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<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN"
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<html xmlns="http://www.w3.org/1999/xhtml">
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<title>Course on Practical Neuroimaging in Python — Practical neuroimaging analysis</title>
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<div class="section" id="day-7-diagnostics-using-principal-component-analysis">
<h1>Day 7: diagnostics using principal component analysis<a class="headerlink" href="#day-7-diagnostics-using-principal-component-analysis" title="Permalink to this headline">¶</a></h1>
<p>4 / 10 / 2015</p>
<p>This class is for us to get an idea of the variation in the FMRI data, and to
start working with images as matrices. We will do this using <a class="reference external" href="https://en.wikipedia.org/wiki/Principal_component_analysis">principal
component analysis</a> (PCA).</p>
<div class="section" id="reading">
<h2>Reading<a class="headerlink" href="#reading" title="Permalink to this headline">¶</a></h2>
<p>In the class we will cover what PCA is and how it works.</p>
<p>For this explanation we need some basic ideas from linear algebra, and in
particular, the idea of projecting a vector onto another vector using the dot
product. This background will also be useful to us later in thinking about
regressors and statistical models.</p>
<p>So the “readings” for this week are some excellent Khan academy videos on
linear algebra.</p>
<div class="section" id="basic-background-on-dot-products">
<h3>Basic background on dot products<a class="headerlink" href="#basic-background-on-dot-products" title="Permalink to this headline">¶</a></h3>
<ul class="simple">
<li><a class="reference external" href="https://www.khanacademy.org/math/linear-algebra/vectors_and_spaces/dot_cross_products/v/vector-dot-product-and-vector-length">Vector dot product and vector length</a>
(9 minutes) (calculating vector length in N dimensions, and the relationship
to the vector dot product);</li>
<li><a class="reference external" href="https://www.khanacademy.org/math/linear-algebra/vectors_and_spaces/dot_cross_products/v/proving-vector-dot-product-properties">Proving vector dot product properties</a>
(11 minutes) (reminding us of - and proving - some mathematical properties
of dot products on vectors).</li>
</ul>
</div>
<div class="section" id="helpful-extra-background">
<h3>Helpful extra background<a class="headerlink" href="#helpful-extra-background" title="Permalink to this headline">¶</a></h3>
<p>Optional but highly recommended:</p>
<ul class="simple">
<li><a class="reference external" href="https://www.khanacademy.org/math/linear-algebra/vectors_and_spaces/dot_cross_products/v/defining-the-angle-between-vectors">Defining the angle between vectors</a>
(25 minutes) (among other things - why orthogonal vectors have dot product
of zero);</li>
<li><a class="reference external" href="https://www.khanacademy.org/math/linear-algebra/matrix_transformations/lin_trans_examples/v/unit-vectors">Unit vectors</a>
(7 minutes).</li>
</ul>
</div>
<div class="section" id="key-video-on-projecting-vectors">
<h3>Key video on projecting vectors<a class="headerlink" href="#key-video-on-projecting-vectors" title="Permalink to this headline">¶</a></h3>
<p>The following video is the key homework for the class. The videos above are
background for this video.</p>
<ul class="simple">
<li><a class="reference external" href="https://www.khanacademy.org/math/linear-algebra/matrix_transformations/lin_trans_examples/v/introduction-to-projections">Introduction to projections</a>
(15 minutes);</li>
</ul>
</div>
<div class="section" id="if-you-are-racing-ahead">
<h3>If you are racing ahead<a class="headerlink" href="#if-you-are-racing-ahead" title="Permalink to this headline">¶</a></h3>
<p>If you have extra time on your hands or you are confident you already know
about matrices and projection and want something more advanced, this is
introductory <a class="reference external" href="http://arxiv.org/abs/1404.1100">tutorial on principal component analysis</a>. It does assume that you know about
projecting vectors, which you will, after covering the Khan academy videos.</p>
</div>
</div>
<div class="section" id="day">
<h2>Day<a class="headerlink" href="#day" title="Permalink to this headline">¶</a></h2>
<ul class="simple">
<li>Get data from image</li>
<li>Run PCA;</li>
<li>Fetch projection matrices, vectors and values;</li>
<li>Reconstruct data using reduced number of components.</li>
<li>Investigate and diagnose components;</li>
<li>Investigate correlation of vectors with data.</li>
</ul>
</div>
<div class="section" id="exercises">
<h2>Exercises<a class="headerlink" href="#exercises" title="Permalink to this headline">¶</a></h2>
<p>The usual instructions:</p>
<ul class="simple">
<li><code class="docutils literal"><span class="pre">cd</span> <span class="pre">pna/pna2015</span></code></li>
<li><code class="docutils literal"><span class="pre">git</span> <span class="pre">pull</span></code></li>
<li><code class="docutils literal"><span class="pre">ipython</span> <span class="pre">notebook</span></code></li>
</ul>
<p>There is a web page listing of the exercise files at
<a class="reference external" href="https://github.com/practical-neuroimaging/pna2015/tree/master/day7">https://github.com/practical-neuroimaging/pna2015/tree/master/day7</a></p>
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<ul>
<li><a class="reference internal" href="#">Day 7: diagnostics using principal component analysis</a><ul>
<li><a class="reference internal" href="#reading">Reading</a><ul>
<li><a class="reference internal" href="#basic-background-on-dot-products">Basic background on dot products</a></li>
<li><a class="reference internal" href="#helpful-extra-background">Helpful extra background</a></li>
<li><a class="reference internal" href="#key-video-on-projecting-vectors">Key video on projecting vectors</a></li>
<li><a class="reference internal" href="#if-you-are-racing-ahead">If you are racing ahead</a></li>
</ul>
</li>
<li><a class="reference internal" href="#day">Day</a></li>
<li><a class="reference internal" href="#exercises">Exercises</a></li>
</ul>
</li>
</ul>
<h4>Previous topic</h4>
<p class="topless"><a href="day6.html"
title="previous chapter">Day 6: regression and the general linear model</a></p>
<h4>Next topic</h4>
<p class="topless"><a href="day8.html"
title="next chapter">Day 8: 1D interpolation and slice timing</a></p>
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>index</a></li>
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<a href="day8.html" title="Day 8: 1D interpolation and slice timing"
>next</a> |</li>
<li class="right" >
<a href="day6.html" title="Day 6: regression and the general linear model"
>previous</a> |</li>
<big><big><big><li><a href="index.html">Home</a> | </li>
<li><a href="https://github.com/practical-neuroimaging/pna2015">Exercises</a> | </li>
<li><a href="https://calmail.berkeley.edu/manage/list/listinfo/practical_fmri@lists.berkeley.edu">Mailing list</a> | </li></big></big></big>
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