multiclass_pta.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 2. Multicategory Perceptron Training Algorithm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import os\n",
    "import path\n",
    "import struct\n",
    "import gzip\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Source for reading the idx files as numpy arrays: https://gist.github.com/tylerneylon\n",
    "def read_idx(filename):\n",
    "    with open(filename, 'rb') as f:\n",
    "        zero, data_type, dims = struct.unpack('>HBB', f.read(4))\n",
    "        shape = tuple(struct.unpack('>I', f.read(4))[0] for d in range(dims))\n",
    "        return np.frombuffer(f.read(), dtype=np.uint8).reshape(shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Source for reading the idx files as numpy arrays: https://gist.github.com/tylerneylon\n",
    "def read_idx_gz(filename):\n",
    "    with gzip.open(filename, 'rb') as f:\n",
    "        zero, data_type, dims = struct.unpack('>HBB', f.read(4))\n",
    "        shape = tuple(struct.unpack('>I', f.read(4))[0] for d in range(dims))\n",
    "        return np.frombuffer(f.read(), dtype=np.uint8).reshape(shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def step_fn(x):\n",
    "    i = 0\n",
    "    y = np.empty([10,1])\n",
    "    for each in x:\n",
    "        if each >= 0:\n",
    "            y[i] = 1.0\n",
    "        else:\n",
    "            y[i] = 0.0\n",
    "        i += 1\n",
    "    return y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def training_errors(epoch, errors):\n",
    "    for i in range(n):\n",
    "        xi = train_data[i]\n",
    "        xi.resize(784, 1)\n",
    "        v = np.matmul(w,xi)\n",
    "        prediction = v.argmax(axis=0)\n",
    "        actual = train_labels[i]\n",
    "        if prediction != actual:\n",
    "            errors[epoch] += 1\n",
    "    return errors[epoch]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def update_weight(w):\n",
    "    for i in range(n):\n",
    "        xi = train_data[i]\n",
    "        xi.resize(784, 1)\n",
    "        y = np.array(step_fn(np.matmul(w,xi)))\n",
    "        label = np.zeros((1,10)).T\n",
    "        label[train_labels[i]] = 1\n",
    "        difference = label - y\n",
    "        xit = np.transpose(xi)\n",
    "        update = learning_rate * np.matmul(difference, xit)\n",
    "        w += update"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def learning_weights(w, epoch, threshold, learning_rate):\n",
    "    while epoch<100:\n",
    "        errors.append(0)\n",
    "        errors[epoch] = training_errors(epoch, errors)\n",
    "        update_weight(w)\n",
    "        epoch += 1\n",
    "        if errors[epoch-1]/n <= threshold:\n",
    "            break"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_graph(errors):\n",
    "    fig, ax = plt.subplots(figsize=(10,10))\n",
    "    plt.plot(range(len(errors)), errors, c = 'green')\n",
    "    plt.ylabel('Number of Misclassifications')\n",
    "    plt.xlabel('Number of Epochs')\n",
    "    plt.title('Errors vs Epochs')\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def find_errors():\n",
    "    test_errors = 0\n",
    "    for i in range(len(test_data)):\n",
    "        xi = test_data[i]\n",
    "        xi.resize(784, 1)\n",
    "        v = np.matmul(w ,xi)\n",
    "        prediction = v.argmax(axis=0)\n",
    "        actual = test_labels[i]\n",
    "        if prediction != actual:\n",
    "            test_errors += 1\n",
    "    print(\"Number of errors in test data: \", test_errors)\n",
    "    print(\"Percentage of test errors: \", test_errors*100/len(test_data))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Data Source: http://yann.lecun.com/exdb/mnist/\n",
    "train_data = read_idx_gz('train-images-idx3-ubyte.gz')\n",
    "train_labels = read_idx_gz('train-labels-idx1-ubyte.gz')\n",
    "test_data = read_idx_gz('t10k-images-idx3-ubyte.gz')\n",
    "test_labels = read_idx_gz('t10k-labels-idx1-ubyte.gz')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [],
   "source": [
    "w = np.random.uniform(-1, 1, size=(10,784))\n",
    "n = 50\n",
    "epoch = 0\n",
    "threshold = 0.0\n",
    "learning_rate = 1.0\n",
    "errors = []"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x111279fd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of errors in test data:  4227\n",
      "Percentage of test errors:  42.27\n"
     ]
    }
   ],
   "source": [
    "learning_weights(w, epoch, threshold, learning_rate)\n",
    "plot_graph(errors)\n",
    "find_errors()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b> (f) Indeed, the training part of the network terminates with 0 errors eventually and number of misclassifications decrease exponentially as number of epochs rise. We have 0% error according to our training samples because our network has been trained on those training examples itself and due to that it overfits those training examples and gives 100% accuracy on only those examples. The learned weights cannot generalize better to new unseen examples and therefore the test accuracy is lower (test error is high) than the training accuracy at a higher epoch. Furthermore, we observe that number of misclassifications in the training set comes down to 0% error after about 3 epochs. <br>\n",
    "    \n",
    "   The network got only 50 examples (small number of samples) to train on and after that it was evaluated on 10,000 test samples. Hence, the network was biased towards those 50 training samples and also had the opportunity to fine tune its weights and learn more but couldn't. Therefore, the test error rate is high and not 0%. <br>\n",
    "   \n",
    "   <br> However at 0th epoch, the percentage of errors obtained in test data is 42.27% and far lower than the initial error obtained in the training data because we have updated the weights accordingly and the network better understands how to process the inputs after being trained for 5 epochs and not just take randomly initialized values for its weights. <b>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {},
   "outputs": [],
   "source": [
    "w = np.random.uniform(-1, 1, size=(10,784))\n",
    "n = 1000\n",
    "epoch = 0\n",
    "threshold = 0.0\n",
    "learning_rate = 1.0\n",
    "errors = []"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11185ff98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of errors in test data:  1673\n",
      "Percentage of test errors:  16.73\n"
     ]
    }
   ],
   "source": [
    "learning_weights(w, epoch, threshold, learning_rate)\n",
    "plot_graph(errors)\n",
    "find_errors()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b> (g) We observe that number of misclassifications in the training set comes down to 0% error after about 33 epochs. The number of epochs the network took to converge increased because there are 1000 training samples now (far more than 50) and it would be more probable to errors this time. <br>\n",
    "    \n",
    "   The network got only 1000 examples to train on and after that it was evaluated on 10,000 test samples. Hence, the network was biased towards those 1000 training samples and also had the opportunity to fine tune its weights and learn more but couldn't. Therefore, the test error rate is high and not 0%. <br>\n",
    "   \n",
    "   <br> The percentage of errors obtained in test data is 16.73% and far lower than the initial error obtained in the training data but not 0% eventually because we have updated the weights accordingly and the network better understands how to process the inputs after being trained for 33 epochs and not just take randomly initialized values for its weights. <br> \n",
    "   \n",
    "   The network has now been trained on 1000 examples (far more than 50 samples as in (f)) which is a lot more data as compared to (f) and the PTA algorithm has also run for far more epochs. Hence, the network now has better approximation of weights and has also approached convergence more far more as compared to (f). It is far more likely that the network might have seen (been trained on) all the 0 - 9 labeled samples which is less probable in the case of (f). The error rate in the test set decreases as the number of training examples in the training set increases as the network has learned more efficiently on a larger set of training samples. Therefore, there is a lower test set error rate of 16.73% in the case of n = 1000 as compared to an error of 42.27% in the case where n = 50. <br>\n",
    "   \n",
    "   However, the error rate approaches 0 but it can never be 0 because we want a more generalized model which is simply not overfitted on training samples and which is capable to handling unseen test samples and does not do a bad job in classifying the test samples.<b>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {},
   "outputs": [],
   "source": [
    "w = np.random.uniform(-1, 1, size=(10,784))\n",
    "n = 60000\n",
    "epoch = 0\n",
    "threshold = 0.0\n",
    "learning_rate = 1.0\n",
    "errors = []"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10893a2b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of errors in test data:  1519\n",
      "Percentage of test errors:  15.19\n"
     ]
    }
   ],
   "source": [
    "learning_weights(w, epoch, threshold, learning_rate)\n",
    "plot_graph(errors)\n",
    "find_errors()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b> (h) The number of epochs have been limited to 100. After the first few epochs, we observe that the error rate does not fall anymore and we just keeps oscillating between 7,000 to 12,000 for the training data. <br>\n",
    "    \n",
    "   For the testing data, the percentage of misclassified data is 15.19% which is more or less similar to n = 1000. This means that the network has learned a sufficient amount of knowledge from just 1000 samples and performs only a little bit better when trained over all 60,000 training samples. <b>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b> (i) Based on the above results the threshold value I have chosen is 0.15 because it converges quickly and the results are still comparable to a lower threshold value <br> <b>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### First Time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "w = np.random.uniform(-1, 1, size=(10,784))\n",
    "n = 60000\n",
    "epoch = 0\n",
    "threshold = 0.15\n",
    "learning_rate = 1.0\n",
    "errors = []"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x110b98390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of errors in test data:  1626\n",
      "Percentage of test errors:  16.26\n"
     ]
    }
   ],
   "source": [
    "learning_weights(w, epoch, threshold, learning_rate)\n",
    "plot_graph(errors)\n",
    "find_errors()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Second Time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "w = np.random.uniform(-1, 1, size=(10,784))\n",
    "n = 60000\n",
    "epoch = 0\n",
    "threshold = 0.15\n",
    "learning_rate = 1.0\n",
    "errors = []"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x110b83240>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of errors in test data:  1482\n",
      "Percentage of test errors:  14.82\n"
     ]
    }
   ],
   "source": [
    "learning_weights(w, epoch, threshold, learning_rate)\n",
    "plot_graph(errors)\n",
    "find_errors()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Third Time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "w = np.random.uniform(-1, 1, size=(10,784))\n",
    "n = 60000\n",
    "epoch = 0\n",
    "threshold = 0.15\n",
    "learning_rate = 1.0\n",
    "errors = []"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1110cb0f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of errors in test data:  1562\n",
      "Percentage of test errors:  15.62\n"
     ]
    }
   ],
   "source": [
    "learning_weights(w, epoch, threshold, learning_rate)\n",
    "plot_graph(errors)\n",
    "find_errors()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b> As we can see the graph looks similar for all three attempts. The percentage of error varies from 14-16% which is still comparable to the results where n = 1000. <b>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.6.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}