wk-10b-Fall 2016-PCA

wk-10b-Fall 2016-PCA.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from sklearn.decomposition import PCA\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.preprocessing import scale\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "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>x1</th>\n",
       "      <th>x2</th>\n",
       "      <th>x3</th>\n",
       "      <th>x4</th>\n",
       "      <th>x5</th>\n",
       "      <th>x6</th>\n",
       "      <th>x7</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>4.19</td>\n",
       "      <td>16.15</td>\n",
       "      <td>12.05</td>\n",
       "      <td>32.62</td>\n",
       "      <td>46.90</td>\n",
       "      <td>62.87</td>\n",
       "      <td>64.69</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>3.42</td>\n",
       "      <td>11.03</td>\n",
       "      <td>13.21</td>\n",
       "      <td>13.81</td>\n",
       "      <td>30.18</td>\n",
       "      <td>55.04</td>\n",
       "      <td>62.54</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>5.20</td>\n",
       "      <td>6.22</td>\n",
       "      <td>15.15</td>\n",
       "      <td>35.29</td>\n",
       "      <td>28.50</td>\n",
       "      <td>36.53</td>\n",
       "      <td>91.71</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4.31</td>\n",
       "      <td>8.82</td>\n",
       "      <td>16.89</td>\n",
       "      <td>27.40</td>\n",
       "      <td>43.41</td>\n",
       "      <td>65.96</td>\n",
       "      <td>78.77</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4.32</td>\n",
       "      <td>12.75</td>\n",
       "      <td>18.66</td>\n",
       "      <td>34.15</td>\n",
       "      <td>13.97</td>\n",
       "      <td>51.44</td>\n",
       "      <td>50.80</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     x1     x2     x3     x4     x5     x6     x7\n",
       "0  4.19  16.15  12.05  32.62  46.90  62.87  64.69\n",
       "1  3.42  11.03  13.21  13.81  30.18  55.04  62.54\n",
       "2  5.20   6.22  15.15  35.29  28.50  36.53  91.71\n",
       "3  4.31   8.82  16.89  27.40  43.41  65.96  78.77\n",
       "4  4.32  12.75  18.66  34.15  13.97  51.44  50.80"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Load data set\n",
    "df = pd.read_csv(\"/home/drk/kanungo/DNSC6211/w10/wk10b-datav2.csv\")\n",
    "dfX = df[['x1','x2','x3','x4','x5','x6','x7']]\n",
    "dfX.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#convert it to numpy arrays\n",
    "X=dfX.values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#Scaling the values\n",
    "\n",
    "X = scale(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "pca = PCA(n_components=7)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "PCA(copy=True, n_components=7, whiten=False)"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca.fit(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#The amount of variance that each PC explains\n",
    "var=pca.explained_variance_ratio_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#Cumulative Variance explains\n",
    "var1=np.cumsum(np.round(pca.explained_variance_ratio_, decimals=4)*100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f392a8334e0>]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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RKUQq9zyybRvcfjtMmRKOjDnmmNiJRKRQqdzzxPr1cMkl0KgRvPkmNG0aO5GIFDLN3PPA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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f392ce117f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(var1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-2.01798158  0.48298814 -0.3638035 ]\n",
      " [-1.82858804  1.51086945 -0.44644853]\n",
      " [-1.68227451  1.6576313  -0.54922029]\n",
      " ..., \n",
      " [ 0.76976208  0.11810341 -0.81083088]\n",
      " [ 1.81608507 -0.53934735 -0.97233128]\n",
      " [ 3.46550699  0.23200896  0.26253754]]\n"
     ]
    }
   ],
   "source": [
    "#Looking at above plot I'm taking 30 variables\n",
    "pca = PCA(n_components=3)\n",
    "pca.fit(X)\n",
    "X1=pca.fit_transform(X)\n",
    "\n",
    "print (X1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7f392a32cf28>"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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GuSXK4YuemLaf3yTTnPK05eDB/2AL8KzrONJ6jjNcgvdIk5yoGOkjHxkxyTTX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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f392a35eda0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X1[:,0],X1[:,1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7f392a230860>"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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majMwrmSuv65JZxUUvdUJwzcns9mkyyKKwl0W1l1XxUm1r1tjn6JgOON2Wlxc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\nEMBizjAMMwT8f5nEC5lv5cNIAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f392a258f28>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X1[:,0],X[:,2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python [conda root]",
   "language": "python",
   "name": "conda-root-py"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}