{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "___\n",
    "\n",
    "<a href='http://www.pieriandata.com'> <img src='../Pierian_Data_Logo.png' /></a>\n",
    "___"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Principal Component Analysis\n",
    "\n",
    "Let's discuss PCA! Since this isn't exactly a full machine learning algorithm, but instead an unsupervised learning algorithm, we will just have a lecture on this topic, but no full machine learning project (although we will walk through the cancer set with PCA).\n",
    "\n",
    "## PCA Review\n",
    "\n",
    "Make sure to watch the video lecture and theory presentation for a full overview of PCA! \n",
    "Remember that PCA is just a transformation of your data and attempts to find out what features explain the most variance in your data. For example:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src='PCA.png' />"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import seaborn as sns\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The Data\n",
    "\n",
    "Let's work with the cancer data set again since it had so many features."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.datasets import load_breast_cancer"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "cancer = load_breast_cancer()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dict_keys(['DESCR', 'data', 'feature_names', 'target_names', 'target'])"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cancer.keys()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Breast Cancer Wisconsin (Diagnostic) Database\n",
      "\n",
      "Notes\n",
      "-----\n",
      "Data Set Characteristics:\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",
      "        largest values) of these features were computed for each image,\n",
      "        resulting in 30 features.  For instance, field 3 is Mean Radius, field\n",
      "        13 is Radius SE, field 23 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",
      "A few of the images can be found at\n",
      "http://www.cs.wisc.edu/~street/images/\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",
      "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",
      "\n"
     ]
    }
   ],
   "source": [
    "print(cancer['DESCR'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "df = pd.DataFrame(cancer['data'],columns=cancer['feature_names'])\n",
    "#(['DESCR', 'data', 'feature_names', 'target_names', 'target'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\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>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",
       "</div>"
      ],
      "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  \\\n",
       "0                 0.07871           ...                    25.38   \n",
       "1                 0.05667           ...                    24.99   \n",
       "2                 0.05999           ...                    23.57   \n",
       "3                 0.09744           ...                    14.91   \n",
       "4                 0.05883           ...                    22.54   \n",
       "\n",
       "   worst texture  worst perimeter  worst area  worst smoothness  \\\n",
       "0          17.33           184.60      2019.0            0.1622   \n",
       "1          23.41           158.80      1956.0            0.1238   \n",
       "2          25.53           152.50      1709.0            0.1444   \n",
       "3          26.50            98.87       567.7            0.2098   \n",
       "4          16.67           152.20      1575.0            0.1374   \n",
       "\n",
       "   worst compactness  worst concavity  worst concave points  worst symmetry  \\\n",
       "0             0.6656           0.7119                0.2654          0.4601   \n",
       "1             0.1866           0.2416                0.1860          0.2750   \n",
       "2             0.4245           0.4504                0.2430          0.3613   \n",
       "3             0.8663           0.6869                0.2575          0.6638   \n",
       "4             0.2050           0.4000                0.1625          0.2364   \n",
       "\n",
       "   worst fractal dimension  \n",
       "0                  0.11890  \n",
       "1                  0.08902  \n",
       "2                  0.08758  \n",
       "3                  0.17300  \n",
       "4                  0.07678  \n",
       "\n",
       "[5 rows x 30 columns]"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## PCA Visualization\n",
    "\n",
    "As we've noticed before it is difficult to visualize high dimensional data, we can use PCA to find the first two principal components, and visualize the data in this new, two-dimensional space, with a single scatter-plot. Before we do this though, we'll need to scale our data so that each feature has a single unit variance."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import StandardScaler"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "StandardScaler(copy=True, with_mean=True, with_std=True)"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scaler = StandardScaler()\n",
    "scaler.fit(df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "scaled_data = scaler.transform(df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "PCA with Scikit Learn uses a very similar process to other preprocessing functions that come with SciKit Learn. We instantiate a PCA object, find the principal components using the fit method, then apply the rotation and dimensionality reduction by calling transform().\n",
    "\n",
    "We can also specify how many components we want to keep when creating the PCA object."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.decomposition import PCA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "pca = PCA(n_components=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "PCA(copy=True, n_components=2, whiten=False)"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca.fit(scaled_data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can transform this data to its first 2 principal components."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "x_pca = pca.transform(scaled_data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(569, 30)"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scaled_data.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(569, 2)"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_pca.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Great! We've reduced 30 dimensions to just 2! Let's plot these two dimensions out!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x11eb56908>"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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2+detW53de6f9p/j1ej1bNp/PqtRnMF6ibLlSdOrUvUDt7dg5B9+qsylVWuZO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\nhPAikviFEEIILyKJXwghhPAi/w/kOKMcWJdehQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11e92d550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8,6))\n",
    "plt.scatter(x_pca[:,0],x_pca[:,1],c=cancer['target'],cmap='plasma')\n",
    "plt.xlabel('First principal component')\n",
    "plt.ylabel('Second Principal Component')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Clearly by using these two components we can easily separate these two classes.\n",
    "\n",
    "## Interpreting the components \n",
    "\n",
    "Unfortunately, with this great power of dimensionality reduction, comes the cost of being able to easily understand what these components represent.\n",
    "\n",
    "The components correspond to combinations of the original features, the components themselves are stored as an attribute of the fitted PCA object:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.21890244, -0.10372458, -0.22753729, -0.22099499, -0.14258969,\n",
       "        -0.23928535, -0.25840048, -0.26085376, -0.13816696, -0.06436335,\n",
       "        -0.20597878, -0.01742803, -0.21132592, -0.20286964, -0.01453145,\n",
       "        -0.17039345, -0.15358979, -0.1834174 , -0.04249842, -0.10256832,\n",
       "        -0.22799663, -0.10446933, -0.23663968, -0.22487053, -0.12795256,\n",
       "        -0.21009588, -0.22876753, -0.25088597, -0.12290456, -0.13178394],\n",
       "       [ 0.23385713,  0.05970609,  0.21518136,  0.23107671, -0.18611302,\n",
       "        -0.15189161, -0.06016536,  0.0347675 , -0.19034877, -0.36657547,\n",
       "         0.10555215, -0.08997968,  0.08945723,  0.15229263, -0.20443045,\n",
       "        -0.2327159 , -0.19720728, -0.13032156, -0.183848  , -0.28009203,\n",
       "         0.21986638,  0.0454673 ,  0.19987843,  0.21935186, -0.17230435,\n",
       "        -0.14359317, -0.09796411,  0.00825724, -0.14188335, -0.27533947]])"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca.components_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this numpy matrix array, each row represents a principal component, and each column relates back to the original features. we can visualize this relationship with a heatmap:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "df_comp = pd.DataFrame(pca.components_,columns=cancer['feature_names'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x11d546f98>"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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smZ7q/dXTXSLiMkmKiEsl3aWijVfbPtf2p2yv3+UB5DwCAABUmI8dZmyfJGnDobumJE1L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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11ee2c048>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(12,6))\n",
    "sns.heatmap(df_comp,cmap='plasma',)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This heatmap and the color bar basically represent the correlation between the various feature and the principal component itself.\n",
    "\n",
    "## Conclusion\n",
    "\n",
    "Hopefully this information is useful to you when dealing with high dimensional data!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Great Job!"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
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