7. Linear Discriminant Analysis.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 134,
   "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"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "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": 136,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# prepare configuration for cross validation test harness\n",
    "seed = 7\n",
    "\n",
    "X_train, X_test, y_train, y_test = model_selection.train_test_split(tf.iloc[:,:9], \n",
    "                                                                    tf.iloc[:,9], \n",
    "                                                                    test_size=0.25, \n",
    "                                                                    random_state=seed)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class LinearDiscriminantAnalysis(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, y_train):\n",
    "        self.trainSet = pd.concat([X_train, y_train],axis=1)\n",
    "        self.n_features = X_train.shape[1]\n",
    "        \n",
    "        trainSet = self.trainSet\n",
    "        \n",
    "        cls_means = self.class_means(trainSet)\n",
    "        self.within_class(cls_means)\n",
    "        self.between_class(cls_means)\n",
    "        \n",
    "        self.eigen(self.S_W,self.S_B)\n",
    "        self.transformation_matrix(self.eig_vals, self.eig_vecs)\n",
    "        self.train_lda = self.transform(trainSet)\n",
    "        self.centroids()\n",
    "        return \n",
    "    \n",
    "    def class_means(self, dataset):\n",
    "        class_means = {}\n",
    "        \n",
    "        for cls in dataset['class'].unique():\n",
    "            cls_data = dataset[dataset['class'] == cls]\n",
    "            mean = cls_data.describe().loc['mean'][:-1]\n",
    "            class_means[cls] = list(mean.values)\n",
    "        \n",
    "        return class_means\n",
    "    \n",
    "    def between_class(self, class_means):\n",
    "        \n",
    "        \"\"\"Create between-class scatter matrix\"\"\"\n",
    "        \n",
    "        trainSet = self.trainSet\n",
    "        n_features = self.n_features\n",
    "        \n",
    "        #vector of overall means\n",
    "        overall_mean = np.asarray(trainSet.describe().loc['mean'])[:-1]\n",
    "        overall_mean = overall_mean.reshape(n_features,1)\n",
    "        \n",
    "        S_B = np.zeros((n_features,n_features))\n",
    "        \n",
    "        for cls in class_means.keys():\n",
    "            cls_data = trainSet[trainSet['class'] == cls][:-1]\n",
    "            n = cls_data.shape[0]\n",
    "            \n",
    "            cls_mean = np.asarray(class_means[cls])\n",
    "            cls_mean = cls_mean.reshape(n_features,1)\n",
    "            \n",
    "            dif_mean = cls_mean - overall_mean\n",
    "            \n",
    "            S_B += n * dif_mean.dot(dif_mean.T)\n",
    "            \n",
    "            self.S_B = S_B\n",
    "            \n",
    "            return S_B\n",
    "        \n",
    "    def within_class(self, class_means):\n",
    "        \n",
    "        \"\"\"Create within-class scatter matrix\"\"\"\n",
    "        \n",
    "        trainSet = self.trainSet\n",
    "        n_features = self.n_features\n",
    "        \n",
    "        #initialize within-class matrix\n",
    "        S_W = np.zeros((self.n_features,self.n_features))\n",
    "        \n",
    "        #for each class..\n",
    "        for cls in class_means.keys():\n",
    "            #initialize class matrix\n",
    "            cls_mtrx = np.zeros((n_features,n_features))\n",
    "            #select class means data\n",
    "            cls_data = np.asarray(trainSet[trainSet['class'] == cls])\n",
    "            \n",
    "            \n",
    "            for row in cls_data:\n",
    "                row = row[:-1]\n",
    "                row = row.reshape(n_features,1)\n",
    "                \n",
    "                cls_mean = np.asarray(class_means[cls])\n",
    "                cls_mean = cls_mean.reshape(n_features,1)\n",
    "                \n",
    "                dif_mean = row - cls_mean\n",
    "                \n",
    "                cls_mtrx += dif_mean.dot(dif_mean.T)\n",
    "           \n",
    "            S_W += cls_mtrx\n",
    "            \n",
    "        self.S_W = S_W\n",
    "           \n",
    "        return S_W\n",
    "    \n",
    "    def eigen(self, mtrx1, mtrx2):\n",
    "       \n",
    "        #calculate eigenvectors and eigenvalues\n",
    "        eig_vals, eig_vecs = np.linalg.eig(np.linalg.inv(mtrx1).dot(mtrx2))\n",
    "\n",
    "        #for i in range(len(eig_vals)):\n",
    "        #    eigvec_sc = eig_vecs[:,i].reshape(self.n_features,1)   \n",
    "        #    print('\\nEigenvector {}: \\n{}'.format(i+1, eigvec_sc.real))\n",
    "        #    print('Eigenvalue {:}: {:.2e}'.format(i+1, eig_vals[i].real))\n",
    "            \n",
    "        self.eig_vals = eig_vals\n",
    "        self.eig_vecs = eig_vecs\n",
    "            \n",
    "        return eig_vals, eig_vecs\n",
    "    \n",
    "    def transformation_matrix(self, eig_vals, eig_vecs):\n",
    "        k = self.k\n",
    "        printing = self.printing\n",
    "        n_features = self.n_features \n",
    "        eigv_sum = sum(eig_vals)\n",
    "        \n",
    "        # Make a list of (eigenvalue, eigenvector) tuples\n",
    "        eig_pairs = [(np.abs(eig_vals[i]), eig_vecs[:,i]) for i in range(len(eig_vals))]\n",
    "\n",
    "        # Sort the (eigenvalue, eigenvector) tuples from high to low\n",
    "        eig_pairs = sorted(eig_pairs, key=lambda k: k[0], reverse=True)\n",
    "        \n",
    "        #choose k eigenvectors with the largest eigenvalues\n",
    "        top_eig_vecs = []\n",
    "        \n",
    "        for i in range(k):\n",
    "            ev = eig_pairs[i][1].reshape(n_features,1)\n",
    "            top_eig_vecs.append(ev)\n",
    "        \n",
    "        #create transformation matrix\n",
    "        W = np.hstack(top_eig_vecs)\n",
    "        self.W = W\n",
    "        \n",
    "        #printing options\n",
    "        if printing:\n",
    "            # Visually confirm that the list is correctly sorted by decreasing eigenvalues\n",
    "            print('Eigenvalues in decreasing order:\\n')\n",
    "            for i in eig_pairs:\n",
    "                print(i[0])\n",
    "            \n",
    "            #variance summary\n",
    "            print('\\nVariance explained:\\n')\n",
    "            for i,j in enumerate(eig_pairs):\n",
    "                print('eigenvalue {0:}: {1:.2%}'.format(i+1, (j[0]/eigv_sum).real))\n",
    "            \n",
    "            #transformation matrix\n",
    "            print('Matrix W:\\n', W.real)\n",
    "            \n",
    "        return W\n",
    "    \n",
    "    #project to k feature dimensions (i.e. k linear discriminants)\n",
    "    def transform(self, dataset):\n",
    "        printing = self.printing\n",
    "        n_features = self.n_features\n",
    "        W = self.W\n",
    "        \n",
    "        dataset = dataset.iloc[:,:n_features]\n",
    "        \n",
    "        lda_matrix = dataset.dot(W)\n",
    "        \n",
    "        if printing:\n",
    "            print(lda_matrix)\n",
    "        \n",
    "        return lda_matrix\n",
    "    \n",
    "    def gaussian_probability(self, x, mean, std):\n",
    "        #find gaussian probability\n",
    "        probability = scipy.stats.norm(mean, std).pdf(x)\n",
    "        return probability\n",
    "    \n",
    "    def centroids(self):\n",
    "        \"\"\"Retrieves mean and stdev for each linear discriminant for each class in training data\"\"\"\n",
    "        train_lda = self.train_lda\n",
    "        cls_vals = self.trainSet.iloc[:,9].astype('int')\n",
    "        df = pd.concat([train_lda, cls_vals], axis=1) \n",
    "        \n",
    "        centroids = {}\n",
    "        \n",
    "        #for each class...\n",
    "        for cls in cls_vals.unique():\n",
    "            #select class data\n",
    "            data = df[df['class'] == cls]\n",
    "            data = data.drop('class',axis=1) #drop class\n",
    "            lda_cls_mean = data.describe().loc['mean'].values #get means of linear discriminants\n",
    "            lda_cls_stdev = data.describe().loc['std'].values #get stdevs of linear discriminants\n",
    "            \n",
    "            centroids[cls] = [lda_cls_mean, lda_cls_stdev] #save linear discriminant means/stdevs\n",
    "            \n",
    "        self.centroids = centroids\n",
    "        \n",
    "        \n",
    "        return centroids    \n",
    "    \n",
    "    def class_probabilities(self, testInstance):\n",
    "        centroids = self.centroids\n",
    "        n_features = self.n_features\n",
    "        \n",
    "        probabilities ={}\n",
    "        \n",
    "        #for each class...\n",
    "        for cls in centroids:\n",
    "            probabilities[cls] = 1 #initialize\n",
    "            lda_cls_mean = centroids[cls][0] #retrieve linear discriminant mean vector\n",
    "            lda_cls_stdev = centroids[cls][1] #retrieve linear discriminant stdev vector\n",
    "            \n",
    "            #for each linear discriminant in k...\n",
    "            for i in range(self.k):\n",
    "                mean = lda_cls_mean[i] #retrieve linear discriminant mean\n",
    "                stdev = lda_cls_stdev[i] #retrieve linear discriminant stdev\n",
    "                x = testInstance[i] #retrieve testInstance linear discriminant value.\n",
    "\n",
    "                #calculate/update class probability by applying the chain rule of probabilities\n",
    "                probabilities[cls] *= self.gaussian_probability(x, mean, stdev)\n",
    "\n",
    "        return probabilities\n",
    "    \n",
    "    #predict class for datapoint\n",
    "    def class_predict(self, testInstance):\n",
    "        probabilities = self.class_probabilities(testInstance)\n",
    "        bestLabel, bestProb = None, -1 #initialize\n",
    "        \n",
    "        #for each class probability...\n",
    "        for cls, probability in probabilities.items():\n",
    "            if bestLabel is None or probability > bestProb: #if most likely...\n",
    "                bestProb = probability #save probability\n",
    "                bestLabel = cls #save class\n",
    "        \n",
    "        return bestLabel\n",
    "            \n",
    "    #make predictions\n",
    "    def predict(self, X_test):\n",
    "        self.testSet = X_test\n",
    "        predictions = []\n",
    "        \n",
    "        #for each testInstance...\n",
    "        for i in range(len(X_test)):\n",
    "            testInstance = X_test.iloc[i] #select testInstance\n",
    "            result = self.class_predict(testInstance) #predict testInstance class\n",
    "            predictions.append(result) #save prediction\n",
    "        return predictions\n",
    "        \n",
    "    #evaluate predictions\n",
    "    def score(self, predictions, y_test):\n",
    "        actual = y_test\n",
    "        correct = sum(predictions == actual) \n",
    "        accuracy = correct / len(actual)\n",
    "        return accuracy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Train Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 138,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "LDA = LinearDiscriminantAnalysis()\n",
    "LDA.fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plot Projection"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 139,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Will\\Anaconda2\\envs\\py35\\lib\\site-packages\\numpy\\core\\numeric.py:583: ComplexWarning: Casting complex values to real discards the imaginary part\n",
      "  return array(a, dtype, copy=False, order=order, subok=True)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<seaborn.axisgrid.PairGrid at 0x27f9404b160>"
      ]
     },
     "execution_count": 139,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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Fb2XZo03lcQsJrn3qsGERrJ0/aiVVzW6iXeknW1jFYv9PlM+Am5tYLOLt1pcs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\nAEEEBAAg6P/naVZbxpV59gAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x27f9516de80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "lda_train = LDA.transform(X_train)\n",
    "cls_vals = y_train.astype('int')\n",
    "\n",
    "df = pd.concat([lda_train, cls_vals], axis=1)\n",
    "df.columns = ['LD1','LD2','class']\n",
    "\n",
    "sns.pairplot(x_vars=[\"LD1\"], y_vars=[\"LD2\"], data=df, \n",
    "hue=\"class\", size=5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Test Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 141,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.97714285714285709"
      ]
     },
     "execution_count": 141,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lda_test = LDA.transform(X_test)\n",
    "predictions = LDA.predict(lda_test)\n",
    "LDA.score(predictions,y_test)"
   ]
  }
 ],
 "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
}