breast cancer data analysis colinearity and dimensional reduction.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Breast cancer data analysis:  collinearity and dimensional reduction"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Data source: Kaggle (https://www.kaggle.com/uciml/breast-cancer-wisconsin-data).\n",
    "Also can be found on UCI Machine Learning Repository: https://archive.ics.uci.edu/ml/datasets/Breast+Cancer+Wisconsin+%28Diagnostic%29\n",
    "\n",
    "Attribute Information:\n",
    "\n",
    "1) ID number \n",
    "2) Diagnosis (M = malignant, B = benign) 3-32)\n",
    "\n",
    "Ten real-valued features are computed for each cell nucleus:\n",
    "\n",
    "a) radius (mean of distances from center to points on the perimeter) b) texture (standard deviation of gray-scale values) c) perimeter d) area e) smoothness (local variation in radius lengths) f) compactness (perimeter^2 / area - 1.0) g) concavity (severity of concave portions of the contour) h) concave points (number of concave portions of the contour) i) symmetry j) fractal dimension (\"coastline approximation\" - 1)\n",
    "\n",
    "The mean, standard error and \"worst\" or largest (mean of the three largest values) of these features were computed for each image, resulting in 30 features. \n",
    "* In this blog, analyses of collinearity and dimensional reduction are discussed.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import seaborn as sns\n",
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "569\n"
     ]
    }
   ],
   "source": [
    "# First, we import the downloaded cvs data \n",
    "bc=pd.read_csv(\"C:\\data science\\project1\\BC.csv\")\n",
    "bc.head(10)     \n",
    "#print(bc.describe())\n",
    "print(np.count_nonzero(bc.diagnosis[]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n"
     ]
    },
    {
     "data": {
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       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>radius_mean</th>\n",
       "      <th>texture_mean</th>\n",
       "      <th>perimeter_mean</th>\n",
       "      <th>area_mean</th>\n",
       "      <th>smoothness_mean</th>\n",
       "      <th>compactness_mean</th>\n",
       "      <th>concavity_mean</th>\n",
       "      <th>concave points_mean</th>\n",
       "      <th>symmetry_mean</th>\n",
       "      <th>fractal_dimension_mean</th>\n",
       "      <th>...</th>\n",
       "      <th>radius_worst</th>\n",
       "      <th>texture_worst</th>\n",
       "      <th>perimeter_worst</th>\n",
       "      <th>area_worst</th>\n",
       "      <th>smoothness_worst</th>\n",
       "      <th>compactness_worst</th>\n",
       "      <th>concavity_worst</th>\n",
       "      <th>concave points_worst</th>\n",
       "      <th>symmetry_worst</th>\n",
       "      <th>fractal_dimension_worst</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": [
       "   radius_mean  texture_mean  perimeter_mean  area_mean  smoothness_mean  \\\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",
       "   compactness_mean  concavity_mean  concave points_mean  symmetry_mean  \\\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",
       "   fractal_dimension_mean           ...             radius_worst  \\\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",
       "   texture_worst  perimeter_worst  area_worst  smoothness_worst  \\\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",
       "   compactness_worst  concavity_worst  concave points_worst  symmetry_worst  \\\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",
       "   fractal_dimension_worst  \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": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# slicing out the predictor variables/features\n",
    "X=bc.iloc[:,2:32]\n",
    "print(type(X))\n",
    "# displaying the first five rows of X\n",
    "X.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.series.Series'>\n",
      "   B  M\n",
      "0  0  1\n",
      "1  0  1\n",
      "2  0  1\n",
      "3  0  1\n",
      "4  0  1\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0    1\n",
       "1    1\n",
       "2    1\n",
       "3    1\n",
       "4    1\n",
       "Name: M, dtype: uint8"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# response variable: 'diagnosis'\n",
    "yr=bc.diagnosis\n",
    "print(type(yr))\n",
    "yr.head()\n",
    "# we use pandas get_dummies function to convert the qualitative values in yr to quantitative \n",
    "yd=pd.get_dummies(yr) # this creates two columns: one for B and another for M\n",
    "print(yd.head())\n",
    "# take the yd.M as the response variable (y) since it assigns 1 for M and 0 for B\n",
    "# this makes sense as we are interested more in predicting M cases than B\n",
    "y=yd.M \n",
    "y.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.  Identifying Collinearity\n",
    "* Now, looking at the covariance matrix of the features, we can identify variables with more than 85% correlation \n",
    "(85% selected as a threshold here, but other values can be used as well)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 209,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0xb2205b0>"
      ]
     },
     "execution_count": 209,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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sWPaTn7njRV0n9tY3vK6ruE9udl7X55y3w8Zdxx55yb5dx/bL/Zus03XsRvc8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\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xbcb2c30>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "cor=np.corrcoef(X.T)\n",
    "type(cor)\n",
    "%matplotlib inline\n",
    "plt.figure(figsize=(10, 8))\n",
    "sns.heatmap(cor, vmin=0.85,vmax=1,\\\n",
    "            cmap=plt.cm.Spectral_r)\n",
    "#cmap='coolwarm'#"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*From the above plot, we can see the following features are highly correlated:*\n",
    "* feature 0,2,3, 20, 22, 23 (radius, area, perimeter),this makes sense since area and perimeter are computed from radius. We keep 0 (mean radius) and 20 (worst radius), and discard the rest.\n",
    "* feature 10, 12, 13 are  highly correlated to eachother. Keeping feature 10, we can leave the rest out. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Summary:**\n",
    "* covariance matrix can only detect one-to-one collinearity leaving the issue of multi-collinearity\n",
    "* High multi-collinearity can be detected by inspecting the eigen values of correlation matrix. A very low eigen value shows that the data are collinear, and the corresponding eigen vector shows which variables are collinear.\n",
    "* If there is no collinearity in the data, you would expect that none of the eigen values are close to zero"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2. Dimensional reduction using Principal Component Analysis (PCA)\n",
    "\n",
    "* PCA is a technique that extracts a smaller but valuable set of predictors by linear combination of the original *p* predictors (x1,x2,x3,...,xp) in a dataset. The new set of predictors captures as much information as possible usually 95% or more of the variance in the original data.  \n",
    "* The new predictors can be written as: \n",
    "    * PC1 = Φ¹¹X¹ + Φ²¹X² + Φ³¹X³ + .... +Φp¹Xp\n",
    "    * PC2 = Φ¹²X¹ + Φ²²X² + Φ³²X³ + .... + Φp2Xp\n",
    "    ...\n",
    "    * Φp¹, and Φp2 are the loading vectors of the first and the second  principal components,respectively. \n",
    "* In this blog, we apply PCA to the original data, and differnet versions of it and try to understand how results from PCA vary.\n",
    "** Data to be used: raw/original data, scaled or standardized data, and scaled data with the removal of collinear predictors."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 2.1. PCA on original data\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 184,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(569, 10)\n",
      "[  9.82044672e-01   1.61764899e-02   1.55751075e-03   1.20931964e-04\n",
      "   8.82724536e-05   6.64883951e-06   4.01713682e-06   8.22017197e-07\n",
      "   3.44135279e-07   1.86018721e-07]\n",
      "0.999999894684\n"
     ]
    }
   ],
   "source": [
    "from sklearn.decomposition import PCA\n",
    "pca=PCA(n_components=10)\n",
    "x_pca=pca.fit_transform(X)\n",
    "print (x_pca.shape)\n",
    "print(pca.explained_variance_ratio_) \n",
    "print (pca.explained_variance_ratio_.sum())\n",
    "loadings = pca.components_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* The above result shows more than 95% of the variance in the data can be expressed just by the first component. This happens in cases where there is high collinearity; the presence of collinearity can cause the PCA to overemphasize the contribution of the variance from the highly correlated (or redundant) varibles and gives less weight to the variables to the uncorrelated variables. This ultimately influence modeling/prediction results if such data is used. \n",
    "\n",
    "* It is also important to note that **we used PCA on unscaled data**. When the data is not scaled, PCA might  give us a result where only one component explains almost all the variance in the data.  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 2.2. PCA on scaled/standardized data\n",
    "* Standardizing transforms the data to a data with zero mean and a standard deviation of one (unit variance).\n",
    "* In cases where the original predictors may have different scales, it is obvious the resulting variances in these predictors will be large. Therefore, performing PCA on unstandardized predictors will result a biased result; PCA assigns large loadings on the predictors with high variances."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 186,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import StandardScaler\n",
    "scaler = StandardScaler()\n",
    "X_scaled=scaler.fit_transform(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 187,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(569, 10)\n",
      "[ 0.44272026  0.18971182  0.09393163  0.06602135  0.05495768  0.04024522\n",
      "  0.02250734  0.01588724  0.01389649  0.01168978]\n",
      "0.951568814337\n"
     ]
    }
   ],
   "source": [
    "pca=PCA(n_components=0.95)\n",
    "x_pca=pca.fit_transform(X_scaled)\n",
    "print (x_pca.shape)\n",
    "print(pca.explained_variance_ratio_) \n",
    "print (pca.explained_variance_ratio_.sum())\n",
    "loadings = pca.components_"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {},
   "source": [
    "* Here, it can be noted, 10 components explain 95% of the variance in the data compared to just 1 when applying PCA on the unscaled data. By using the scaled data PCA projects more features/variables which are crucial to breast cancer prediction. \n",
    "* From this, we can conclude that PCA with out scaling can hide features with smaller magnitude which are usable to the prediction. \n",
    "* We can further see how removing collinear features from the scaled can affect PCA here below."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 2.3. PCA after removing collinear variables\n",
    "* Here, PCA is applied on the saled data after removing some of the collinear features as identified in section 1.  We aim to see how removing redundant/colinear variables can improve PCA results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 193,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(569, 11)\n",
      "[ 0.42661046  0.15932139  0.10294428  0.07788731  0.06489774  0.05015242\n",
      "  0.02145044  0.0187846   0.01505759  0.01197751  0.01117206]\n",
      "0.960255820189\n"
     ]
    }
   ],
   "source": [
    "# Remove area, perimeter,perimeter_worst, area_worst, perimeter_se, area_se  ( columns: 2,3,12,13,22,23,) from the original data: \n",
    "X_scaled=pd.DataFrame(X_scaled)\n",
    "xx=X_scaled.drop(X_scaled.columns[[2, 3, 22, 23, 12, 13]], axis=1) \n",
    "pca=PCA(n_components=0.95)\n",
    "x_pca=pca.fit_transform(xx)\n",
    "print (x_pca.shape)\n",
    "print(pca.explained_variance_ratio_) \n",
    "print (pca.explained_variance_ratio_.sum())\n",
    "loadings = pca.components_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Variance plots"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 190,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0xbd57ad0>"
      ]
     },
     "execution_count": 190,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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jpvgDAAAAMGKKPwAAAAAjpvgDAAAAMGKKPwAAAAAjpvgDAAAAMGKKPwAAAAAj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\nY+OG2D+kRskAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xe379d90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "n=['PC1','PC2','PC3','PC4','PC5','PC6','PC7','PC8','PC9','PC10']\n",
    "index = np.arange (10)\n",
    "\n",
    "var_1=np.array([9.82044672e-01,1.61764899e-02,1.55751075e-03,1.20931964e-04,8.82724536e-05,6.64883951e-06,4.01713682e-06,8.22017197e-07,3.44135279e-07,1.86018721e-07])                \n",
    "var_sc=np.array([0.44272026,0.18971182,0.09393163,0.06602135,0.05495768,0.04024522,0.02250734,0.01588724,0.01389649,0.01168978])\n",
    "var_sc_coll=np.array([0.42661046,0.15932139,0.10294428,0.07788731,0.06489774,0.05015242,0.02145044,0.0187846,0.01505759,0.01197751])\n",
    "var=np.vstack([var_1,var_sc,var_sc_coll]).T\n",
    "\n",
    "# creating pandas datframe from numpy array 'var'\n",
    "df=pd.DataFrame(var,index=n,columns=['original','scaled','scaled_no_colli'])\n",
    "\n",
    "# plotting variance data \n",
    "%matplotlib inline\n",
    "fig, ax= plt.subplots(1,3,sharey=True,figsize=(20,4))\n",
    "r1 = ax[0].bar(index,df['original'],width = 0.6,align='center')\n",
    "ax[0].set_title('PCA on raw data',fontsize=14)\n",
    "\n",
    "r2 = ax[1].bar(index,df['scaled'],width = 0.6,align='center')\n",
    "ax[1].set_title('PCA on scaled data',fontsize=14)\n",
    "\n",
    "r3 = ax[2].bar(index,df['scaled_no_colli'],width= 0.6,align='center')\n",
    "#ax[2].set_xticklabels(n)\n",
    "ax[2].set_title('PCA after removing collinearity',fontsize=14)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Summary:**\n",
    "\n",
    "* By stanrdizing the data, PCA performance has improved quite well in capturing variance of the raw data\n",
    "* Removing collinear features allowed the variance from other variables which were previously ignored to be captured by PCA. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Ploting first and second principal components against diagnosis\n",
    "* First principal component (PC1) is a linear combination of the features/variables which represents the maximum variance in the data set. \n",
    "* Second principal component (PC2) is also a linear combination of the features/variables which represents the remaining variance in the data set and is uncorrelated with the first principal component (PC1)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 201,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <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>PC6</th>\n",
       "      <th>PC7</th>\n",
       "      <th>PC8</th>\n",
       "      <th>PC9</th>\n",
       "      <th>PC10</th>\n",
       "      <th>PC11</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>diagnosis</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>M</th>\n",
       "      <td>8.066802</td>\n",
       "      <td>0.414765</td>\n",
       "      <td>-2.538073</td>\n",
       "      <td>-2.608014</td>\n",
       "      <td>-1.344494</td>\n",
       "      <td>1.435172</td>\n",
       "      <td>-1.713811</td>\n",
       "      <td>-0.491329</td>\n",
       "      <td>0.655096</td>\n",
       "      <td>0.544224</td>\n",
       "      <td>0.718321</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>M</th>\n",
       "      <td>0.106798</td>\n",
       "      <td>-2.761727</td>\n",
       "      <td>-0.141345</td>\n",
       "      <td>-1.395074</td>\n",
       "      <td>0.130814</td>\n",
       "      <td>0.017362</td>\n",
       "      <td>-0.333451</td>\n",
       "      <td>-0.389474</td>\n",
       "      <td>-0.706687</td>\n",
       "      <td>0.114084</td>\n",
       "      <td>0.405121</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>M</th>\n",
       "      <td>4.386099</td>\n",
       "      <td>-1.969883</td>\n",
       "      <td>-0.226679</td>\n",
       "      <td>-1.108399</td>\n",
       "      <td>-0.700594</td>\n",
       "      <td>0.477506</td>\n",
       "      <td>0.287285</td>\n",
       "      <td>-0.079434</td>\n",
       "      <td>-0.352640</td>\n",
       "      <td>-0.654396</td>\n",
       "      <td>-0.284427</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                PC1       PC2       PC3       PC4       PC5       PC6  \\\n",
       "diagnosis                                                               \n",
       "M          8.066802  0.414765 -2.538073 -2.608014 -1.344494  1.435172   \n",
       "M          0.106798 -2.761727 -0.141345 -1.395074  0.130814  0.017362   \n",
       "M          4.386099 -1.969883 -0.226679 -1.108399 -0.700594  0.477506   \n",
       "\n",
       "                PC7       PC8       PC9      PC10      PC11  \n",
       "diagnosis                                                    \n",
       "M         -1.713811 -0.491329  0.655096  0.544224  0.718321  \n",
       "M         -0.333451 -0.389474 -0.706687  0.114084  0.405121  \n",
       "M          0.287285 -0.079434 -0.352640 -0.654396 -0.284427  "
      ]
     },
     "execution_count": 201,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "n=['PC1','PC2','PC3','PC4','PC5','PC6','PC7','PC8','PC9','PC10','PC11']\n",
    "xx_pca=pd.DataFrame(x_pca,columns = n, index=bc.diagnosis)\n",
    "xx_pca.head(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 202,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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FACBCFW4s1ZZdRyVJ1pp6VW/brIKC+YqPj5fV2qiFCx8kqwoAiFgEqwAARKjqepvz57Ts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OS55xZit1k5m7gO7Dbixj5U51w4nr0jt7VzQCn7flzN3LmP0alTF6fq2+dS73PeUEu25zMzW6y1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\nyN3YCTEAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xb21c950>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#plotting the first 2 pca compenents vs diagnosis\n",
    "%matplotlib inline\n",
    "ax = xx_pca.plot(kind='scatter', x='PC1', y='PC2', figsize=(16,8))\n",
    "for i, diagnosis in enumerate(xx_pca.index):\n",
    "    ax.annotate(diagnosis,(xx_pca.iloc[i].PC1, xx_pca.iloc[i].PC2))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Summary:**\n",
    "\n",
    "* PCA resulted clear regions of benine and malignant cases (as the above plot shows). This helps the modeling/prediction be more effective and accurate.\n",
    "* After this, a model can be fitted on this data."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}