ML_DeepLearning.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# CSE 152: Intro to Computer Vision - Spring 2019 Assignment 4\n",
    "## Instructor: David Kriegman\n",
    "### Assignment published on Wednesday, May 29, 2019\n",
    "### Due on Friday, June 7, 2019 at 11:59pm\n",
    "\n",
    "## Instructions\n",
    "* This assignment must be completed individually. Review the academic integrity and collaboration policies on the course website.\n",
    "* All solutions should be written in this notebook. Show your work for written questions.\n",
    "* If you want to modify the skeleton code, you may do so. It has been merely been provided as a framework for your solution.\n",
    "* You may use Python packages for basic linear algebra (e.g. NumPy or SciPy for basic operations), but you may not use packages that directly solve the problem. If you are unsure about using a specific package or function, ask the instructor and/or teaching assistants for clarification.\n",
    "* You must submit this notebook exported as a PDF. You must also submit this notebook as an `.ipynb` file. Submit both files (`.pdf` and `.ipynb`) on Gradescope. **You must mark the PDF pages associated with each question in Gradescope. If you fail to do so, we may dock points.**\n",
    "* It is highly recommended that you begin working on this assignment early.\n",
    "* **Late policy:** a penalty of 10% per day after the due date.\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problem 1: Machine Learning [10 pts]\n",
    "\n",
    "In this problem, you will implement K-Nearest Neighbors (KNN) algorithm for computer vision problems."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Part 1: Data preparation [1 pts]\n",
    "\n",
    "Download the MNIST data from http://yann.lecun.com/exdb/mnist/.\n",
    "\n",
    "Download the 4 zipped files, extract them into one folder, and change the variable 'path' in the code below. (Code taken from https://gist.github.com/akesling/5358964 )\n",
    "\n",
    "Plot one random example image corresponding to each label from the training data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import os\n",
    "import struct\n",
    "import numpy as np\n",
    "\n",
    "# Change path as required\n",
    "path = \"/home/apurba/Documents/quarter_3/cse_152_cv/HW4/mnist_data\"\n",
    "\n",
    "def read(dataset=\"training\", datatype='images'):\n",
    "    \"\"\"\n",
    "    Python function for importing the MNIST data set.  It returns an iterator\n",
    "    of 2-tuples with the first element being the label and the second element\n",
    "    being a numpy.uint8 2D array of pixel data for the given image.\n",
    "    \"\"\"\n",
    "\n",
    "    if dataset is \"training\":\n",
    "        fname_img = os.path.join(path, 'train-images-idx3-ubyte')\n",
    "        fname_lbl = os.path.join(path, 'train-labels-idx1-ubyte')\n",
    "    elif dataset is \"testing\":\n",
    "        fname_img = os.path.join(path, 't10k-images-idx3-ubyte')\n",
    "        fname_lbl = os.path.join(path, 't10k-labels-idx1-ubyte')\n",
    "\n",
    "    # Load everything in some numpy arrays\n",
    "    with open(fname_lbl, 'rb') as flbl:\n",
    "        magic, num = struct.unpack(\">II\", flbl.read(8))\n",
    "        lbl = np.fromfile(flbl, dtype=np.int8)\n",
    "\n",
    "    with open(fname_img, 'rb') as fimg:\n",
    "        magic, num, rows, cols = struct.unpack(\">IIII\", fimg.read(16))\n",
    "        img = np.fromfile(fimg, dtype=np.uint8).reshape(len(lbl), rows, cols)\n",
    "    \n",
    "    if(datatype=='images'):\n",
    "        get_data = lambda idx: img[idx]\n",
    "    elif(datatype=='labels'):\n",
    "        get_data = lambda idx: lbl[idx]\n",
    "\n",
    "    # Create an iterator which returns each image in turn\n",
    "    for i in range(len(lbl)):\n",
    "        yield get_data(i)\n",
    "        \n",
    "trainData=np.array(list(read('training','images')))\n",
    "trainLabels=np.array(list(read('training','labels')))\n",
    "testData=np.array(list(read('testing','images')))\n",
    "testLabels=np.array(list(read('testing','labels')))\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Some helper functions are given below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Random classifier accuracy: 9.510000 \n",
      "\n",
      "Plot random training images for each class:\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 10 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# a generator for batches of data\n",
    "# yields data (batchsize, 3, 32, 32) and labels (batchsize)\n",
    "# if shuffle, it will load batches in a random order\n",
    "import matplotlib.pyplot as plt\n",
    "def DataBatch(data, label, batchsize, shuffle=True):\n",
    "    n = data.shape[0]\n",
    "    if shuffle:\n",
    "        index = np.random.permutation(n)\n",
    "    else:\n",
    "        index = np.arange(n)\n",
    "    for i in range(int(np.ceil(n/batchsize))):\n",
    "        inds = index[i*batchsize : min(n,(i+1)*batchsize)]\n",
    "        yield data[inds], label[inds]\n",
    "\n",
    "# tests the accuracy of a classifier\n",
    "def test(testData, testLabels, classifier):\n",
    "    batchsize=50\n",
    "    correct=0.\n",
    "    for data,label in DataBatch(testData,testLabels,batchsize,shuffle=False):\n",
    "        prediction = classifier(data)\n",
    "        correct += np.sum(prediction==label)\n",
    "    return correct/testData.shape[0]*100\n",
    "\n",
    "# a sample classifier\n",
    "# given an input it outputs a random class\n",
    "class RandomClassifier():\n",
    "    def __init__(self, classes=10):\n",
    "        self.classes=classes\n",
    "    def __call__(self, x):\n",
    "        return np.random.randint(self.classes, size=x.shape[0])\n",
    "\n",
    "randomClassifier = RandomClassifier()\n",
    "print('Random classifier accuracy: %f \\n' % \n",
    "      test(testData, testLabels, randomClassifier))\n",
    "\n",
    "print('Plot random training images for each class:')\n",
    "count = 0\n",
    "check = np.zeros(10)\n",
    "imgs = np.zeros((10, 28, 28))\n",
    "for img, lb in DataBatch(trainData, trainLabels, 1, shuffle=True):\n",
    "    img = np.squeeze(img)\n",
    "    if check[lb] == 1:\n",
    "        continue\n",
    "    else:\n",
    "        check[lb] += 1\n",
    "        count += 1\n",
    "        imgs[lb,:,:] = img\n",
    "    if count == 10:\n",
    "        break\n",
    "\n",
    "fig, ax = plt.subplots(nrows=2, ncols=5)\n",
    "i = 0\n",
    "for row in ax:\n",
    "    for col in row:\n",
    "        col.imshow(imgs[i,:,:])\n",
    "        i += 1\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Part 2: Confusion Matrix [3 pts]\n",
    "Here you will implement a function that computes the confusion matrix for a classifier.\n",
    "The matrix (M) should be nxn where n is the number of classes.\n",
    "Entry M[i,j] should contain the fraction of images of class i that were classified as class j."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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84uT69AJP6O7DVfWuJF/Lsa+Cfqa77xhea8KVSd6e5Laq+u7xx/65u78yuBMz3p3khuMXJfckeefwPqdVd++pqhuT3JJj3zV0a87CZ855xhzAoDPpdgTAyhFhgEEiDDBIhAEGiTDAIBEGGCTCAINEGGDQ/wFTGLU1O3S6jAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 1008x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.1  0.07 0.09 0.1  0.1  0.11 0.1  0.1  0.11 0.09]\n",
      " [0.11 0.1  0.1  0.11 0.12 0.13 0.12 0.11 0.11 0.15]\n",
      " [0.12 0.08 0.08 0.1  0.12 0.11 0.12 0.1  0.1  0.11]\n",
      " [0.12 0.09 0.1  0.11 0.11 0.1  0.11 0.1  0.1  0.07]\n",
      " [0.12 0.08 0.08 0.1  0.1  0.1  0.11 0.09 0.11 0.09]\n",
      " [0.09 0.08 0.09 0.12 0.09 0.09 0.09 0.07 0.09 0.08]\n",
      " [0.09 0.08 0.08 0.1  0.09 0.1  0.11 0.11 0.09 0.11]\n",
      " [0.1  0.07 0.1  0.09 0.11 0.13 0.11 0.1  0.12 0.1 ]\n",
      " [0.08 0.1  0.08 0.08 0.11 0.11 0.1  0.11 0.11 0.08]\n",
      " [0.09 0.08 0.12 0.1  0.11 0.11 0.1  0.09 0.11 0.1 ]]\n"
     ]
    }
   ],
   "source": [
    "# Using the tqdm module to visualize run time is suggested\n",
    "from tqdm import tqdm\n",
    "import time\n",
    "\n",
    "# It would be a good idea to return the accuracy, along with the confusion \n",
    "# matrix, since both can be calculated in one iteration over test data, to \n",
    "# save time\n",
    "def Confusion(testData, testLabels, classifier):\n",
    "    '''\n",
    "    Your code here\n",
    "    '''\n",
    "    M = np.zeros((10,10))\n",
    "    #10000 array\n",
    "    predicted_values= classifier(testData)\n",
    "    for i in range(0, predicted_values.shape[0]):\n",
    "        M[testLabels[i],predicted_values[i]]+=1\n",
    "    \n",
    "    #now find the accuracy\n",
    "    accuracy = np.trace(M)/predicted_values.shape[0]\n",
    "    M= M/np.sum(M,axis=1)\n",
    "    return M, accuracy\n",
    "\n",
    "def VisualizeConfusion(M):\n",
    "    plt.figure(figsize=(14, 6))\n",
    "    plt.imshow(M)\n",
    "    plt.show()\n",
    "    print(np.round(M,2))\n",
    "    \n",
    "M, _ = Confusion(testData, testLabels, randomClassifier)\n",
    "VisualizeConfusion(M)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Part 3: K-Nearest Neighbors (KNN) [6 pts]\n",
    "\n",
    "* Here you will implement a simple knn classifier. The distance metric is Euclidean in pixel space. k refers to the number of neighbors involved in voting on the class, and should be 3. You are allowed to use sklearn.neighbors.KNeighborsClassifier.\n",
    "* Display the confusion matrix and accuracy for your KNN classifier trained on the entire training dataset. (should be ~97%)\n",
    "* After evaluating the classifier on the test set, based on the confusion matrix, mention the number that the number '4' is most often predicted to be, other than '4'. Write your comment below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "KNN classifier accuracy: 64.760000\n"
     ]
    }
   ],
   "source": [
    "from sklearn.neighbors import KNeighborsClassifier\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "class KNNClassifer():\n",
    "    def __init__(self, k=3):\n",
    "        # k is the number of neighbors involved in voting\n",
    "        self.knn_model = KNeighborsClassifier(k)\n",
    "        \n",
    "\n",
    "    def train(self, trainData, trainLabels):\n",
    "        '''\n",
    "        your code here\n",
    "        '''\n",
    "        trainData_reshape = trainData.reshape(trainData.shape[0], -1)\n",
    "        self.knn_model.fit(trainData_reshape, trainLabels)\n",
    "        \n",
    "    def __call__(self, x):\n",
    "        # this method should take a batch of images\n",
    "        # and return a batch of predictions\n",
    "        '''\n",
    "        your code here\n",
    "        '''\n",
    "        x_reshape = x.reshape(x.shape[0],-1)\n",
    "        return self.knn_model.predict(x_reshape)\n",
    "# test your classifier with only the first 100 training examples (use this\n",
    "# while debugging)\n",
    "# note you should get ~ 65 % accuracy\n",
    "knnClassiferX = KNNClassifer()\n",
    "knnClassiferX.train(trainData[:100], trainLabels[:100])\n",
    "print ('KNN classifier accuracy: %f'%test(testData, testLabels, knnClassiferX))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1008x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.92 0.01 0.   0.01 0.01 0.01 0.03 0.01 0.   0.  ]\n",
      " [0.   1.   0.   0.   0.   0.   0.   0.   0.   0.  ]\n",
      " [0.03 0.38 0.39 0.02 0.05 0.01 0.03 0.02 0.04 0.01]\n",
      " [0.04 0.06 0.02 0.8  0.01 0.   0.   0.01 0.03 0.01]\n",
      " [0.   0.07 0.   0.01 0.66 0.   0.02 0.01 0.   0.2 ]\n",
      " [0.07 0.06 0.01 0.35 0.07 0.19 0.05 0.03 0.03 0.06]\n",
      " [0.03 0.06 0.01 0.01 0.06 0.01 0.8  0.   0.   0.  ]\n",
      " [0.   0.1  0.01 0.02 0.05 0.   0.   0.69 0.01 0.12]\n",
      " [0.08 0.11 0.05 0.12 0.05 0.01 0.04 0.02 0.47 0.04]\n",
      " [0.02 0.03 0.01 0.06 0.35 0.   0.01 0.07 0.   0.47]]\n",
      "[[9.17346939e-01 5.28634361e-03 9.68992248e-04 1.18811881e-02\n",
      "  7.12830957e-03 1.23318386e-02 3.02713987e-02 9.72762646e-03\n",
      "  0.00000000e+00 4.95540139e-03]\n",
      " [0.00000000e+00 9.99118943e-01 0.00000000e+00 9.90099010e-04\n",
      "  0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
      "  0.00000000e+00 0.00000000e+00]\n",
      " [3.26530612e-02 3.77092511e-01 3.94379845e-01 1.78217822e-02\n",
      "  5.09164969e-02 6.72645740e-03 2.50521921e-02 2.33463035e-02\n",
      "  3.59342916e-02 7.92864222e-03]\n",
      " [4.28571429e-02 6.43171806e-02 1.84108527e-02 8.04950495e-01\n",
      "  5.09164969e-03 3.36322870e-03 2.08768267e-03 8.75486381e-03\n",
      "  3.18275154e-02 1.28840436e-02]\n",
      " [2.04081633e-03 6.87224670e-02 2.90697674e-03 5.94059406e-03\n",
      "  6.63951120e-01 1.12107623e-03 2.40083507e-02 1.16731518e-02\n",
      "  0.00000000e+00 2.03171457e-01]\n",
      " [7.14285714e-02 5.99118943e-02 1.06589147e-02 3.48514851e-01\n",
      "  6.61914460e-02 1.89461883e-01 4.59290188e-02 2.62645914e-02\n",
      "  3.08008214e-02 5.55004955e-02]\n",
      " [3.26530612e-02 6.34361233e-02 6.78294574e-03 6.93069307e-03\n",
      "  6.21181263e-02 6.72645740e-03 8.04801670e-01 9.72762646e-04\n",
      "  0.00000000e+00 9.91080278e-04]\n",
      " [1.02040816e-03 1.00440529e-01 7.75193798e-03 1.78217822e-02\n",
      "  5.49898167e-02 0.00000000e+00 1.04384134e-03 6.86770428e-01\n",
      "  9.24024641e-03 1.15956392e-01]\n",
      " [7.55102041e-02 1.05726872e-01 5.23255814e-02 1.16831683e-01\n",
      "  4.68431772e-02 5.60538117e-03 3.96659708e-02 2.04280156e-02\n",
      "  4.66119097e-01 4.36075322e-02]\n",
      " [1.53061224e-02 3.08370044e-02 1.25968992e-02 5.64356436e-02\n",
      "  3.46232179e-01 0.00000000e+00 6.26304802e-03 6.80933852e-02\n",
      "  2.05338809e-03 4.66798811e-01]]\n",
      "Linear classifier accuracy: 0.647600\n"
     ]
    }
   ],
   "source": [
    "M,accuracy = Confusion(testData, testLabels, knnClassiferX)\n",
    "VisualizeConfusion(M)\n",
    "print(M)\n",
    "print ('Linear classifier accuracy: %f'%accuracy)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The second maximum element 9\n"
     ]
    }
   ],
   "source": [
    "array_4 =M[4]\n",
    "print(\"The second maximum element\",array_4.argsort()[-2])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Comment:\n",
    "The second most number that 4 is predicted to be after 4 itself is 9. This is so because 9 resembles 4 the most after 4."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "KNN classifier accuracy: 97.050000\n"
     ]
    }
   ],
   "source": [
    "\n",
    "# test your classifier trained with all the training examples (This may take a while)\n",
    "knnClassifer = KNNClassifer()\n",
    "knnClassifer.train(trainData, trainLabels)\n",
    "print ('KNN classifier accuracy: %f'%test(testData, testLabels, knnClassifer))\n",
    "# display confusion matrix for your KNN classifier with all the training examples\n",
    "\n",
    "M,accuracy = Confusion(testData, testLabels, knnClassifer)\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1008x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.99 0.   0.   0.   0.   0.   0.   0.   0.   0.  ]\n",
      " [0.   1.   0.   0.   0.   0.   0.   0.   0.   0.  ]\n",
      " [0.01 0.01 0.97 0.   0.   0.   0.   0.01 0.   0.  ]\n",
      " [0.   0.   0.   0.97 0.   0.01 0.   0.01 0.   0.  ]\n",
      " [0.   0.01 0.   0.   0.97 0.   0.   0.   0.   0.02]\n",
      " [0.01 0.   0.   0.01 0.   0.96 0.01 0.   0.   0.  ]\n",
      " [0.01 0.   0.   0.   0.   0.   0.99 0.   0.   0.  ]\n",
      " [0.   0.02 0.   0.   0.   0.   0.   0.96 0.   0.01]\n",
      " [0.01 0.   0.   0.02 0.01 0.01 0.   0.   0.94 0.  ]\n",
      " [0.   0.   0.   0.01 0.01 0.   0.   0.01 0.   0.96]]\n",
      "Accuracy of the KNN is 0.9705\n"
     ]
    }
   ],
   "source": [
    "VisualizeConfusion(M)\n",
    "print(\"Accuracy of the KNN is\",accuracy)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The second maximum element 9\n"
     ]
    }
   ],
   "source": [
    "array_4 =M[4]\n",
    "print(\"The second maximum element\",array_4.argsort()[-2])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Comment:\n",
    "The second most number that 4 is predicted to be after 4 itself is 9. This is so because 9 resembles 4 the most after 4."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problem 2: Deep Learning [18 pts]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Part 1: Initial setup [0 pts]\n",
    "\n",
    "Follow the directions on https://pytorch.org/get-started/locally/ to install PyTorch on your computer.\n",
    "\n",
    "Note: You will not need GPU support for this assignment so don't worry if you don't have one. In any case, installing with GPU support is often more difficult to configure, so it is suggested that you install the CPU-only version regardless.\n",
    "\n",
    "To ensure that PyTorch was installed correctly, we will now verify the installation by running some sample PyTorch code. Here we construct a randomly initialized tensor."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([[0.6292, 0.7832, 0.7472],\n",
      "        [0.7347, 0.7767, 0.6589],\n",
      "        [0.0705, 0.1515, 0.4561],\n",
      "        [0.3218, 0.1807, 0.6005],\n",
      "        [0.7806, 0.9664, 0.8590]])\n"
     ]
    }
   ],
   "source": [
    "from __future__ import print_function\n",
    "import torch\n",
    "x = torch.rand(5, 3)\n",
    "print(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Part 2:  Training with PyTorch [3 pts]\n",
    "Below is some helper code to train your deep networks. \n",
    "Complete the train function for PTClassifier below. You should write down the training operations in this function. This function will be used in the following questions with different networks.\n",
    "You can look at https://pytorch.org/tutorials/beginner/pytorch_with_examples.html for reference."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch:1 Accuracy: 89.320000\n",
      "Epoch:2 Accuracy: 90.720000\n",
      "Epoch:3 Accuracy: 91.390000\n",
      "Epoch:4 Accuracy: 91.620000\n",
      "Epoch:5 Accuracy: 91.880000\n",
      "Epoch:6 Accuracy: 92.040000\n",
      "Epoch:7 Accuracy: 92.130000\n",
      "Epoch:8 Accuracy: 92.250000\n",
      "Epoch:9 Accuracy: 92.320000\n",
      "Epoch:10 Accuracy: 92.300000\n",
      "Linear classifier accuracy: 92.300000\n"
     ]
    }
   ],
   "source": [
    "# base class for your PyTorch networks. It implements the training loop\n",
    "# (__init__), (train) and prediction(__call__)  for you.\n",
    "# You will need to complete the (train) function to define the training operations\n",
    "# structures in the following problems.\n",
    "import torch.nn as nn\n",
    "from torch.nn.parameter import Parameter\n",
    "import torch.nn.functional as F\n",
    "import torch.nn.init\n",
    "import torch.optim as optim\n",
    "from torch.autograd import Variable\n",
    "from tqdm import tqdm\n",
    "from scipy.stats import truncnorm\n",
    "\n",
    "class PTClassifier():\n",
    "    def __init__(self, net):\n",
    "        #constructor SLP\n",
    "        self.net = net()\n",
    "    \n",
    "    def train(self, trainData, trainLabels, testData, testLabels, epochs=1, batchsize=50):\n",
    "        criterion = nn.CrossEntropyLoss()\n",
    "        learning_rate=3e-4\n",
    "        optimizer = optim.Adam(self.net.parameters(),lr=learning_rate)\n",
    "        #loss_fn = nn.MSELoss(reduction='sum')\n",
    "        #loss_fn = nn.MSELoss()\n",
    "        criterion = nn.CrossEntropyLoss()\n",
    "        for epoch in range(epochs):\n",
    "            for i, (data,label) in enumerate(DataBatch(trainData, trainLabels, batchsize, shuffle=True)):\n",
    "                inputs = Variable(torch.FloatTensor(data))\n",
    "                targets = Variable(torch.LongTensor(label))\n",
    "                \n",
    "                # YOUR CODE HERE\n",
    "                # Train the model using the optimizer and the batch data\n",
    "                y_prediction = self.net.forward(inputs)\n",
    "                \n",
    "                #y_prediction_max = torch.argmax(y_prediction,1)\n",
    "                #y_pred = Variable(torch.FloatTensor(y_prediction_max),requires_grad = True)\n",
    "                #y_pred = Variable(torch.Tensor(y_prediction_max),requires_grad = True)\n",
    "                \n",
    "            \n",
    "                loss = criterion(y_prediction,targets)\n",
    "                \n",
    "                #loss = (y_prediction_max - targets).pow(2).sum()\n",
    "                #loss = loss_fn(y_prediction,)\n",
    "                optimizer.zero_grad()\n",
    "\n",
    "                #backprop\n",
    "                loss.backward()\n",
    "                #parameter update\n",
    "                optimizer.step()\n",
    "                    \n",
    "                \n",
    "            print ('Epoch:%d Accuracy: %f'%(epoch+1, test(testData, testLabels, self)))\n",
    "    \n",
    "    def __call__(self, x):\n",
    "        inputs = Variable(torch.FloatTensor(x))\n",
    "        prediction = self.net(inputs)\n",
    "        return np.argmax(prediction.data.cpu().numpy(), 1)\n",
    "    \n",
    "    def get_first_layer_weights(self):\n",
    "        return self.net.weight1.data.cpu().numpy()\n",
    "    \n",
    "\n",
    "# helper function to get weight variable\n",
    "def weight_variable(shape):\n",
    "    initial = torch.Tensor(truncnorm.rvs(-1/0.01, 1/0.01, scale=0.01, size=shape))\n",
    "    return Parameter(initial, requires_grad=True)\n",
    "\n",
    "# helper function to get bias variable\n",
    "def bias_variable(shape):\n",
    "    initial = torch.Tensor(np.ones(shape)*0.1)\n",
    "    return Parameter(initial, requires_grad=True)\n",
    "    \n",
    "# Define Single Layer Perceptron network\n",
    "class SLP(nn.Module):\n",
    "    def __init__(self, in_features=28*28, classes=10):\n",
    "        super(SLP, self).__init__()\n",
    "        # model variables\n",
    "        self.weight1 = weight_variable((classes, in_features))\n",
    "        self.bias1 = bias_variable((classes))\n",
    "        \n",
    "    def forward(self, x):\n",
    "        # linear operation\n",
    "        y_pred = torch.addmm(self.bias1, x.view(list(x.size())[0], -1), self.weight1.t())\n",
    "        return y_pred\n",
    "        \n",
    "\n",
    "# test the example linear classifier (note you should get around 92% accuracy\n",
    "# for 10 epochs and batchsize 50)\n",
    "trainData=np.array(list(read('training','images')))\n",
    "trainData=np.float32(np.expand_dims(trainData,-1))/255\n",
    "trainData=trainData.transpose((0,3,1,2))\n",
    "trainLabels=np.int32(np.array(list(read('training','labels'))))\n",
    "\n",
    "testData=np.array(list(read('testing','images')))\n",
    "testData=np.float32(np.expand_dims(testData,-1))/255\n",
    "testData=testData.transpose((0,3,1,2))\n",
    "testLabels=np.int32(np.array(list(read('testing','labels'))))\n",
    "\n",
    "linearClassifier = PTClassifier(SLP)\n",
    "linearClassifier.train(trainData, trainLabels, testData, testLabels, epochs=10)\n",
    "print ('Linear classifier accuracy: %f'%test(testData, testLabels, linearClassifier))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Part 3: Single Layer Perceptron [3 pts]\n",
    "The simple linear classifier implemented in the cell already performs quite well. Plot the filter weights corresponding to each output class (weights, not biases) as images. (Normalize weights to lie between 0 and 1 and use color maps like 'inferno' or 'plasma' for good results). Comment on what the weights look like and why that may be so.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x1080 with 10 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Your code here.\n",
    "weights = linearClassifier.get_first_layer_weights();\n",
    "#normalise \n",
    "weights = (weights - np.min(weights))/(np.max(weights) - np.min(weights))\n",
    "#reshape 10*784 to 10*28*28\n",
    "#weights = weights.reshape(28, 28, -1)\n",
    "weights = weights.reshape(10,28,28)\n",
    "fig = plt.figure(figsize=(15,15))\n",
    "#plt.inferno()\n",
    "for i in range(weights.shape[0]):\n",
    "    weight = weights[i, :, :]\n",
    "    plt.subplot(5, 2, i+1)\n",
    "    plt.imshow(weight,cmap = 'inferno')\n",
    "plt.show()\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Comment\n",
    "The weights of the different classes show the activation for the different inputs. The input data is mapped to the output in the single layer perceptron through the weights activation. Hence the weights seem to resemble the class of images which it pertains to. eg: 0 represents 0, 1 represents 1\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Part 4: Multi Layer Perceptron (MLP) [7 pts]\n",
    "Here you will implement an MLP. The MLP shoud consist of 2 layers (matrix multiplication and bias offset) that map to the following feature dimensions:\n",
    "\n",
    "* 28x28 -> hidden (100)\n",
    "* hidden -> classes\n",
    "\n",
    "* The hidden layer should be followed with a ReLU nonlinearity. The final layer should not have a nonlinearity applied as we desire the raw logits output.\n",
    "* The final output of the computation graph should be stored in self.y as that will be used in the training.\n",
    "\n",
    "Display the confusion matrix and accuracy after training. Note: You should get around 97% accuracy for 10 epochs and batch size 50.\n",
    "\n",
    "Plot the filter weights corresponding to the mapping from the inputs to the first 10 hidden layer outputs (out of 100). Do the weights look similar to the weights plotted in the previous problem? Why or why not?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch:1 Accuracy: 91.570000\n",
      "Epoch:2 Accuracy: 92.870000\n",
      "Epoch:3 Accuracy: 93.720000\n",
      "Epoch:4 Accuracy: 94.780000\n",
      "Epoch:5 Accuracy: 95.480000\n",
      "Epoch:6 Accuracy: 96.020000\n",
      "Epoch:7 Accuracy: 96.420000\n",
      "Epoch:8 Accuracy: 96.590000\n",
      "Epoch:9 Accuracy: 96.720000\n",
      "Epoch:10 Accuracy: 96.860000\n",
      "Linear classifier accuracy: 96.860000\n"
     ]
    }
   ],
   "source": [
    "# Define Multi Layer Perceptron network\n",
    "class MLP(nn.Module):\n",
    "    def __init__(self, in_features=28*28, hidden=100, classes=10):\n",
    "        super(MLP, self).__init__()\n",
    "        '''\n",
    "        your code here\n",
    "        '''\n",
    "        self.weight1 = weight_variable((hidden, in_features))\n",
    "        self.bias1 = bias_variable((hidden))\n",
    "        self.weight2 = weight_variable((classes,hidden))\n",
    "        self.bias2 = bias_variable((classes))\n",
    "        \n",
    "        \n",
    "    def forward(self, x):\n",
    "        '''\n",
    "        your code here\n",
    "        '''\n",
    "        y_first = torch.addmm(self.bias1, x.view(list(x.size())[0], -1), self.weight1.t())\n",
    "        hidden = torch.nn.functional.relu(y_first)\n",
    "        test_sh = hidden.view(list(hidden.size())[0],-1)\n",
    "        y_pred = torch.addmm(self.bias2, hidden.view(list(hidden.size())[0], -1), self.weight2.t())\n",
    "        return y_pred\n",
    "        \n",
    "        \n",
    "\n",
    "mlpClassifier = PTClassifier(MLP)\n",
    "mlpClassifier.train(trainData, trainLabels, testData, testLabels, epochs=10)\n",
    "print ('Linear classifier accuracy: %f'%test(testData, testLabels, mlpClassifier))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1008x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.99 0.   0.   0.   0.   0.   0.   0.   0.   0.  ]\n",
      " [0.   0.99 0.   0.   0.   0.   0.   0.   0.   0.  ]\n",
      " [0.01 0.   0.96 0.01 0.   0.   0.01 0.01 0.01 0.  ]\n",
      " [0.   0.   0.   0.98 0.   0.   0.   0.01 0.   0.  ]\n",
      " [0.   0.   0.01 0.   0.95 0.   0.01 0.   0.   0.02]\n",
      " [0.   0.   0.   0.01 0.   0.96 0.01 0.   0.01 0.  ]\n",
      " [0.01 0.   0.   0.   0.   0.01 0.97 0.   0.   0.  ]\n",
      " [0.   0.01 0.01 0.01 0.   0.   0.   0.96 0.   0.01]\n",
      " [0.01 0.   0.   0.01 0.   0.   0.   0.   0.96 0.  ]\n",
      " [0.   0.01 0.   0.01 0.01 0.01 0.   0.   0.   0.96]]\n",
      "Linear classifier accuracy: 0.968600\n"
     ]
    }
   ],
   "source": [
    "# Confusion Matrix and Accuracy\n",
    "'''\n",
    "your code here\n",
    "'''\n",
    "M,accuracy = Confusion(testData, testLabels, mlpClassifier)\n",
    "VisualizeConfusion(M)\n",
    "print ('Linear classifier accuracy: %f'%accuracy)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(10, 784)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x1080 with 10 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot filter weights\n",
    "'''\n",
    "your code here\n",
    "'''\n",
    "weights = mlpClassifier.net.weight1.data.cpu().numpy()\n",
    "weights = (weights - np.min(weights))/(np.max(weights) - np.min(weights))\n",
    "weights = weights[:10]\n",
    "print(weights.shape)\n",
    "weights = weights.reshape(10,28,28)\n",
    "fig = plt.figure(figsize=(15,15))\n",
    "\n",
    "for i in range(weights.shape[0]):\n",
    "    weight = weights[i, :, :]\n",
    "    plt.subplot(5, 2, i+1)\n",
    "    plt.imshow(weight,cmap ='inferno')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Comment\n",
    "No the images dont resemble the class. This can be attributed to the reasons below:\n",
    "->There are 100 hidden nodes in the intermediate layer with the weight matrix being 100 * 784 for the first layer. However we are plotting only the first 10 weights which does not capture all the information\n",
    "-> The network contains two layers, matrix multiplication and bias. So a single layer would not encode all the information for classification."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Part 5: Convolutional Neural Network (CNN) [5 pts]\n",
    "Here you will implement a CNN with the following architecture:\n",
    "\n",
    "* n=5\n",
    "* ReLU( Conv(kernel_size=4x4, stride=2, output_features=n) )\n",
    "* ReLU( Conv(kernel_size=4x4, stride=2, output_features=n*2) )\n",
    "* ReLU( Conv(kernel_size=4x4, stride=2, output_features=n*4) )\n",
    "* Linear(output_features=classes)\n",
    "\n",
    "Display the confusion matrix and accuracy after training. You should get around 98% accuracy for 10 epochs and batch size 50."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch:1 Accuracy: 90.700000\n",
      "Epoch:2 Accuracy: 93.190000\n",
      "Epoch:3 Accuracy: 94.500000\n",
      "Epoch:4 Accuracy: 95.890000\n",
      "Epoch:5 Accuracy: 96.580000\n",
      "Epoch:6 Accuracy: 97.090000\n",
      "Epoch:7 Accuracy: 97.180000\n",
      "Epoch:8 Accuracy: 97.440000\n",
      "Epoch:9 Accuracy: 97.350000\n",
      "Epoch:10 Accuracy: 97.720000\n",
      "Linear classifier accuracy: 97.720000\n"
     ]
    }
   ],
   "source": [
    "def conv2d(x, W, stride):\n",
    "    # x: input\n",
    "    # W: weights (out, in, kH, kW)\n",
    "    return F.conv2d(x, W, stride=stride, padding=1)\n",
    "\n",
    "# Define Convolutional Neural Network\n",
    "class CNN(nn.Module):\n",
    "    def __init__(self, classes=10, n=5):\n",
    "        super(CNN, self).__init__()\n",
    "        '''\n",
    "        your code here\n",
    "        '''\n",
    "        self.weight1 = weight_variable([n,1,4,4])\n",
    "        #self.weight1 = weight_variable([1,n,4,4])\n",
    "        self.bias1 = bias_variable([n,1,1])\n",
    "        self.weight2 = weight_variable([2*n,n,4,4])\n",
    "        #self.weight2 = weight_variable([n,2*n,4,4])\n",
    "        self.bias2 = bias_variable([2*n,1,1])\n",
    "        self.weight3 = weight_variable([4*n,2*n,4,4])\n",
    "        #self.weight3 = weight_variable([2*n,4*n,4,4])\n",
    "        self.bias3 = bias_variable([4*n,1,1])\n",
    "        self.weight4 = weight_variable([ classes,4*n*3*3,])\n",
    "        self.bias4 = weight_variable([classes])\n",
    "        \n",
    "        \n",
    "    def forward(self, x):\n",
    "        '''\n",
    "        your code here\n",
    "        '''\n",
    "        #x = x.view(list(x.size())[0], -1)\n",
    "        x = x.reshape(x.shape[0],1,28,28)\n",
    "        #x = x.reshape(28,28,1,50)\n",
    "\n",
    "        x= F.relu(conv2d(x, self.weight1,2) + self.bias1)\n",
    "        x= F.relu(conv2d(x, self.weight2,2) + self.bias2)\n",
    "        x= F.relu(conv2d(x, self.weight3,2) + self.bias3)\n",
    "        y_pred = torch.addmm(self.bias4, x.view(list(x.size())[0], -1), self.weight4.t())\n",
    "        return y_pred\n",
    "\n",
    "cnnClassifer = PTClassifier(CNN)\n",
    "cnnClassifer.train(trainData, trainLabels, testData, testLabels, epochs=10)\n",
    "print ('Linear classifier accuracy: %f'%test(testData, testLabels, cnnClassifer))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<Figure size 1008x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.99 0.   0.   0.   0.   0.   0.   0.   0.   0.  ]\n",
      " [0.   0.99 0.   0.   0.   0.   0.   0.   0.   0.  ]\n",
      " [0.01 0.   0.98 0.   0.   0.   0.   0.   0.01 0.  ]\n",
      " [0.   0.   0.01 0.97 0.   0.01 0.   0.01 0.01 0.  ]\n",
      " [0.   0.   0.01 0.   0.98 0.   0.01 0.   0.   0.01]\n",
      " [0.   0.   0.   0.   0.   0.97 0.01 0.   0.01 0.  ]\n",
      " [0.01 0.   0.   0.   0.   0.01 0.98 0.   0.   0.  ]\n",
      " [0.   0.   0.01 0.   0.   0.   0.   0.98 0.   0.  ]\n",
      " [0.   0.   0.   0.   0.   0.   0.   0.   0.98 0.  ]\n",
      " [0.   0.   0.   0.01 0.01 0.01 0.   0.01 0.   0.95]]\n",
      "Linear classifier accuracy: 0.977200\n"
     ]
    }
   ],
   "source": [
    "# Confusion Matrix and Accuracy\n",
    "'''\n",
    "your code here\n",
    "'''\n",
    "M,accuracy = Confusion(testData, testLabels, cnnClassifer)\n",
    "VisualizeConfusion(M)\n",
    "print ('Linear classifier accuracy: %f'%accuracy)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Note that the MLP/ConvNet approaches lead to an accuracy a little higher than the K-NN approach. \n",
    "* In general, neural net approaches lead to a significant increase in accuracy, but in this case the problem is not too hard, so the increase in accuracy will not be very high.\n",
    "* However, this is still quite significant considering the fact that the ConvNets we've used are relatively simple while the accuracy achieved using K-NN is with a search over 60,000 training images for every test image.\n",
    "* You can look at the performance of various machine learning methods on this problem at http://yann.lecun.com/exdb/mnist/\n",
    "* You can learn more about PyTorch at https://pytorch.org/tutorials/index.html\n",
    "* You can find another image classifier training example at https://pytorch.org/tutorials/beginner/blitz/cifar10_tutorial.html#sphx-glr-beginner-blitz-cifar10-tutorial-py\n",
    "* You can play with a demo of neural network created by Daniel Smilkov and Shan Carter at https://playground.tensorflow.org/"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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