8. Principal Component Analysis.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import random\n",
    "import operator\n",
    "import scipy.stats\n",
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "from sklearn import model_selection\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "from sklearn import decomposition"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#load data\n",
    "df = pd.read_csv('../data/breast-cancer-wisconsin.data.txt')\n",
    "\n",
    "#clean data\n",
    "df = df.replace('?',-99999)\n",
    "df = df.astype(float)\n",
    "df = df.drop(['id'],1)\n",
    "\n",
    "#shuffle data\n",
    "df = df.reindex(np.random.permutation(df.index))\n",
    "df = df.reset_index(drop=True)\n",
    "\n",
    "#copy data\n",
    "tf = df.copy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Scale data\n",
    "standard_scaler = StandardScaler()\n",
    "X = standard_scaler.fit_transform(tf.iloc[:,:9])\n",
    "\n",
    "y = tf.iloc[:,9].astype('int')\n",
    "\n",
    "X, y = pd.DataFrame(X), pd.Series(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class PrincipalComponentAnalysis(object):\n",
    "    \n",
    "    def __init__(self, printing=False, k=2):\n",
    "        self.printing = printing\n",
    "        self.k = k\n",
    "        \n",
    "    def fit(self,X_train):\n",
    "        self.trainSet = X_train #class is ignored\n",
    "        self.n_features = X_train.shape[1]\n",
    "        \n",
    "        trainSet = self.trainSet\n",
    "        \n",
    "        #get feature means\n",
    "        _means = trainSet.describe().loc['mean'].values \n",
    "        \n",
    "        #create covariance matrix\n",
    "        cov_mat = self.covariance_matrix(trainSet.T)\n",
    "        \n",
    "        #compute eigenvectors and eigenvalues from covariance matrix\n",
    "        eig_pairs = self.eigen(cov_mat)\n",
    "        \n",
    "        ##create transformation matrix\n",
    "        self.transformation_matrix(eig_pairs)\n",
    "        \n",
    "        return\n",
    "    \n",
    "    def covariance_matrix(self, dataset):\n",
    "        \"\"\"Computes the covariance matrix of a dataset\"\"\"\n",
    "        cov_mat = np.cov(dataset)\n",
    "        self.cov_mat = cov_mat\n",
    "        return cov_mat\n",
    "    \n",
    "    def eigen(self, cov_mat):\n",
    "        \"\"\"Returns a sorted list of eigenvector/-value pairs\"\"\"\n",
    "        # eigenvectors and eigenvalues for the from the covariance matrix\n",
    "        eig_val, eig_vec = np.linalg.eig(cov_mat)\n",
    "        \n",
    "        #sorts eigenvalues to find corresponding eigenvectors -- strongest principal components\n",
    "        top_eig_vals = np.sort(eig_val)\n",
    "        self.top_eig_vals = top_eig_vals[::-1]\n",
    "        \n",
    "        #create pairs of eig_vals and eig_vecs\n",
    "        eig_pairs = {}\n",
    "        \n",
    "        for i, val in enumerate(eig_val):\n",
    "            eig_pairs[val] = eig_vec[i]\n",
    "        \n",
    "        self.eig_pairs = eig_pairs\n",
    "        \n",
    "        return eig_pairs\n",
    "    \n",
    "    def transformation_matrix(self, eig_pairs):\n",
    "        \"\"\"Uses k top eigenvectors as a transformation matrix\"\"\"\n",
    "        k = self.k\n",
    "        printing = self.printing\n",
    "        \n",
    "        #choose k eigenvectors with the largest eigenvalues\n",
    "        top_eig_vals = self.top_eig_vals[0:k]\n",
    "        \n",
    "        #retrieve eigenvectors for the top k eigenvalues\n",
    "        top_eig_vecs = []\n",
    "        \n",
    "        for val in top_eig_vals:\n",
    "            eigvec = eig_pairs[val]\n",
    "            top_eig_vecs.append(eigvec)\n",
    "            \n",
    "        #create transformation matrix from eigenvectors\n",
    "        W = np.hstack(top_eig_vecs)\n",
    "        W = W.reshape(k,self.n_features)\n",
    "        self.W = W\n",
    "        \n",
    "        #printing options\n",
    "        if printing:            \n",
    "            print('Matrix W:\\n', W)\n",
    "            \n",
    "        return W\n",
    "    \n",
    "    #project to k feature dimensions (i.e. k principle components)\n",
    "    def transform(self, dataset):\n",
    "        \"\"\"Transform dataset\"\"\"\n",
    "        printing = self.printing\n",
    "        W = self.W\n",
    "        \n",
    "        pca_matrix = W.dot(dataset.T)\n",
    "        \n",
    "        if printing:\n",
    "            print(pca_matrix)\n",
    "        \n",
    "        self.pca_matrix = pca_matrix\n",
    "        \n",
    "        return pca_matrix"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Train Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "PCA = PrincipalComponentAnalysis()\n",
    "PCA.fit(X)\n",
    "pca = PCA.transform(X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plot Projection"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#return PCA matrix\n",
    "pca = pd.DataFrame(pca).T\n",
    "pca = pd.concat([pca, pd.Series(list(y.index))],axis=1)\n",
    "pca.columns = ['PC1','PC2','index']\n",
    "pca = pca.set_index('index')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<seaborn.axisgrid.PairGrid at 0x1e217a34e10>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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lL9F7mg/CId8hH0QOoAYu+U8qzzDSvuuudYgFopT6NMSMmtvCvg56L7YeJCCyTD6/wISX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\nECX/D1IsiXKmO24mAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1e217a34e48>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#add class to PCA matrix for plotting\n",
    "cls_vals = y.astype('int')\n",
    "df = pd.concat([pca, cls_vals], axis=1)\n",
    "df.columns = ['PC1','PC2','class']\n",
    "\n",
    "#plot PCA matrix\n",
    "sns.pairplot(x_vars=[\"PC1\"], y_vars=[\"PC2\"], data=df, \n",
    "hue=\"class\", size=5)"
   ]
  }
 ],
 "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": "3.5.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}