02-MulticategoryPerceptronTrainingAlgorithm.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Multicategory Perceptron Training Algorithm\n",
    "***Author: Pratyush Bagaria (pbagar2@uic.edu)***"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 155,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import idx2numpy\n",
    "\n",
    "training_images = idx2numpy.convert_from_file('train-images.idx3-ubyte')\n",
    "training_labels = idx2numpy.convert_from_file('train-labels.idx1-ubyte')\n",
    "test_images = idx2numpy.convert_from_file('t10k-images.idx3-ubyte')\n",
    "test_labels = idx2numpy.convert_from_file('t10k-labels.idx1-ubyte')\n",
    "w = np.random.uniform(-1,1,size=(10,784))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 156,
   "metadata": {},
   "outputs": [],
   "source": [
    "def u_function(M):\n",
    "    i = 0\n",
    "    u = np.empty([10,1])\n",
    "    for val in M:\n",
    "        if val >= 0:\n",
    "            u[i] = 1.0\n",
    "        else:\n",
    "            u[i] = 0.0\n",
    "        i += 1\n",
    "    return u"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 157,
   "metadata": {},
   "outputs": [],
   "source": [
    "def networkTrainAlgo(w, n, eta, epsilon, training_images, training_labels):\n",
    "    epoch = 0\n",
    "    train_errors = []\n",
    "    while(True):\n",
    "        train_errors.append(0)\n",
    "        for i in range(n):  \n",
    "            xi = training_images[i]\n",
    "            xi.resize(784, 1)\n",
    "            v = np.matmul(w,xi)\n",
    "            label = v.argmax(axis=0)\n",
    "            if(label != training_labels[i]):\n",
    "                train_errors[epoch] = train_errors[epoch] + 1\n",
    "        epoch = epoch + 1    \n",
    "        \n",
    "        ## loop to update the weights ##\n",
    "        for i in range(n):\n",
    "            xi = training_images[i]\n",
    "            xi.resize(784, 1)\n",
    "            u = np.array(u_function(np.matmul(w,xi)))\n",
    "            dxi = np.zeros((1,10)).T\n",
    "            dxi[training_labels[i]] = 1\n",
    "            dxi_minus_u = np.subtract(dxi, u)\n",
    "            p = np.multiply(dxi_minus_u, np.transpose(xi))\n",
    "            w = w + eta*p\n",
    "        ## while loop terminates when algorithm converges or when number of epoch is 100\n",
    "        ## when training data is quite high, eta is 1 and epsilon is 0 then\n",
    "        ## there are high chances of algorithm not getting converged\n",
    "        ## making while loop run infinitely, so max. epochs is set to 100\n",
    "        if(train_errors[epoch - 1]/n <= epsilon or epoch==100):\n",
    "            break\n",
    "    return w, train_errors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 158,
   "metadata": {},
   "outputs": [],
   "source": [
    "def networkTestAlgo(W, test_images, test_labels):\n",
    "    test_errors = 0  \n",
    "    for i in range(len(test_images)):  \n",
    "        xi = test_images[i]\n",
    "        xi.resize(784, 1)\n",
    "        vPrime = np.matmul(W ,xi)\n",
    "        label = vPrime.argmax(axis=0)\n",
    "        if(label != test_labels[i]):\n",
    "            test_errors = test_errors + 1\n",
    "    print('Error Count on Test data:',test_errors)\n",
    "    print('Error Percentage:', test_errors*100/len(test_images))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 159,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plotGraph(train_errors):\n",
    "    plt.title('\\nepoch number VS number of misclassification (Train Errors)\\n')\n",
    "    plt.ylabel('\\nnumber of misclassification (Train Errors)\\n')\n",
    "    plt.xlabel('\\nepoch number\\n')\n",
    "    plt.plot(range(len(train_errors)), train_errors, color = 'b')\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 160,
   "metadata": {},
   "outputs": [],
   "source": [
    "def compareAndPlotGraphs(train_errors_1, train_errors_2, train_errors_3):\n",
    "    plt.subplot(1, 3, 1)\n",
    "    plt.plot(range(len(train_errors_1)), train_errors_1)\n",
    "    plt.xlabel('\\nepoch number\\n (for W1)\\n',fontsize=18)\n",
    "    plt.ylabel('\\nnumber of misclassifications\\n',fontsize=18)\n",
    "\n",
    "    plt.subplot(1, 3, 2)\n",
    "    plt.plot(range(len(train_errors_2)), train_errors_2)\n",
    "    plt.xlabel('\\nepoch number\\n (for W2)\\n',fontsize=18)\n",
    "    plt.ylabel('\\nnumber of misclassifications\\n',fontsize=18)\n",
    "\n",
    "\n",
    "    plt.subplot(1, 3, 3)\n",
    "    plt.plot(range(len(train_errors_3)), train_errors_3)\n",
    "    plt.xlabel('\\nepoch number\\n (for W3)\\n',fontsize=18)\n",
    "    plt.ylabel('\\nnumber of misclassifications\\n',fontsize=18)\n",
    "\n",
    "    plt.tight_layout(rect=[0, 0, 5, 2])\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Results when n=50, eta=1 and epsilon = 0 below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 172,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Error Count on Test data: 4353\n",
      "Error Percentage: 43.53\n"
     ]
    }
   ],
   "source": [
    "n = 50\n",
    "eta = 1\n",
    "epsilon = 0.0\n",
    "W, train_errors = networkTrainAlgo(w, n, eta, epsilon, training_images, training_labels)\n",
    "plotGraph(train_errors)\n",
    "networkTestAlgo(W, n, test_images, test_labels)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Results when n=1000, eta=1 and epsilon = 0 below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 173,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Error Count on Test data: 1764\n",
      "Error Percentage: 17.64\n"
     ]
    }
   ],
   "source": [
    "n = 1000\n",
    "eta = 1\n",
    "epsilon = 0.0\n",
    "W, train_errors = networkTrainAlgo(w, n, eta, epsilon, training_images, training_labels)\n",
    "plotGraph(train_errors)\n",
    "networkTestAlgo(W, n, test_images, test_labels)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Results when n=60000, eta=1 and epsilon = 0 below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 174,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Error Count on Test data: 1504\n",
      "Error Percentage: 15.04\n"
     ]
    }
   ],
   "source": [
    "n = 60000\n",
    "eta = 1\n",
    "epsilon = 0.0\n",
    "W, train_errors = networkTrainAlgo(w, n, eta, epsilon, training_images, training_labels)\n",
    "plotGraph(train_errors)\n",
    "networkTestAlgo(W, n, test_images, test_labels)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Results when n=60000, eta=1, epsilon = 0.15 and three different randomly assigned weights for three runs:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 166,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "***Below are the graphs obtained on training data***\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 432x288 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "***Below are the results obtained on test data***\n",
      "\n",
      "Run #1 - When w1 was initial weights for training\n",
      "Error Count on Test data: 1545\n",
      "Error Percentage: 15.45\n",
      "\n",
      "Run #2 - When w2 was initial weights for training\n",
      "Error Count on Test data: 1560\n",
      "Error Percentage: 15.6\n",
      "\n",
      "Run #3 - When w3 was initial weights for training\n",
      "Error Count on Test data: 1609\n",
      "Error Percentage: 16.09\n"
     ]
    }
   ],
   "source": [
    "### considering three different weights as w1, w2 and w3 for three different runs\n",
    "w1 = np.random.uniform(-1,1,size=(10,784))\n",
    "w2 = np.random.uniform(-1,1,size=(10,784))\n",
    "w3 = np.random.uniform(-1,1,size=(10,784))\n",
    "n = 60000\n",
    "eta = 1\n",
    "epsilon = 0.15\n",
    "W1, train_errors_1 = networkTrainAlgo(w1, n, eta, epsilon, training_images, training_labels)\n",
    "W2, train_errors_2 = networkTrainAlgo(w2, n, eta, epsilon, training_images, training_labels)\n",
    "W3, train_errors_3 = networkTrainAlgo(w3, n, eta, epsilon, training_images, training_labels)\n",
    "print (\"\\n***Below are the graphs obtained on training data***\")\n",
    "compareAndPlotGraphs(train_errors_1, train_errors_2, train_errors_3)\n",
    "print (\"\\n***Below are the results obtained on test data***\")\n",
    "print (\"\\nRun #1 - When w1 was initial weights for training\")\n",
    "networkTestAlgo(W1, test_images, test_labels)\n",
    "print (\"\\nRun #2 - When w2 was initial weights for training\")\n",
    "networkTestAlgo(W2, test_images, test_labels)\n",
    "print (\"\\nRun #3 - When w3 was initial weights for training\")\n",
    "networkTestAlgo(W3, test_images, test_labels)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Observations:\n",
    "1. __Error percentage is 43.53 on the test images when n=50.__ The error percentage is quite high for test images because the network was trained on a small set of 50 training images which converged in 4 epochs and zero training errors.\n",
    "2. __Error percentage is 17.64 on the test images when n=1000.__ The error percentage reduced to a great extent compared with what was obtained when n was 50. This is because the network learned more number of training samples and convereged in 36 epochs with zero training errors. Though 1000 samples were also not enough so there is ~18% error rate on test images.\n",
    "3. __Error percentage is 15.04 on the test images when n=60000.__ The error percentage insignificantly reduced from ~18% to ~15%  but this was achieved when number of epochs reached 100 and further there was no hope of algorithm to converge. From the graph it can be inferred that the number of misclassifications is around 6000 to 12000 after 1st epoch or in other words error percentage on training images is near around 15% in all the epochs greater than 1.\n",
    "4. __Error percentage is 15.45, 15.6 & 16.09 on the test images for n=60000, η=1, Ɛ=0.15 and when the algorithm was run thrice on 3 different initial weights.__ It was hence observed that choosing η and Ɛ appropriately the algorithm converges in finite number of epochs even for 60,000 test images irrespective of the number of times the algorithm is run with different randomly assigned initial weights (3, 5 and 3 epochs in this case for w1, w2 and w3 respectively). Moreover, it is noticed that the error percentage on test images hovers around 15% to 18% in all the cases except the case when the test images was 50."
   ]
  }
 ],
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