13-10-2021(PCA).ipynb

{
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  {
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   "id": "74ae66fc",
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   "source": [
    "Dimensionality Reduction\n",
    "- used to transform from high dimensional space to low dimensional space\n",
    "- retain some meaningful properties from the original data\n",
    "\n",
    "***Why Dimesionality Reduction***  \n",
    "\n",
    "- higher dimensions leads to dimensionality curse\n",
    "- if there are higher dimesions model performnace will be low\n",
    "Use cases:\n",
    "    - signal processing\n",
    "    - speech recognition"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5c5b2521",
   "metadata": {},
   "source": [
    "***Tools for Dimensionality reduction***   \n",
    "\n",
    "linear methods\n",
    "- PCA-Principal Component Analysis\n",
    "- LDA-Linear Discriminant Analysis   \n",
    "\n",
    "Non Linear Methods  \n",
    "\n",
    "- Kernel PCA\n",
    "- Graph Based PCA\n",
    "- GDA(generalised Discriminant Analysis)\n",
    "- Auto encoders"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d53bbe33",
   "metadata": {},
   "source": [
    "#### Approches Dimensionality\n",
    "- Feature Selection/Elimination\n",
    "- Feature Extraction"
   ]
  },
  {
   "cell_type": "raw",
   "id": "fd4dcef5",
   "metadata": {},
   "source": [
    "Steps in PCA:\n",
    "    - standardizing the data\n",
    "    - covariance[a,a   a,b\n",
    "                 b,a   b,b]\n",
    "        - negative value--->indirectlty proportional\n",
    "        - positive value----->directly proportional\n",
    "    - calculate eigen values and eigen vectors\n",
    "    - compute principal component analysis(30--->3)\n",
    "    - reduce the dimensions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "6b7a8f7a",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.datasets import load_breast_cancer\n",
    "cancer=load_breast_cancer()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "0094f014",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      ".. _breast_cancer_dataset:\n",
      "\n",
      "Breast cancer wisconsin (diagnostic) dataset\n",
      "--------------------------------------------\n",
      "\n",
      "**Data Set Characteristics:**\n",
      "\n",
      "    :Number of Instances: 569\n",
      "\n",
      "    :Number of Attributes: 30 numeric, predictive attributes and the class\n",
      "\n",
      "    :Attribute Information:\n",
      "        - radius (mean of distances from center to points on the perimeter)\n",
      "        - texture (standard deviation of gray-scale values)\n",
      "        - perimeter\n",
      "        - area\n",
      "        - smoothness (local variation in radius lengths)\n",
      "        - compactness (perimeter^2 / area - 1.0)\n",
      "        - concavity (severity of concave portions of the contour)\n",
      "        - concave points (number of concave portions of the contour)\n",
      "        - symmetry\n",
      "        - fractal dimension (\"coastline approximation\" - 1)\n",
      "\n",
      "        The mean, standard error, and \"worst\" or largest (mean of the three\n",
      "        worst/largest values) of these features were computed for each image,\n",
      "        resulting in 30 features.  For instance, field 0 is Mean Radius, field\n",
      "        10 is Radius SE, field 20 is Worst Radius.\n",
      "\n",
      "        - class:\n",
      "                - WDBC-Malignant\n",
      "                - WDBC-Benign\n",
      "\n",
      "    :Summary Statistics:\n",
      "\n",
      "    ===================================== ====== ======\n",
      "                                           Min    Max\n",
      "    ===================================== ====== ======\n",
      "    radius (mean):                        6.981  28.11\n",
      "    texture (mean):                       9.71   39.28\n",
      "    perimeter (mean):                     43.79  188.5\n",
      "    area (mean):                          143.5  2501.0\n",
      "    smoothness (mean):                    0.053  0.163\n",
      "    compactness (mean):                   0.019  0.345\n",
      "    concavity (mean):                     0.0    0.427\n",
      "    concave points (mean):                0.0    0.201\n",
      "    symmetry (mean):                      0.106  0.304\n",
      "    fractal dimension (mean):             0.05   0.097\n",
      "    radius (standard error):              0.112  2.873\n",
      "    texture (standard error):             0.36   4.885\n",
      "    perimeter (standard error):           0.757  21.98\n",
      "    area (standard error):                6.802  542.2\n",
      "    smoothness (standard error):          0.002  0.031\n",
      "    compactness (standard error):         0.002  0.135\n",
      "    concavity (standard error):           0.0    0.396\n",
      "    concave points (standard error):      0.0    0.053\n",
      "    symmetry (standard error):            0.008  0.079\n",
      "    fractal dimension (standard error):   0.001  0.03\n",
      "    radius (worst):                       7.93   36.04\n",
      "    texture (worst):                      12.02  49.54\n",
      "    perimeter (worst):                    50.41  251.2\n",
      "    area (worst):                         185.2  4254.0\n",
      "    smoothness (worst):                   0.071  0.223\n",
      "    compactness (worst):                  0.027  1.058\n",
      "    concavity (worst):                    0.0    1.252\n",
      "    concave points (worst):               0.0    0.291\n",
      "    symmetry (worst):                     0.156  0.664\n",
      "    fractal dimension (worst):            0.055  0.208\n",
      "    ===================================== ====== ======\n",
      "\n",
      "    :Missing Attribute Values: None\n",
      "\n",
      "    :Class Distribution: 212 - Malignant, 357 - Benign\n",
      "\n",
      "    :Creator:  Dr. William H. Wolberg, W. Nick Street, Olvi L. Mangasarian\n",
      "\n",
      "    :Donor: Nick Street\n",
      "\n",
      "    :Date: November, 1995\n",
      "\n",
      "This is a copy of UCI ML Breast Cancer Wisconsin (Diagnostic) datasets.\n",
      "https://goo.gl/U2Uwz2\n",
      "\n",
      "Features are computed from a digitized image of a fine needle\n",
      "aspirate (FNA) of a breast mass.  They describe\n",
      "characteristics of the cell nuclei present in the image.\n",
      "\n",
      "Separating plane described above was obtained using\n",
      "Multisurface Method-Tree (MSM-T) [K. P. Bennett, \"Decision Tree\n",
      "Construction Via Linear Programming.\" Proceedings of the 4th\n",
      "Midwest Artificial Intelligence and Cognitive Science Society,\n",
      "pp. 97-101, 1992], a classification method which uses linear\n",
      "programming to construct a decision tree.  Relevant features\n",
      "were selected using an exhaustive search in the space of 1-4\n",
      "features and 1-3 separating planes.\n",
      "\n",
      "The actual linear program used to obtain the separating plane\n",
      "in the 3-dimensional space is that described in:\n",
      "[K. P. Bennett and O. L. Mangasarian: \"Robust Linear\n",
      "Programming Discrimination of Two Linearly Inseparable Sets\",\n",
      "Optimization Methods and Software 1, 1992, 23-34].\n",
      "\n",
      "This database is also available through the UW CS ftp server:\n",
      "\n",
      "ftp ftp.cs.wisc.edu\n",
      "cd math-prog/cpo-dataset/machine-learn/WDBC/\n",
      "\n",
      ".. topic:: References\n",
      "\n",
      "   - W.N. Street, W.H. Wolberg and O.L. Mangasarian. Nuclear feature extraction \n",
      "     for breast tumor diagnosis. IS&T/SPIE 1993 International Symposium on \n",
      "     Electronic Imaging: Science and Technology, volume 1905, pages 861-870,\n",
      "     San Jose, CA, 1993.\n",
      "   - O.L. Mangasarian, W.N. Street and W.H. Wolberg. Breast cancer diagnosis and \n",
      "     prognosis via linear programming. Operations Research, 43(4), pages 570-577, \n",
      "     July-August 1995.\n",
      "   - W.H. Wolberg, W.N. Street, and O.L. Mangasarian. Machine learning techniques\n",
      "     to diagnose breast cancer from fine-needle aspirates. Cancer Letters 77 (1994) \n",
      "     163-171.\n"
     ]
    }
   ],
   "source": [
    "print(cancer.DESCR)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "9f1731fc",
   "metadata": {
    "collapsed": true
   },
   "outputs": [
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean radius</th>\n",
       "      <th>mean texture</th>\n",
       "      <th>mean perimeter</th>\n",
       "      <th>mean area</th>\n",
       "      <th>mean smoothness</th>\n",
       "      <th>mean compactness</th>\n",
       "      <th>mean concavity</th>\n",
       "      <th>mean concave points</th>\n",
       "      <th>mean symmetry</th>\n",
       "      <th>mean fractal dimension</th>\n",
       "      <th>...</th>\n",
       "      <th>worst radius</th>\n",
       "      <th>worst texture</th>\n",
       "      <th>worst perimeter</th>\n",
       "      <th>worst area</th>\n",
       "      <th>worst smoothness</th>\n",
       "      <th>worst compactness</th>\n",
       "      <th>worst concavity</th>\n",
       "      <th>worst concave points</th>\n",
       "      <th>worst symmetry</th>\n",
       "      <th>worst fractal dimension</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>17.99</td>\n",
       "      <td>10.38</td>\n",
       "      <td>122.80</td>\n",
       "      <td>1001.0</td>\n",
       "      <td>0.11840</td>\n",
       "      <td>0.27760</td>\n",
       "      <td>0.3001</td>\n",
       "      <td>0.14710</td>\n",
       "      <td>0.2419</td>\n",
       "      <td>0.07871</td>\n",
       "      <td>...</td>\n",
       "      <td>25.38</td>\n",
       "      <td>17.33</td>\n",
       "      <td>184.60</td>\n",
       "      <td>2019.0</td>\n",
       "      <td>0.1622</td>\n",
       "      <td>0.6656</td>\n",
       "      <td>0.7119</td>\n",
       "      <td>0.2654</td>\n",
       "      <td>0.4601</td>\n",
       "      <td>0.11890</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>20.57</td>\n",
       "      <td>17.77</td>\n",
       "      <td>132.90</td>\n",
       "      <td>1326.0</td>\n",
       "      <td>0.08474</td>\n",
       "      <td>0.07864</td>\n",
       "      <td>0.0869</td>\n",
       "      <td>0.07017</td>\n",
       "      <td>0.1812</td>\n",
       "      <td>0.05667</td>\n",
       "      <td>...</td>\n",
       "      <td>24.99</td>\n",
       "      <td>23.41</td>\n",
       "      <td>158.80</td>\n",
       "      <td>1956.0</td>\n",
       "      <td>0.1238</td>\n",
       "      <td>0.1866</td>\n",
       "      <td>0.2416</td>\n",
       "      <td>0.1860</td>\n",
       "      <td>0.2750</td>\n",
       "      <td>0.08902</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>19.69</td>\n",
       "      <td>21.25</td>\n",
       "      <td>130.00</td>\n",
       "      <td>1203.0</td>\n",
       "      <td>0.10960</td>\n",
       "      <td>0.15990</td>\n",
       "      <td>0.1974</td>\n",
       "      <td>0.12790</td>\n",
       "      <td>0.2069</td>\n",
       "      <td>0.05999</td>\n",
       "      <td>...</td>\n",
       "      <td>23.57</td>\n",
       "      <td>25.53</td>\n",
       "      <td>152.50</td>\n",
       "      <td>1709.0</td>\n",
       "      <td>0.1444</td>\n",
       "      <td>0.4245</td>\n",
       "      <td>0.4504</td>\n",
       "      <td>0.2430</td>\n",
       "      <td>0.3613</td>\n",
       "      <td>0.08758</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>11.42</td>\n",
       "      <td>20.38</td>\n",
       "      <td>77.58</td>\n",
       "      <td>386.1</td>\n",
       "      <td>0.14250</td>\n",
       "      <td>0.28390</td>\n",
       "      <td>0.2414</td>\n",
       "      <td>0.10520</td>\n",
       "      <td>0.2597</td>\n",
       "      <td>0.09744</td>\n",
       "      <td>...</td>\n",
       "      <td>14.91</td>\n",
       "      <td>26.50</td>\n",
       "      <td>98.87</td>\n",
       "      <td>567.7</td>\n",
       "      <td>0.2098</td>\n",
       "      <td>0.8663</td>\n",
       "      <td>0.6869</td>\n",
       "      <td>0.2575</td>\n",
       "      <td>0.6638</td>\n",
       "      <td>0.17300</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>20.29</td>\n",
       "      <td>14.34</td>\n",
       "      <td>135.10</td>\n",
       "      <td>1297.0</td>\n",
       "      <td>0.10030</td>\n",
       "      <td>0.13280</td>\n",
       "      <td>0.1980</td>\n",
       "      <td>0.10430</td>\n",
       "      <td>0.1809</td>\n",
       "      <td>0.05883</td>\n",
       "      <td>...</td>\n",
       "      <td>22.54</td>\n",
       "      <td>16.67</td>\n",
       "      <td>152.20</td>\n",
       "      <td>1575.0</td>\n",
       "      <td>0.1374</td>\n",
       "      <td>0.2050</td>\n",
       "      <td>0.4000</td>\n",
       "      <td>0.1625</td>\n",
       "      <td>0.2364</td>\n",
       "      <td>0.07678</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 30 columns</p>\n",
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      "text/plain": [
       "   mean radius  mean texture  mean perimeter  mean area  mean smoothness  \\\n",
       "0        17.99         10.38          122.80     1001.0          0.11840   \n",
       "1        20.57         17.77          132.90     1326.0          0.08474   \n",
       "2        19.69         21.25          130.00     1203.0          0.10960   \n",
       "3        11.42         20.38           77.58      386.1          0.14250   \n",
       "4        20.29         14.34          135.10     1297.0          0.10030   \n",
       "\n",
       "   mean compactness  mean concavity  mean concave points  mean symmetry  \\\n",
       "0           0.27760          0.3001              0.14710         0.2419   \n",
       "1           0.07864          0.0869              0.07017         0.1812   \n",
       "2           0.15990          0.1974              0.12790         0.2069   \n",
       "3           0.28390          0.2414              0.10520         0.2597   \n",
       "4           0.13280          0.1980              0.10430         0.1809   \n",
       "\n",
       "   mean fractal dimension  ...  worst radius  worst texture  worst perimeter  \\\n",
       "0                 0.07871  ...         25.38          17.33           184.60   \n",
       "1                 0.05667  ...         24.99          23.41           158.80   \n",
       "2                 0.05999  ...         23.57          25.53           152.50   \n",
       "3                 0.09744  ...         14.91          26.50            98.87   \n",
       "4                 0.05883  ...         22.54          16.67           152.20   \n",
       "\n",
       "   worst area  worst smoothness  worst compactness  worst concavity  \\\n",
       "0      2019.0            0.1622             0.6656           0.7119   \n",
       "1      1956.0            0.1238             0.1866           0.2416   \n",
       "2      1709.0            0.1444             0.4245           0.4504   \n",
       "3       567.7            0.2098             0.8663           0.6869   \n",
       "4      1575.0            0.1374             0.2050           0.4000   \n",
       "\n",
       "   worst concave points  worst symmetry  worst fractal dimension  \n",
       "0                0.2654          0.4601                  0.11890  \n",
       "1                0.1860          0.2750                  0.08902  \n",
       "2                0.2430          0.3613                  0.08758  \n",
       "3                0.2575          0.6638                  0.17300  \n",
       "4                0.1625          0.2364                  0.07678  \n",
       "\n",
       "[5 rows x 30 columns]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "df=pd.DataFrame(cancer.data,columns=cancer.feature_names)\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "dd4ac09a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(569, 30)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "b5a929cf",
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "mean radius                float64\n",
       "mean texture               float64\n",
       "mean perimeter             float64\n",
       "mean area                  float64\n",
       "mean smoothness            float64\n",
       "mean compactness           float64\n",
       "mean concavity             float64\n",
       "mean concave points        float64\n",
       "mean symmetry              float64\n",
       "mean fractal dimension     float64\n",
       "radius error               float64\n",
       "texture error              float64\n",
       "perimeter error            float64\n",
       "area error                 float64\n",
       "smoothness error           float64\n",
       "compactness error          float64\n",
       "concavity error            float64\n",
       "concave points error       float64\n",
       "symmetry error             float64\n",
       "fractal dimension error    float64\n",
       "worst radius               float64\n",
       "worst texture              float64\n",
       "worst perimeter            float64\n",
       "worst area                 float64\n",
       "worst smoothness           float64\n",
       "worst compactness          float64\n",
       "worst concavity            float64\n",
       "worst concave points       float64\n",
       "worst symmetry             float64\n",
       "worst fractal dimension    float64\n",
       "dtype: object"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.dtypes    #what type of data we have in every coloumn\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "3c1043ca",
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['mean radius', 'mean texture', 'mean perimeter', 'mean area',\n",
       "       'mean smoothness', 'mean compactness', 'mean concavity',\n",
       "       'mean concave points', 'mean symmetry', 'mean fractal dimension',\n",
       "       'radius error', 'texture error', 'perimeter error', 'area error',\n",
       "       'smoothness error', 'compactness error', 'concavity error',\n",
       "       'concave points error', 'symmetry error', 'fractal dimension error',\n",
       "       'worst radius', 'worst texture', 'worst perimeter', 'worst area',\n",
       "       'worst smoothness', 'worst compactness', 'worst concavity',\n",
       "       'worst concave points', 'worst symmetry', 'worst fractal dimension'],\n",
       "      dtype='object')"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "386dd981",
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
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       "  <thead>\n",
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       "      <th></th>\n",
       "      <th>mean radius</th>\n",
       "      <th>mean texture</th>\n",
       "      <th>mean perimeter</th>\n",
       "      <th>mean area</th>\n",
       "      <th>mean smoothness</th>\n",
       "      <th>mean compactness</th>\n",
       "      <th>mean concavity</th>\n",
       "      <th>mean concave points</th>\n",
       "      <th>mean symmetry</th>\n",
       "      <th>mean fractal dimension</th>\n",
       "      <th>...</th>\n",
       "      <th>worst radius</th>\n",
       "      <th>worst texture</th>\n",
       "      <th>worst perimeter</th>\n",
       "      <th>worst area</th>\n",
       "      <th>worst smoothness</th>\n",
       "      <th>worst compactness</th>\n",
       "      <th>worst concavity</th>\n",
       "      <th>worst concave points</th>\n",
       "      <th>worst symmetry</th>\n",
       "      <th>worst fractal dimension</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>569.000000</td>\n",
       "      <td>569.000000</td>\n",
       "      <td>569.000000</td>\n",
       "      <td>569.000000</td>\n",
       "      <td>569.000000</td>\n",
       "      <td>569.000000</td>\n",
       "      <td>569.000000</td>\n",
       "      <td>569.000000</td>\n",
       "      <td>569.000000</td>\n",
       "      <td>569.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>569.000000</td>\n",
       "      <td>569.000000</td>\n",
       "      <td>569.000000</td>\n",
       "      <td>569.000000</td>\n",
       "      <td>569.000000</td>\n",
       "      <td>569.000000</td>\n",
       "      <td>569.000000</td>\n",
       "      <td>569.000000</td>\n",
       "      <td>569.000000</td>\n",
       "      <td>569.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>14.127292</td>\n",
       "      <td>19.289649</td>\n",
       "      <td>91.969033</td>\n",
       "      <td>654.889104</td>\n",
       "      <td>0.096360</td>\n",
       "      <td>0.104341</td>\n",
       "      <td>0.088799</td>\n",
       "      <td>0.048919</td>\n",
       "      <td>0.181162</td>\n",
       "      <td>0.062798</td>\n",
       "      <td>...</td>\n",
       "      <td>16.269190</td>\n",
       "      <td>25.677223</td>\n",
       "      <td>107.261213</td>\n",
       "      <td>880.583128</td>\n",
       "      <td>0.132369</td>\n",
       "      <td>0.254265</td>\n",
       "      <td>0.272188</td>\n",
       "      <td>0.114606</td>\n",
       "      <td>0.290076</td>\n",
       "      <td>0.083946</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>3.524049</td>\n",
       "      <td>4.301036</td>\n",
       "      <td>24.298981</td>\n",
       "      <td>351.914129</td>\n",
       "      <td>0.014064</td>\n",
       "      <td>0.052813</td>\n",
       "      <td>0.079720</td>\n",
       "      <td>0.038803</td>\n",
       "      <td>0.027414</td>\n",
       "      <td>0.007060</td>\n",
       "      <td>...</td>\n",
       "      <td>4.833242</td>\n",
       "      <td>6.146258</td>\n",
       "      <td>33.602542</td>\n",
       "      <td>569.356993</td>\n",
       "      <td>0.022832</td>\n",
       "      <td>0.157336</td>\n",
       "      <td>0.208624</td>\n",
       "      <td>0.065732</td>\n",
       "      <td>0.061867</td>\n",
       "      <td>0.018061</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>6.981000</td>\n",
       "      <td>9.710000</td>\n",
       "      <td>43.790000</td>\n",
       "      <td>143.500000</td>\n",
       "      <td>0.052630</td>\n",
       "      <td>0.019380</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.106000</td>\n",
       "      <td>0.049960</td>\n",
       "      <td>...</td>\n",
       "      <td>7.930000</td>\n",
       "      <td>12.020000</td>\n",
       "      <td>50.410000</td>\n",
       "      <td>185.200000</td>\n",
       "      <td>0.071170</td>\n",
       "      <td>0.027290</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.156500</td>\n",
       "      <td>0.055040</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>11.700000</td>\n",
       "      <td>16.170000</td>\n",
       "      <td>75.170000</td>\n",
       "      <td>420.300000</td>\n",
       "      <td>0.086370</td>\n",
       "      <td>0.064920</td>\n",
       "      <td>0.029560</td>\n",
       "      <td>0.020310</td>\n",
       "      <td>0.161900</td>\n",
       "      <td>0.057700</td>\n",
       "      <td>...</td>\n",
       "      <td>13.010000</td>\n",
       "      <td>21.080000</td>\n",
       "      <td>84.110000</td>\n",
       "      <td>515.300000</td>\n",
       "      <td>0.116600</td>\n",
       "      <td>0.147200</td>\n",
       "      <td>0.114500</td>\n",
       "      <td>0.064930</td>\n",
       "      <td>0.250400</td>\n",
       "      <td>0.071460</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>13.370000</td>\n",
       "      <td>18.840000</td>\n",
       "      <td>86.240000</td>\n",
       "      <td>551.100000</td>\n",
       "      <td>0.095870</td>\n",
       "      <td>0.092630</td>\n",
       "      <td>0.061540</td>\n",
       "      <td>0.033500</td>\n",
       "      <td>0.179200</td>\n",
       "      <td>0.061540</td>\n",
       "      <td>...</td>\n",
       "      <td>14.970000</td>\n",
       "      <td>25.410000</td>\n",
       "      <td>97.660000</td>\n",
       "      <td>686.500000</td>\n",
       "      <td>0.131300</td>\n",
       "      <td>0.211900</td>\n",
       "      <td>0.226700</td>\n",
       "      <td>0.099930</td>\n",
       "      <td>0.282200</td>\n",
       "      <td>0.080040</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>15.780000</td>\n",
       "      <td>21.800000</td>\n",
       "      <td>104.100000</td>\n",
       "      <td>782.700000</td>\n",
       "      <td>0.105300</td>\n",
       "      <td>0.130400</td>\n",
       "      <td>0.130700</td>\n",
       "      <td>0.074000</td>\n",
       "      <td>0.195700</td>\n",
       "      <td>0.066120</td>\n",
       "      <td>...</td>\n",
       "      <td>18.790000</td>\n",
       "      <td>29.720000</td>\n",
       "      <td>125.400000</td>\n",
       "      <td>1084.000000</td>\n",
       "      <td>0.146000</td>\n",
       "      <td>0.339100</td>\n",
       "      <td>0.382900</td>\n",
       "      <td>0.161400</td>\n",
       "      <td>0.317900</td>\n",
       "      <td>0.092080</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>28.110000</td>\n",
       "      <td>39.280000</td>\n",
       "      <td>188.500000</td>\n",
       "      <td>2501.000000</td>\n",
       "      <td>0.163400</td>\n",
       "      <td>0.345400</td>\n",
       "      <td>0.426800</td>\n",
       "      <td>0.201200</td>\n",
       "      <td>0.304000</td>\n",
       "      <td>0.097440</td>\n",
       "      <td>...</td>\n",
       "      <td>36.040000</td>\n",
       "      <td>49.540000</td>\n",
       "      <td>251.200000</td>\n",
       "      <td>4254.000000</td>\n",
       "      <td>0.222600</td>\n",
       "      <td>1.058000</td>\n",
       "      <td>1.252000</td>\n",
       "      <td>0.291000</td>\n",
       "      <td>0.663800</td>\n",
       "      <td>0.207500</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>8 rows × 30 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "       mean radius  mean texture  mean perimeter    mean area  \\\n",
       "count   569.000000    569.000000      569.000000   569.000000   \n",
       "mean     14.127292     19.289649       91.969033   654.889104   \n",
       "std       3.524049      4.301036       24.298981   351.914129   \n",
       "min       6.981000      9.710000       43.790000   143.500000   \n",
       "25%      11.700000     16.170000       75.170000   420.300000   \n",
       "50%      13.370000     18.840000       86.240000   551.100000   \n",
       "75%      15.780000     21.800000      104.100000   782.700000   \n",
       "max      28.110000     39.280000      188.500000  2501.000000   \n",
       "\n",
       "       mean smoothness  mean compactness  mean concavity  mean concave points  \\\n",
       "count       569.000000        569.000000      569.000000           569.000000   \n",
       "mean          0.096360          0.104341        0.088799             0.048919   \n",
       "std           0.014064          0.052813        0.079720             0.038803   \n",
       "min           0.052630          0.019380        0.000000             0.000000   \n",
       "25%           0.086370          0.064920        0.029560             0.020310   \n",
       "50%           0.095870          0.092630        0.061540             0.033500   \n",
       "75%           0.105300          0.130400        0.130700             0.074000   \n",
       "max           0.163400          0.345400        0.426800             0.201200   \n",
       "\n",
       "       mean symmetry  mean fractal dimension  ...  worst radius  \\\n",
       "count     569.000000              569.000000  ...    569.000000   \n",
       "mean        0.181162                0.062798  ...     16.269190   \n",
       "std         0.027414                0.007060  ...      4.833242   \n",
       "min         0.106000                0.049960  ...      7.930000   \n",
       "25%         0.161900                0.057700  ...     13.010000   \n",
       "50%         0.179200                0.061540  ...     14.970000   \n",
       "75%         0.195700                0.066120  ...     18.790000   \n",
       "max         0.304000                0.097440  ...     36.040000   \n",
       "\n",
       "       worst texture  worst perimeter   worst area  worst smoothness  \\\n",
       "count     569.000000       569.000000   569.000000        569.000000   \n",
       "mean       25.677223       107.261213   880.583128          0.132369   \n",
       "std         6.146258        33.602542   569.356993          0.022832   \n",
       "min        12.020000        50.410000   185.200000          0.071170   \n",
       "25%        21.080000        84.110000   515.300000          0.116600   \n",
       "50%        25.410000        97.660000   686.500000          0.131300   \n",
       "75%        29.720000       125.400000  1084.000000          0.146000   \n",
       "max        49.540000       251.200000  4254.000000          0.222600   \n",
       "\n",
       "       worst compactness  worst concavity  worst concave points  \\\n",
       "count         569.000000       569.000000            569.000000   \n",
       "mean            0.254265         0.272188              0.114606   \n",
       "std             0.157336         0.208624              0.065732   \n",
       "min             0.027290         0.000000              0.000000   \n",
       "25%             0.147200         0.114500              0.064930   \n",
       "50%             0.211900         0.226700              0.099930   \n",
       "75%             0.339100         0.382900              0.161400   \n",
       "max             1.058000         1.252000              0.291000   \n",
       "\n",
       "       worst symmetry  worst fractal dimension  \n",
       "count      569.000000               569.000000  \n",
       "mean         0.290076                 0.083946  \n",
       "std          0.061867                 0.018061  \n",
       "min          0.156500                 0.055040  \n",
       "25%          0.250400                 0.071460  \n",
       "50%          0.282200                 0.080040  \n",
       "75%          0.317900                 0.092080  \n",
       "max          0.663800                 0.207500  \n",
       "\n",
       "[8 rows x 30 columns]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "668179b6",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Standardise the data\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "sc=StandardScaler()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "6cdc5fae",
   "metadata": {},
   "outputs": [],
   "source": [
    "scaled_data=sc.fit_transform(df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "5abfc898",
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.09706398, -2.07333501,  1.26993369, ...,  2.29607613,\n",
       "         2.75062224,  1.93701461],\n",
       "       [ 1.82982061, -0.35363241,  1.68595471, ...,  1.0870843 ,\n",
       "        -0.24388967,  0.28118999],\n",
       "       [ 1.57988811,  0.45618695,  1.56650313, ...,  1.95500035,\n",
       "         1.152255  ,  0.20139121],\n",
       "       ...,\n",
       "       [ 0.70228425,  2.0455738 ,  0.67267578, ...,  0.41406869,\n",
       "        -1.10454895, -0.31840916],\n",
       "       [ 1.83834103,  2.33645719,  1.98252415, ...,  2.28998549,\n",
       "         1.91908301,  2.21963528],\n",
       "       [-1.80840125,  1.22179204, -1.81438851, ..., -1.74506282,\n",
       "        -0.04813821, -0.75120669]])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scaled_data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "7b54559d",
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean radius</th>\n",
       "      <th>mean texture</th>\n",
       "      <th>mean perimeter</th>\n",
       "      <th>mean area</th>\n",
       "      <th>mean smoothness</th>\n",
       "      <th>mean compactness</th>\n",
       "      <th>mean concavity</th>\n",
       "      <th>mean concave points</th>\n",
       "      <th>mean symmetry</th>\n",
       "      <th>mean fractal dimension</th>\n",
       "      <th>...</th>\n",
       "      <th>worst radius</th>\n",
       "      <th>worst texture</th>\n",
       "      <th>worst perimeter</th>\n",
       "      <th>worst area</th>\n",
       "      <th>worst smoothness</th>\n",
       "      <th>worst compactness</th>\n",
       "      <th>worst concavity</th>\n",
       "      <th>worst concave points</th>\n",
       "      <th>worst symmetry</th>\n",
       "      <th>worst fractal dimension</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.097064</td>\n",
       "      <td>-2.073335</td>\n",
       "      <td>1.269934</td>\n",
       "      <td>0.984375</td>\n",
       "      <td>1.568466</td>\n",
       "      <td>3.283515</td>\n",
       "      <td>2.652874</td>\n",
       "      <td>2.532475</td>\n",
       "      <td>2.217515</td>\n",
       "      <td>2.255747</td>\n",
       "      <td>...</td>\n",
       "      <td>1.886690</td>\n",
       "      <td>-1.359293</td>\n",
       "      <td>2.303601</td>\n",
       "      <td>2.001237</td>\n",
       "      <td>1.307686</td>\n",
       "      <td>2.616665</td>\n",
       "      <td>2.109526</td>\n",
       "      <td>2.296076</td>\n",
       "      <td>2.750622</td>\n",
       "      <td>1.937015</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.829821</td>\n",
       "      <td>-0.353632</td>\n",
       "      <td>1.685955</td>\n",
       "      <td>1.908708</td>\n",
       "      <td>-0.826962</td>\n",
       "      <td>-0.487072</td>\n",
       "      <td>-0.023846</td>\n",
       "      <td>0.548144</td>\n",
       "      <td>0.001392</td>\n",
       "      <td>-0.868652</td>\n",
       "      <td>...</td>\n",
       "      <td>1.805927</td>\n",
       "      <td>-0.369203</td>\n",
       "      <td>1.535126</td>\n",
       "      <td>1.890489</td>\n",
       "      <td>-0.375612</td>\n",
       "      <td>-0.430444</td>\n",
       "      <td>-0.146749</td>\n",
       "      <td>1.087084</td>\n",
       "      <td>-0.243890</td>\n",
       "      <td>0.281190</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.579888</td>\n",
       "      <td>0.456187</td>\n",
       "      <td>1.566503</td>\n",
       "      <td>1.558884</td>\n",
       "      <td>0.942210</td>\n",
       "      <td>1.052926</td>\n",
       "      <td>1.363478</td>\n",
       "      <td>2.037231</td>\n",
       "      <td>0.939685</td>\n",
       "      <td>-0.398008</td>\n",
       "      <td>...</td>\n",
       "      <td>1.511870</td>\n",
       "      <td>-0.023974</td>\n",
       "      <td>1.347475</td>\n",
       "      <td>1.456285</td>\n",
       "      <td>0.527407</td>\n",
       "      <td>1.082932</td>\n",
       "      <td>0.854974</td>\n",
       "      <td>1.955000</td>\n",
       "      <td>1.152255</td>\n",
       "      <td>0.201391</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-0.768909</td>\n",
       "      <td>0.253732</td>\n",
       "      <td>-0.592687</td>\n",
       "      <td>-0.764464</td>\n",
       "      <td>3.283553</td>\n",
       "      <td>3.402909</td>\n",
       "      <td>1.915897</td>\n",
       "      <td>1.451707</td>\n",
       "      <td>2.867383</td>\n",
       "      <td>4.910919</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.281464</td>\n",
       "      <td>0.133984</td>\n",
       "      <td>-0.249939</td>\n",
       "      <td>-0.550021</td>\n",
       "      <td>3.394275</td>\n",
       "      <td>3.893397</td>\n",
       "      <td>1.989588</td>\n",
       "      <td>2.175786</td>\n",
       "      <td>6.046041</td>\n",
       "      <td>4.935010</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1.750297</td>\n",
       "      <td>-1.151816</td>\n",
       "      <td>1.776573</td>\n",
       "      <td>1.826229</td>\n",
       "      <td>0.280372</td>\n",
       "      <td>0.539340</td>\n",
       "      <td>1.371011</td>\n",
       "      <td>1.428493</td>\n",
       "      <td>-0.009560</td>\n",
       "      <td>-0.562450</td>\n",
       "      <td>...</td>\n",
       "      <td>1.298575</td>\n",
       "      <td>-1.466770</td>\n",
       "      <td>1.338539</td>\n",
       "      <td>1.220724</td>\n",
       "      <td>0.220556</td>\n",
       "      <td>-0.313395</td>\n",
       "      <td>0.613179</td>\n",
       "      <td>0.729259</td>\n",
       "      <td>-0.868353</td>\n",
       "      <td>-0.397100</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 30 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "   mean radius  mean texture  mean perimeter  mean area  mean smoothness  \\\n",
       "0     1.097064     -2.073335        1.269934   0.984375         1.568466   \n",
       "1     1.829821     -0.353632        1.685955   1.908708        -0.826962   \n",
       "2     1.579888      0.456187        1.566503   1.558884         0.942210   \n",
       "3    -0.768909      0.253732       -0.592687  -0.764464         3.283553   \n",
       "4     1.750297     -1.151816        1.776573   1.826229         0.280372   \n",
       "\n",
       "   mean compactness  mean concavity  mean concave points  mean symmetry  \\\n",
       "0          3.283515        2.652874             2.532475       2.217515   \n",
       "1         -0.487072       -0.023846             0.548144       0.001392   \n",
       "2          1.052926        1.363478             2.037231       0.939685   \n",
       "3          3.402909        1.915897             1.451707       2.867383   \n",
       "4          0.539340        1.371011             1.428493      -0.009560   \n",
       "\n",
       "   mean fractal dimension  ...  worst radius  worst texture  worst perimeter  \\\n",
       "0                2.255747  ...      1.886690      -1.359293         2.303601   \n",
       "1               -0.868652  ...      1.805927      -0.369203         1.535126   \n",
       "2               -0.398008  ...      1.511870      -0.023974         1.347475   \n",
       "3                4.910919  ...     -0.281464       0.133984        -0.249939   \n",
       "4               -0.562450  ...      1.298575      -1.466770         1.338539   \n",
       "\n",
       "   worst area  worst smoothness  worst compactness  worst concavity  \\\n",
       "0    2.001237          1.307686           2.616665         2.109526   \n",
       "1    1.890489         -0.375612          -0.430444        -0.146749   \n",
       "2    1.456285          0.527407           1.082932         0.854974   \n",
       "3   -0.550021          3.394275           3.893397         1.989588   \n",
       "4    1.220724          0.220556          -0.313395         0.613179   \n",
       "\n",
       "   worst concave points  worst symmetry  worst fractal dimension  \n",
       "0              2.296076        2.750622                 1.937015  \n",
       "1              1.087084       -0.243890                 0.281190  \n",
       "2              1.955000        1.152255                 0.201391  \n",
       "3              2.175786        6.046041                 4.935010  \n",
       "4              0.729259       -0.868353                -0.397100  \n",
       "\n",
       "[5 rows x 30 columns]"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df1=pd.DataFrame(scaled_data,columns=cancer.feature_names)\n",
    "df1.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "b0f34f2b",
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean radius</th>\n",
       "      <th>mean texture</th>\n",
       "      <th>mean perimeter</th>\n",
       "      <th>mean area</th>\n",
       "      <th>mean smoothness</th>\n",
       "      <th>mean compactness</th>\n",
       "      <th>mean concavity</th>\n",
       "      <th>mean concave points</th>\n",
       "      <th>mean symmetry</th>\n",
       "      <th>mean fractal dimension</th>\n",
       "      <th>...</th>\n",
       "      <th>worst radius</th>\n",
       "      <th>worst texture</th>\n",
       "      <th>worst perimeter</th>\n",
       "      <th>worst area</th>\n",
       "      <th>worst smoothness</th>\n",
       "      <th>worst compactness</th>\n",
       "      <th>worst concavity</th>\n",
       "      <th>worst concave points</th>\n",
       "      <th>worst symmetry</th>\n",
       "      <th>worst fractal dimension</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>569.000000</td>\n",
       "      <td>569.000000</td>\n",
       "      <td>569.000000</td>\n",
       "      <td>569.000000</td>\n",
       "      <td>569.000000</td>\n",
       "      <td>569.000000</td>\n",
       "      <td>569.000000</td>\n",
       "      <td>569.000000</td>\n",
       "      <td>569.000000</td>\n",
       "      <td>569.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>569.000000</td>\n",
       "      <td>569.000000</td>\n",
       "      <td>569.000000</td>\n",
       "      <td>569.000000</td>\n",
       "      <td>569.000000</td>\n",
       "      <td>569.000000</td>\n",
       "      <td>569.000000</td>\n",
       "      <td>569.000000</td>\n",
       "      <td>569.000000</td>\n",
       "      <td>569.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>14.127292</td>\n",
       "      <td>19.289649</td>\n",
       "      <td>91.969033</td>\n",
       "      <td>654.889104</td>\n",
       "      <td>0.096360</td>\n",
       "      <td>0.104341</td>\n",
       "      <td>0.088799</td>\n",
       "      <td>0.048919</td>\n",
       "      <td>0.181162</td>\n",
       "      <td>0.062798</td>\n",
       "      <td>...</td>\n",
       "      <td>16.269190</td>\n",
       "      <td>25.677223</td>\n",
       "      <td>107.261213</td>\n",
       "      <td>880.583128</td>\n",
       "      <td>0.132369</td>\n",
       "      <td>0.254265</td>\n",
       "      <td>0.272188</td>\n",
       "      <td>0.114606</td>\n",
       "      <td>0.290076</td>\n",
       "      <td>0.083946</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>3.524049</td>\n",
       "      <td>4.301036</td>\n",
       "      <td>24.298981</td>\n",
       "      <td>351.914129</td>\n",
       "      <td>0.014064</td>\n",
       "      <td>0.052813</td>\n",
       "      <td>0.079720</td>\n",
       "      <td>0.038803</td>\n",
       "      <td>0.027414</td>\n",
       "      <td>0.007060</td>\n",
       "      <td>...</td>\n",
       "      <td>4.833242</td>\n",
       "      <td>6.146258</td>\n",
       "      <td>33.602542</td>\n",
       "      <td>569.356993</td>\n",
       "      <td>0.022832</td>\n",
       "      <td>0.157336</td>\n",
       "      <td>0.208624</td>\n",
       "      <td>0.065732</td>\n",
       "      <td>0.061867</td>\n",
       "      <td>0.018061</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>6.981000</td>\n",
       "      <td>9.710000</td>\n",
       "      <td>43.790000</td>\n",
       "      <td>143.500000</td>\n",
       "      <td>0.052630</td>\n",
       "      <td>0.019380</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.106000</td>\n",
       "      <td>0.049960</td>\n",
       "      <td>...</td>\n",
       "      <td>7.930000</td>\n",
       "      <td>12.020000</td>\n",
       "      <td>50.410000</td>\n",
       "      <td>185.200000</td>\n",
       "      <td>0.071170</td>\n",
       "      <td>0.027290</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.156500</td>\n",
       "      <td>0.055040</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>11.700000</td>\n",
       "      <td>16.170000</td>\n",
       "      <td>75.170000</td>\n",
       "      <td>420.300000</td>\n",
       "      <td>0.086370</td>\n",
       "      <td>0.064920</td>\n",
       "      <td>0.029560</td>\n",
       "      <td>0.020310</td>\n",
       "      <td>0.161900</td>\n",
       "      <td>0.057700</td>\n",
       "      <td>...</td>\n",
       "      <td>13.010000</td>\n",
       "      <td>21.080000</td>\n",
       "      <td>84.110000</td>\n",
       "      <td>515.300000</td>\n",
       "      <td>0.116600</td>\n",
       "      <td>0.147200</td>\n",
       "      <td>0.114500</td>\n",
       "      <td>0.064930</td>\n",
       "      <td>0.250400</td>\n",
       "      <td>0.071460</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>13.370000</td>\n",
       "      <td>18.840000</td>\n",
       "      <td>86.240000</td>\n",
       "      <td>551.100000</td>\n",
       "      <td>0.095870</td>\n",
       "      <td>0.092630</td>\n",
       "      <td>0.061540</td>\n",
       "      <td>0.033500</td>\n",
       "      <td>0.179200</td>\n",
       "      <td>0.061540</td>\n",
       "      <td>...</td>\n",
       "      <td>14.970000</td>\n",
       "      <td>25.410000</td>\n",
       "      <td>97.660000</td>\n",
       "      <td>686.500000</td>\n",
       "      <td>0.131300</td>\n",
       "      <td>0.211900</td>\n",
       "      <td>0.226700</td>\n",
       "      <td>0.099930</td>\n",
       "      <td>0.282200</td>\n",
       "      <td>0.080040</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>15.780000</td>\n",
       "      <td>21.800000</td>\n",
       "      <td>104.100000</td>\n",
       "      <td>782.700000</td>\n",
       "      <td>0.105300</td>\n",
       "      <td>0.130400</td>\n",
       "      <td>0.130700</td>\n",
       "      <td>0.074000</td>\n",
       "      <td>0.195700</td>\n",
       "      <td>0.066120</td>\n",
       "      <td>...</td>\n",
       "      <td>18.790000</td>\n",
       "      <td>29.720000</td>\n",
       "      <td>125.400000</td>\n",
       "      <td>1084.000000</td>\n",
       "      <td>0.146000</td>\n",
       "      <td>0.339100</td>\n",
       "      <td>0.382900</td>\n",
       "      <td>0.161400</td>\n",
       "      <td>0.317900</td>\n",
       "      <td>0.092080</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>28.110000</td>\n",
       "      <td>39.280000</td>\n",
       "      <td>188.500000</td>\n",
       "      <td>2501.000000</td>\n",
       "      <td>0.163400</td>\n",
       "      <td>0.345400</td>\n",
       "      <td>0.426800</td>\n",
       "      <td>0.201200</td>\n",
       "      <td>0.304000</td>\n",
       "      <td>0.097440</td>\n",
       "      <td>...</td>\n",
       "      <td>36.040000</td>\n",
       "      <td>49.540000</td>\n",
       "      <td>251.200000</td>\n",
       "      <td>4254.000000</td>\n",
       "      <td>0.222600</td>\n",
       "      <td>1.058000</td>\n",
       "      <td>1.252000</td>\n",
       "      <td>0.291000</td>\n",
       "      <td>0.663800</td>\n",
       "      <td>0.207500</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>8 rows × 30 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "       mean radius  mean texture  mean perimeter    mean area  \\\n",
       "count   569.000000    569.000000      569.000000   569.000000   \n",
       "mean     14.127292     19.289649       91.969033   654.889104   \n",
       "std       3.524049      4.301036       24.298981   351.914129   \n",
       "min       6.981000      9.710000       43.790000   143.500000   \n",
       "25%      11.700000     16.170000       75.170000   420.300000   \n",
       "50%      13.370000     18.840000       86.240000   551.100000   \n",
       "75%      15.780000     21.800000      104.100000   782.700000   \n",
       "max      28.110000     39.280000      188.500000  2501.000000   \n",
       "\n",
       "       mean smoothness  mean compactness  mean concavity  mean concave points  \\\n",
       "count       569.000000        569.000000      569.000000           569.000000   \n",
       "mean          0.096360          0.104341        0.088799             0.048919   \n",
       "std           0.014064          0.052813        0.079720             0.038803   \n",
       "min           0.052630          0.019380        0.000000             0.000000   \n",
       "25%           0.086370          0.064920        0.029560             0.020310   \n",
       "50%           0.095870          0.092630        0.061540             0.033500   \n",
       "75%           0.105300          0.130400        0.130700             0.074000   \n",
       "max           0.163400          0.345400        0.426800             0.201200   \n",
       "\n",
       "       mean symmetry  mean fractal dimension  ...  worst radius  \\\n",
       "count     569.000000              569.000000  ...    569.000000   \n",
       "mean        0.181162                0.062798  ...     16.269190   \n",
       "std         0.027414                0.007060  ...      4.833242   \n",
       "min         0.106000                0.049960  ...      7.930000   \n",
       "25%         0.161900                0.057700  ...     13.010000   \n",
       "50%         0.179200                0.061540  ...     14.970000   \n",
       "75%         0.195700                0.066120  ...     18.790000   \n",
       "max         0.304000                0.097440  ...     36.040000   \n",
       "\n",
       "       worst texture  worst perimeter   worst area  worst smoothness  \\\n",
       "count     569.000000       569.000000   569.000000        569.000000   \n",
       "mean       25.677223       107.261213   880.583128          0.132369   \n",
       "std         6.146258        33.602542   569.356993          0.022832   \n",
       "min        12.020000        50.410000   185.200000          0.071170   \n",
       "25%        21.080000        84.110000   515.300000          0.116600   \n",
       "50%        25.410000        97.660000   686.500000          0.131300   \n",
       "75%        29.720000       125.400000  1084.000000          0.146000   \n",
       "max        49.540000       251.200000  4254.000000          0.222600   \n",
       "\n",
       "       worst compactness  worst concavity  worst concave points  \\\n",
       "count         569.000000       569.000000            569.000000   \n",
       "mean            0.254265         0.272188              0.114606   \n",
       "std             0.157336         0.208624              0.065732   \n",
       "min             0.027290         0.000000              0.000000   \n",
       "25%             0.147200         0.114500              0.064930   \n",
       "50%             0.211900         0.226700              0.099930   \n",
       "75%             0.339100         0.382900              0.161400   \n",
       "max             1.058000         1.252000              0.291000   \n",
       "\n",
       "       worst symmetry  worst fractal dimension  \n",
       "count      569.000000               569.000000  \n",
       "mean         0.290076                 0.083946  \n",
       "std          0.061867                 0.018061  \n",
       "min          0.156500                 0.055040  \n",
       "25%          0.250400                 0.071460  \n",
       "50%          0.282200                 0.080040  \n",
       "75%          0.317900                 0.092080  \n",
       "max          0.663800                 0.207500  \n",
       "\n",
       "[8 rows x 30 columns]"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "b4f5f447",
   "metadata": {},
   "outputs": [],
   "source": [
    "### convert 30 features to 5features\n",
    "from sklearn.decomposition import PCA\n",
    "model=PCA(n_components=5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "e1dd3ab9",
   "metadata": {},
   "outputs": [],
   "source": [
    "trans_data=model.fit_transform(df1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "48b2e1c6",
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 9.19283682,  1.9485831 , -1.12316657,  3.63373126, -1.19510974],\n",
       "       [ 2.3878018 , -3.76817178, -0.52929228,  1.11826377,  0.62177433],\n",
       "       [ 5.73389628, -1.07517377, -0.55174785,  0.91208266, -0.17708551],\n",
       "       ...,\n",
       "       [ 1.25617928, -1.90229672,  0.56273064, -2.08922699,  1.8099911 ],\n",
       "       [10.37479406,  1.67201011, -1.87702935, -2.35603094, -0.03374195],\n",
       "       [-5.4752433 , -0.67063674,  1.49044242, -2.29915702, -0.18470234]])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "trans_data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "c515a039",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(569, 5)"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "trans_data.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "2921b08b",
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 9.19283682,  1.9485831 , -1.12316657,  3.63373126, -1.19510974],\n",
       "       [ 2.3878018 , -3.76817178, -0.52929228,  1.11826377,  0.62177433],\n",
       "       [ 5.73389628, -1.07517377, -0.55174785,  0.91208266, -0.17708551],\n",
       "       ...,\n",
       "       [ 1.25617928, -1.90229672,  0.56273064, -2.08922699,  1.8099911 ],\n",
       "       [10.37479406,  1.67201011, -1.87702935, -2.35603094, -0.03374195],\n",
       "       [-5.4752433 , -0.67063674,  1.49044242, -2.29915702, -0.18470234]])"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "trans_data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "434b6524",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>PC1</th>\n",
       "      <th>PC2</th>\n",
       "      <th>PC3</th>\n",
       "      <th>PC4</th>\n",
       "      <th>PC5</th>\n",
       "      <th>target</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>9.192837</td>\n",
       "      <td>1.948583</td>\n",
       "      <td>-1.123167</td>\n",
       "      <td>3.633731</td>\n",
       "      <td>-1.195110</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2.387802</td>\n",
       "      <td>-3.768172</td>\n",
       "      <td>-0.529292</td>\n",
       "      <td>1.118264</td>\n",
       "      <td>0.621774</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>5.733896</td>\n",
       "      <td>-1.075174</td>\n",
       "      <td>-0.551748</td>\n",
       "      <td>0.912083</td>\n",
       "      <td>-0.177086</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>7.122953</td>\n",
       "      <td>10.275589</td>\n",
       "      <td>-3.232789</td>\n",
       "      <td>0.152547</td>\n",
       "      <td>-2.960878</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>3.935302</td>\n",
       "      <td>-1.948072</td>\n",
       "      <td>1.389767</td>\n",
       "      <td>2.940639</td>\n",
       "      <td>0.546747</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>564</th>\n",
       "      <td>6.439315</td>\n",
       "      <td>-3.576817</td>\n",
       "      <td>2.459486</td>\n",
       "      <td>1.177314</td>\n",
       "      <td>-0.074824</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>565</th>\n",
       "      <td>3.793382</td>\n",
       "      <td>-3.584048</td>\n",
       "      <td>2.088477</td>\n",
       "      <td>-2.506028</td>\n",
       "      <td>-0.510723</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>566</th>\n",
       "      <td>1.256179</td>\n",
       "      <td>-1.902297</td>\n",
       "      <td>0.562731</td>\n",
       "      <td>-2.089227</td>\n",
       "      <td>1.809991</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>567</th>\n",
       "      <td>10.374794</td>\n",
       "      <td>1.672010</td>\n",
       "      <td>-1.877029</td>\n",
       "      <td>-2.356031</td>\n",
       "      <td>-0.033742</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>568</th>\n",
       "      <td>-5.475243</td>\n",
       "      <td>-0.670637</td>\n",
       "      <td>1.490442</td>\n",
       "      <td>-2.299157</td>\n",
       "      <td>-0.184702</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>569 rows × 6 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "           PC1        PC2       PC3       PC4       PC5  target\n",
       "0     9.192837   1.948583 -1.123167  3.633731 -1.195110       0\n",
       "1     2.387802  -3.768172 -0.529292  1.118264  0.621774       0\n",
       "2     5.733896  -1.075174 -0.551748  0.912083 -0.177086       0\n",
       "3     7.122953  10.275589 -3.232789  0.152547 -2.960878       0\n",
       "4     3.935302  -1.948072  1.389767  2.940639  0.546747       0\n",
       "..         ...        ...       ...       ...       ...     ...\n",
       "564   6.439315  -3.576817  2.459486  1.177314 -0.074824       0\n",
       "565   3.793382  -3.584048  2.088477 -2.506028 -0.510723       0\n",
       "566   1.256179  -1.902297  0.562731 -2.089227  1.809991       0\n",
       "567  10.374794   1.672010 -1.877029 -2.356031 -0.033742       0\n",
       "568  -5.475243  -0.670637  1.490442 -2.299157 -0.184702       1\n",
       "\n",
       "[569 rows x 6 columns]"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Reduced_df=pd.DataFrame(trans_data,columns=[\"PC1\",'PC2','PC3','PC4','PC5'])\n",
    "Reduced_df[\"target\"]=cancer.target\n",
    "Reduced_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f2ab4ebd",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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