PCA.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Once deleted, variables cannot be recovered. Proceed (y/[n])? y\n"
     ]
    }
   ],
   "source": [
    "%reset\n",
    "import os\n",
    "from math import *\n",
    "from PIL import Image\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from helpers import *\n",
    "from classifiers.pca import *\n",
    "from classifiers.knn import *\n",
    "%matplotlib inline\n",
    "%load_ext autoreload\n",
    "%autoreload 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "root = 'orl_faces'\n",
    "X, y = load_faces(root)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X_train = X[0:400:2,:]\n",
    "X_test = X[1:400:2,:]\n",
    "y_train = y[0:400:2]\n",
    "y_test = y[1:400:2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "34\n",
      "(10304,) (10304, 34)\n",
      "50\n",
      "(10304,) (10304, 50)\n",
      "74\n",
      "(10304,) (10304, 74)\n",
      "114\n",
      "(10304,) (10304, 114)\n"
     ]
    }
   ],
   "source": [
    "# pca\n",
    "alpha = [0.8, 0.85, 0.9, 0.95]\n",
    "U = []\n",
    "pca = []\n",
    "for x in range(0,len(alpha)):\n",
    "    o = PCA()\n",
    "    pca.append(o)\n",
    "    U.append(pca[x].train(X_train, alpha=alpha[x], load_path='./pca_projection.npz', verbose=False))\n",
    "    U[x] = np.real(U[x])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7f60450747f0>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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WOIWcfTadEoLrXCBkOuiRlAAHMScs4FQNtubZq36sHjuAhbiePjqOr01Y5H2psX1N1zTn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\nH15Hxwzw/wNUwAu1br2/KgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f60454d0be0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(U[0][:,6].reshape((112,92)),cmap='gray')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X_train_pca = []\n",
    "for y in range(0,len(U)):\n",
    "    X_train_pca.append(pca[y].project(X_train))\n",
    "X_test_pca = []\n",
    "for y in range(0,len(U)):\n",
    "    X_test_pca.append(pca[y].project(X_test))  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "training accuracy 0 = 1.0\n",
      "testing accuracy 0 = 0.74\n",
      "training accuracy 1 = 1.0\n",
      "testing accuracy 1 = 0.705\n",
      "training accuracy 2 = 1.0\n",
      "testing accuracy 2 = 0.675\n",
      "training accuracy 3 = 1.0\n",
      "testing accuracy 3 = 0.625\n"
     ]
    }
   ],
   "source": [
    "for x in range(0,len(alpha)):\n",
    "    knn_1 = K_nearest_neighbour()\n",
    "    knn_1.train(X_train_pca[x], y_train)\n",
    "    test_predictions = knn_1.predict(X_test_pca[x])\n",
    "    train_predictions = knn_1.predict(X_train_pca[x])\n",
    "    train_accuracy = np.mean(train_predictions == y_train)\n",
    "    test_accuracy = np.mean(test_predictions == y_test)\n",
    "    print(f'training accuracy {x} = {train_accuracy}')\n",
    "    print(f'testing accuracy {x} = {test_accuracy}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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PVLNmzWLhwoXMmDHjgK9hEJQkSZI0JY2NjXHssceyaNEikhzwdb76ze8wY+cT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\nJElSxxgEJUmSJKlj/jfKGUDlnGtTXQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6044e2a4a8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6044e2a550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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9tBMkFyUZTTK6cePG/Vi6JEmSJPXMPvII5s2e+eQdwCOmHca82TOZfeQRexy7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\nUJIkSZI6xiAoSZIkSR1jEJQkSZKkjvnfEH97K7egxysAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f60449e9550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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MQVCSJEmSOqbVIJjktCSrkqxOctEE589Psi7JHc3nzX3nzktyb/M5r806JUmSJKlLDm7r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\nSR1jEJQkSZKkjjEISpIkSVLH/P8H4E6kSrwcdQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6044c15f98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def knn_class(alpha):\n",
    "    Ks = [1, 3, 5, 7]\n",
    "    train_accs, test_accs = [],[]\n",
    "\n",
    "    for k in Ks:\n",
    "        knn = K_nearest_neighbour(k=k)\n",
    "        knn.train(X_train_pca[alpha], y_train)\n",
    "        test_predictions = knn.predict(X_test_pca[alpha])\n",
    "        train_predictions = knn.predict(X_train_pca[alpha])\n",
    "        train_accs.append(np.mean(train_predictions == y_train))\n",
    "        test_accs.append(np.mean(test_predictions == y_test))\n",
    "\n",
    "    plt.scatter(Ks,test_accs, label='test')\n",
    "    plt.legend(loc='lower right')\n",
    "    plt.title('Accuracy against K')\n",
    "    plt.xlabel('k value')\n",
    "    plt.ylabel('accuracy')\n",
    "    plt.gcf().set_size_inches(15,5)\n",
    "    plt.show()\n",
    "\n",
    "for x in range(0,len(alpha)):\n",
    "    knn_class(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Once deleted, variables cannot be recovered. Proceed (y/[n])? y\n"
     ]
    }
   ],
   "source": [
    "%reset"
   ]
  }
 ],
 "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": "3.6.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}