].loc[results['outliers']['y_bool_spe'], :])
--------T2------------ y_proba y_score y_bool y_bool_spe y_score_spe 2 0.040551 13.160880 True True 3.679935 @@ -15771,270 +8012,168 @@
# Outlier detection + +# Outlier detection fig, ax = model.biplot(SPE=True, HT2=True, figsize=(10, 6)) - -
# Outlier detection fig, ax = model.biplot(SPE=True, HT2=True, figsize=(10, 6))
# 3D plots + +# 3D plots fig, ax = model.scatter3d(figsize=(10, 6)) fig, ax = model.biplot3d(figsize=(10, 6)) fig, ax = model.biplot3d(SPE=True, HT2=True, figsize=(10, 6)) - -
# 3D plots fig, ax = model.scatter3d(figsize=(10, 6)) fig, ax = model.biplot3d(figsize=(10, 6)) fig, ax = model.biplot3d(SPE=True, HT2=True, figsize=(10, 6))
[pca] >Plot PC1 vs PC2 vs PC3 with loadings.
fig, ax = model.biplot3d(SPE=True, HT2=True, visible=False, figsize=(10, 6)) + +fig, ax = model.biplot3d(SPE=True, HT2=True, visible=False, figsize=(10, 6)) # Set the figure again to True and show the figure. fig.set_visible(True) fig - -
fig, ax = model.biplot3d(SPE=True, HT2=True, visible=False, figsize=(10, 6)) # Set the figure again to True and show the figure. fig.set_visible(True) fig
# Normalize out PCs + +