lec19.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%load_ext autoreload\n",
    "%autoreload 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 612x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "from numpy import random as rand\n",
    "from numpy import linalg as lin\n",
    "import random\n",
    "from cs771 import genSyntheticData as gsd\n",
    "from cs771 import plotData as pd\n",
    "from cs771 import utils\n",
    "from keras.datasets import mnist\n",
    "\n",
    "d = 2 \n",
    "n = 20\n",
    "r = 3\n",
    "\n",
    "mu1 = np.array( [0,5] )\n",
    "mu2 = np.array( [-5,-5] )\n",
    "mu3 = np.array( [5,-5] )\n",
    "\n",
    "tmp1 = gsd.genSphericalData( d, n, mu1, r )\n",
    "tmp2 = gsd.genSphericalData( d, n, mu2, r )\n",
    "tmp3 = gsd.genSphericalData( d, n, mu3, r )\n",
    "X = np.vstack( (tmp1, tmp2, tmp3) )\n",
    "\n",
    "# Perform soft assignments\n",
    "def getSoftAssignments( X, muVals ):\n",
    "    pi = np.exp( -utils.getAllPairsDistances( X, muVals )/2 )\n",
    "    rowSum = pi.sum( axis = 1 )\n",
    "    pi = pi / rowSum[:, np.newaxis]\n",
    "    return pi\n",
    "\n",
    "# Update every centroid to the weighted mean of all data points\n",
    "def updateCentroidsSoftly( X, pi, k, prevMuVals ):\n",
    "    muVals = np.zeros( (k, X.shape[1]) )\n",
    "    for i in range( k ):\n",
    "        z = pi[:, i]\n",
    "        amountData = sum(z)\n",
    "        # Recall that in soft clustering, only part of a data point may be assigned to a cluster\n",
    "        # Thus, amountData could be a fractional value as well\n",
    "        if amountData > 1:\n",
    "            muVals[i,:] = (X.T).dot(z)/amountData\n",
    "        # If some cluster is almost empty, return the old value of its centroid\n",
    "        else:\n",
    "            muVals[i,:] = prevMuVals[i,:]\n",
    "    return muVals\n",
    "\n",
    "# Execute the soft k-means (i.e. the EM) algorithm\n",
    "def doSoftkmeans( X, k, init, niter ):\n",
    "    muVals = init\n",
    "    # Perform the EM algorithm for niter steps\n",
    "    for t in range( niter ):\n",
    "        pi = getSoftAssignments( X, muVals ) # E Step\n",
    "        muVals = updateCentroidsSoftly( X, pi, k, muVals ) # M Step\n",
    "    return (muVals, pi)\n",
    "\n",
    "init = np.array( [[10,0], [10,-2], [11,2]] )\n",
    "# Even the soft k-means algorithm (EM algorithm) can get stuck if not initialized properly\n",
    "# Proper initialization is an absolute must for the EM algorithm as well\n",
    "# No matter how long we run EM, it does not get unstuck\n",
    "(muVals, pi) = doSoftkmeans( X, 3, init, 1000)\n",
    "\n",
    "fig = pd.getFigure( 8.5, 7 )\n",
    "pd.plot2D( X[pi[:,0] > 0.5 ], fig, color = 'r', marker = 'o' )\n",
    "pd.plot2D( X[pi[:,1] > 0.5 ], fig, color = 'g', marker = 'o' )\n",
    "pd.plot2D( X[pi[:,2] > 0.5 ], fig, color = 'b', marker = 'o' )\n",
    "pd.plot2D( muVals, fig, color = 'k', marker = 'x' )\n",
    "pd.plot2D( init, fig, color = 'y', marker = '+' )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x648 with 15 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Caution: when executing this line for the first time, sklearn will attempt to download\n",
    "# this dataset from an internet source -- make sure you have a working internet connection\n",
    "((XTrain, yTrain), (XTest, yTest)) = mnist.load_data()\n",
    "n = XTrain.shape[0]\n",
    "# What is the shape of these images?\n",
    "imShape = XTrain.shape[1:]\n",
    "\n",
    "# Normalize data coordinates otherwise numbers in later calculations explode\n",
    "XTrain = XTrain/256\n",
    "\n",
    "numRows = 3\n",
    "numCols = 5\n",
    "\n",
    "# Show the first 15 images in the dataset\n",
    "fig2, axs2 = pd.getFigList( numRows, numCols )\n",
    "labels = [\"Label is %s\" % yTrain[i] for i in range( numRows * numCols )]\n",
    "pd.showImagesNoAxes( axs2, XTrain[:numRows*numCols], numRows, numCols, labelList = labels )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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rp7KCBnmEEXeyAAAAAMAjmiwAAAAA8IgmCwAAAAA8oskCAAAAAI9CPfiif//+KrPWqqxly5YqS7QBF66PO5rjEJkff/zR6/U2b96sstzcXOexy5YtU9m3336rsuPHj6tsxowZgdYpU6aMyq666ipnPaVKlVLZTz/9pLLGjRs7z0fx8vPPP6vMNfTkrrvuUllBrzfGGJW5hhA89dRTKnv44YdV5vr398YbbwSup0ePHirr3bu381jEz913362y5cuXq+y1114LdL377rsvUBYJ1x5z7fei8Omnn6pswYIFKvvjH/8Yi3JQgE2bNqnMNTAlJydHZQW9D/Ctbt26MVnHxfVvyPW5CAPuZAEAAACARzRZAAAAAOARTRYAAAAAeESTBQAAAAAehWbwxZtvvqky18ODrgdM27VrVyQ1FSeuj9uVFfTb7KG5hj2IuD+vrofkXQ/tB+UafFHQQ/slS5ZU2RlnnKGy+vXrq8w1rKBRo0Yqcw2PKeg3vVevXl1lR44cUdnFF1/sPB/Fy6xZs1TmenA+kof769Wrp7K1a9cGyhYtWqSyXbt2qWz37t0qO/vss531/P3vf3fmKP5cg1BmzpwZh0oKFqvBFy6rV69WGYMvYufjjz9WWceOHVW2b98+laWkpBRJTcWJa+DHsWPHVBbWzwV3sgAAAADAI5osAAAAAPCIJgsAAAAAPKLJAgAAAACPQjP4wvXg/PHjx1XmerD59ttvL5KaYsH1AOCIESMCnXvDDTeobPTo0dGWlDT+9re/OfNatWqp7MMPP/S6ds2aNVXWvn1757ENGjRQWdOmTb3W45Kenu7Mf/jhB5VdcMEFRV0OPHj99ddV9oc//EFlp59+usoqVqyostdee825TqVKlVTWv39/la1YsUJlrmEYrqEwrmEDe/bscdZTo0YNlS1fvlxlderUcZ4PnOAa6uLai61bt1aZ699QWlqan8IQF/369VPZN998E4dKiqc5c+aozPUaH1bcyQIAAAAAj2iyAAAAAMAjmiwAAAAA8IgmCwAAAAA8Cs3gi6BKly6tsmrVqsWhksi4BlyIiDzxxBMqGzt2rMpcD24//PDDKitXrlwhqsPJHnvssXiXUCwsW7Ys8LG/+93virAS+DJp0iSVuV5bhgwZorK77rorqrVfeOEFld1zzz0qW7VqVaHXyM3NdebXXXedyhhykZzOOussZ+76d/DII4+o7M477yz02hs3blQZgy+Sl+u9Xph9/vnnKhswYECgc2vXrq0y1/v94oY7WQAAAADgEU0WAAAAAHhEkwUAAAAAHtFkAQAAAIBHNFkAAAAA4FHCTRds165dvEv4rzZt2qSygqbIvP766ypr3769yubNmxd9YUARue222+JdAgJwvbZ07NhRZa5Ja9Has2ePyj755JNA586aNUtll156aeC1q1evHvhYFC+uKZA9evRQ2Zdffqmy+vXrq+zee+91rnPZZZcVorr4e+edd1S2b98+lVWqVCkW5SACBU26LO5cUwRF3F9fXK/7VatWVdmcOXMCHVfccCcLAAAAADyiyQIAAAAAj2iyAAAAAMAjmiwAAAAA8Cg0gy+stYGyBQsWqOyvf/1rkdQUxDPPPKOyUaNGqWz//v3O87t27aqyqVOnRl8YAJzigQceiMk6rte72bNnBzqubt26KuvcubOfwhA6FSpUUNnf//73OFRSPH377bcqO378eBwqSU6u96k5OTmBzu3Zs6fKunfvHm1JhXbw4EGVuepxvQ8viGtwzZtvvqmyiy66KPA1ixPuZAEAAACARzRZAAAAAOARTRYAAAAAeESTBQAAAAAehWbwhTEmUJaRkaGyfv36qeyuu+5yruP6DdurV69W2bRp01S2efNmlX3zzTcqq1WrlspuueUWZz0F/fZ5IEy2b9+usquvvjoOlaA4+Nvf/qayCRMmqKxq1aoqe++994qkJiDeKlasqLJq1ao5j/3uu+8Kvc7jjz+usvT0dJWVKBGat4jF1pAhQ1S2ZcsWlWVnZwe63nXXXacy13thEZH27durzDVAYuzYsSpzDew4duyYytauXauysmXLOusZNGiQyjp27BioxrDiThYAAAAAeESTBQAAAAAe0WQBAAAAgEc0WQAAAADgUcI91fjzzz+r7MUXX1TZnDlznOefeeaZKtu2bVuh67nmmmtUdv3116ts5MiRhV4DKO5yc3PjXQLiYMeOHc588uTJKjvtNP09v3vuuUdl1atXj74woBg6//zzVTZ37lznsR06dFDZ999/H2idV199VWXjx49XGYMvonfDDTeobN68eSpzDYBwDcNYsWKFylJSUpxrf/DBB0FKdMrJyQm0TvPmzVXWo0cP5zW7d+9e6HrCijtZAAAAAOARTRYAAAAAeESTBQAAAAAe0WQBAAAAgEehearx6quvVtmVV16psjVr1gS6XkZGhjMP+uBoamqqyu644w6V/fWvfw10PSCRrVq1SmU9e/aMfSGIqZtuusmZuwZidOvWTWVpaWneawLC5KqrrnLmCxcuVFnbtm1VlpmZGWiddevWqaxFixaBzkVkXJ/XLVu2qCw9PV1lo0aNKpKaTnXOOeeozDXkYtKkSSpzDZBLVtzJAgAAAACPaLIAAAAAwCOaLAAAAADwiCYLAAAAADwKzeCL6tWrq8z1W7NdD+FF+6DgAw88oLK+ffuqrF69elGtAwCJpKDhJkOHDlVZu3btirgaIHE0adJEZc8884zK/vKXv6isTZs2KmvcuLGfwlAo5513nspcg38uuOAClbn+G4uIbN26VWUXX3yxyh599NFA6zRr1sy5DgrGnSwAAAAA8IgmCwAAAAA8oskCAAAAAI9osgAAAADAo9AMvnCpVq2aykaMGBEoAxCdW2+91ZnPnj07xpWguBo0aFBEOYDC69KlS6AM4dWjR49AGYoH7mQBAAAAgEc0WQAAAADgEU0WAAAAAHhEkwUAAAAAHtFkAQAAAIBHoZ4uCCB+evbsGVEOAACQLLiTBQAAAAAe0WQBAAAAgEc0WQAAAADgEU0WAAAAAHhEkwUAAAAAHtFkAQAAAIBHNFkAAAAA4BFNFgAAAAB4RJMFAAAAAB7RZAEAAACARzRZAAAAAOARTRYAAAAAeESTBQAAAAAe0WQBAAAAgEfGWhv8YGMyRWRH0ZWDBFfLWlsllguyZxEl9izChj2LsGHPImwC7dmImiwAAAAAwC/jxwUBAAAAwCOaLAAAAADwiCYLAAAAADyiyQIAAAAAj2iyAAAAAMAjmiwAAAAA8IgmCwAAAAA8oskCAAAAAI9osgAAAADAI5osAAAAAPCIJgsAAAAAPKLJcjDGLDfG3O37XGPMIGPMS9FVB2jsWYQNexZhw55FGLFv4yehmyxjzNfGmBvjXccJ1tqnrLWF2ugiIsaYesaYo8aY6T7rQvGRKHvWGFPZGDPfGHPIGLPDGNOlKOpD/LFnETbsWYRRouzbE5LhPW2JeBeAiLwoImvjXQQQwIsiclxEqorIFSKyxBiz2Vr7SXzLAgrEnkXYsGcRZgn/njah72QVxBhTyRjzpjEm0xizL//v1U85rI4xZo0xZr8xZqExpvJJ5zc1xnxojMkyxmw2xrQMuO6IEx27Maa0MWa6MWZv/nXWGmOq/sK5d4hIlogsi/wjRtiFac8aY8qKSCcRGWqtPWit/aeILBKRboX9+BE+7FmEDXsWYRSmfXvSuUnxnjYpmyzJ+7hfEZFaIlJTRI6IyAunHNNdRO4SkXNF5GcReV5ExBhznogsEZEnRKSyiDwiInONMVUirKGHiJwpIjVE5CwR6ZNfh2KMqSAiI0Xk4QjXQOII0569UERyrLXbTso2i8glEa6HcGPPImzYswijMO3bpHpPm5RNlrV2r7V2rrX2sLX2gIg8KSItTjlsmrX2Y2vtIREZKiKdjTEpItJVRJZaa5daa3Otte+KyDoRaR1hGT9J3kasa63Nsdaut9ZmF3DsKBF52Vr7TYRrIEGEbM+WE5H9p2T7RaR8hOshxNizCBv2LMIoZPtWJIne0yZlk2WMOcMYM8nkPSiaLSIrRaRi/oY74eT/+DtEpKSIpEredwp+n387NMsYkyUizUSkWoRlTBORt0VkljFmtzFmrDGmpKPWK0TkRhF5NsLrI4GEac+KyEERqXBKVkFEDkS4HkKMPYuwYc8ijMK0b5PtPW1SNlmSd4vyIhG5ylpbQUSa5+fmpGNqnPT3mpLXpe+RvI06zVpb8aQ/Za21oyMpwFr7k7U2zVrbQESuEZE2knc791QtRaS2iOw0xmRI3q3cTsaYDZGsh9AL057dJiIljDH1Tsp+JSI8jJ1c2LMIG/YswihM+7alJNF72mRoskrmP5B34k8JybudfkREsvIf/hvuOK+rMaaBMeYMyfvZ0TnW2hwRmS4ibY0xrYwxKfnXbOl4yPAXGWOuM8Zclv+dhmzJ2/A5jkPTRaSO5E0OukJEJkrez8+2imQ9hEqo92z+jyPME5GRxpiyxphrRaS95H2nC4mJPYuwYc8ijEK9byXJ3tMmQ5O1VPI234k/I0TkOREpI3ld/GoRectx3jQRmSIiGSJSWkT6iYjk/wxpexEZJCKZkvddgEcl8s/lOSIyR/I242ciskLyNvv/kf8zthkn/kjejwgctdZmRrgewiPUezbfvfn1/iAiM0Wkr2WscCJjzyJs2LMIo1Dv22R7T2ustfGuAQAAAAASRjLcyQIAAACAmKHJAgAAAACPaLIAAAAAwCOaLAAAAADwiCYLAAAAADwqEcnBqamptnbt2kVUChLd+vXr91hrq8RyTfYsosGeRdiwZxE27FmETdA9G1GTVbt2bVm3bl3hq0JSM8bsiPWa7FlEgz2LsGHPImzYswiboHuWHxcEAAAAAI9osgAAAADAI5osAAAAAPCIJgsAAAAAPKLJAgAAAACPaLIAAAAAwCOaLAAAAADwiCYLAAAAADyiyQIAAAAAj2iyAAAAAMAjmiwAAAAA8IgmCwAAAAA8oskCAAAAAI9osgAAAADAI5osAAAAAPCIJgsAAAAAPKLJAgAAAACPaLIAAAAAwCOaLAAAAADwqES8CwAAIBr/+Mc/VPbb3/5WZeedd57z/PT0dJU1btxYZVWqVClEdQCAZMSdLAAAAADwiCYLAAAAADyiyQIAAAAAj2iyAAAAAMAjBl8ASWzt2rUqu/LKK1VmjIlqnZEjR6psyJAhUV0T+CUpKSkqy8jIcB7brl07lbVt21Zl8+bNi74wJLQtW7ao7F//+pfK7r333liUIxUrVlTZhx9+qLL69evHohwgqXAnCwAAAAA8oskCAAAAAI9osgAAAADAI5osAAAAAPCIwRfFxM6dO51506ZNVfbOO++o7NJLL/VeExJfWlqaylxDLlxDBKJdJzMzU2WdOnVSWfPmzaNaG+GVlZWlMtfAgJUrV3pfu3Hjxt6vifDavn27yubPn6+yCRMmqOzrr79WWbTDhILav3+/yjp37qyyl19+WWWuIUgAguNOFgAAAAB4RJMFAAAAAB7RZAEAAACARzRZAAAAAOBR0g6+2LZtmzMvXbq0ymrWrFnU5UifPn2cealSpVRWvnz5oi4HIed60LpVq1Yqy8jIiEE1buPHj1dZvXr1VMbgi+S1ZcsWlf373/9W2e7du1UW7bCW4cOHq+ySSy5RWfv27aNaB8VLdna2M+/WrZvK1qxZU9TlFIlPPvlEZa7hMQy+wH/z6aefquypp55yHjtz5kyVvffeeypr0aJF9IUVE9zJAgAAAACPaLIAAAAAwCOaLAAAAADwiCYLAAAAADxKisEXrt/K3qNHD+exaWlpKnvooYe81rNq1SqVLVu2zHnswIEDVVarVi2v9SDx/PTTTyr78ssv41AJUHj79u1T2eHDh+NQSZ7evXur7LTT9Pcq27ZtG4tyEIGsrCyVPfjggypbvHix83zXXowF1/ArEZFKlSqpLJ6DjBBe33//vcoOHTqksgsuuEBlruEornNFRJ599lmV+R5y8cYbb6js97//vdc1IsGdLAAAAADwiCYLAAAAADyiyQIAAAAAj2iyAAAAAMCjpBh8MX36dJXddtttzmN9D7lwWbhwocpcgwpERDp16lTU5SABDR8+vMjXmDz/d5/nAAAgAElEQVR5sjNft26dyiZNmlTU5SBEHnjgAZWNHz++0Nez1qosJyen0NcriOsB8R07dnhfB/7NnTtXZVOnTo1DJZE5//zznfnDDz+ssl69ehV1OQi5n3/+WWV33nmnyr744guVuV7rXEMubr75Zufaf/zjH4OUGJV4DkZy4U4WAAAAAHhEkwUAAAAAHtFkAQAAAIBHNFkAAAAA4FFSDL748MMPVdatW7c4VJJn9+7dKnM9uA2c7B//+Icz/+1vf+t1nSFDhqhs5MiRgc/Pzs5WmWsIAXs+eRljVJaSklLo67n2V+fOnVXWrFkz5/kffPCByubNmxdoHddxd9xxh8pSU1Oda8O/7777TmWvvvpqTNYePHiwyi644AKVvfXWWyp74403VPb444871zl+/HghqkMyce2Rrl27quz9999X2dVXX62y5cuXB1p36NChzrx8+fKBzk8k3MkCAAAAAI9osgAAAADAI5osAAAAAPCIJgsAAAAAPKLJAgAAAACPEm66oGty39GjR1Xmmm4VK3PmzFFZ2bJlnceWLl26qMtByEUzlc0lkkmCLkEnx7kmtSG8du3apbKVK1c6j502bVqga1asWFFlril9jRo1UtmLL76osjJlyjjXyczMDFSPi2sy4f79+1XGdMHYad26tco2b94c6NyCXk8rV66ssnvvvVdlAwYMUJlr37Vv315lo0aNUlmdOnWc9Rw8eFBlromFc+fOdZ6PxHHkyBFn/uSTT6rMNcGyYcOGKps/f77KZs6cGaie2rVrBzquKLj+ncYTd7IAAAAAwCOaLAAAAADwiCYLAAAAADyiyQIAAAAAjxJu8MW5556rMtfD04cOHXKef+zYMZWVKlUq+sJO4npI8YorrnAe63roNRY1ovgZPny492u6/r0Edfz4cWe+Z8+eQl8T4eAaItC1a1eVffLJJ87zgw5r6datm8qeeeaZQOe6bN++3Zk/9dRThb4m4uvf//63yr766qtCX6+gB+e///77Ql8z6DqRPLSflZWlMtfAFSQW19fdu+66y3nsrFmzVHbRRRepbPz48Sqz1qps2LBhKqtZs6bKypUr56wnFtq2bRu3tV24kwUAAAAAHtFkAQAAAIBHNFkAAAAA4BFNFgAAAAB4lHCDL1x+//vfq2zcuHHOYzMzM1X25z//WWUXXHBB9IWdpKAHdW+88UaVDRo0SGU33XST13pQ/DRu3NiZb9y4sdDXTE9PL/S5rodlRRgikAxWrlypss8//zwOlUSmoEEvvXv3VtmkSZMKvY5rSM306dMLfT0UzPX1OTs7u9DXu/fee6MpJ2b+93//N1CGxPLOO++ozDXgoiBXXnmlynbt2qWyBQsWqOzAgQMqa9Kkicpcw+YisWnTJpW5hhY1a9ZMZdWqVYtqbd+4kwUAAAAAHtFkAQAAAIBHNFkAAAAA4BFNFgAAAAB4lBSDLx5//HGV/ec//3EeO3v27EBZ586dVVa6dGmVffnll0FKLPA3tbdr105lDLlIThMnTnTmKSkpgc53/Sb0Ro0aFbqeaIZmIDwOHTqkss8++0xlOTk5KrPWOq958cUXq8z1QHesHmLOzc1VWdCPx/Wx/OUvf/FTGIrU4MGDVTZgwIA4VAIEc+utt6qsZ8+ezmOnTJmismnTpgXKgtq6davK+vbtG/j85cuXq+yLL75Q2U8//aSyxYsXq6xNmzaB144F7mQBAAAAgEc0WQAAAADgEU0WAAAAAHhEkwUAAAAAHiXF4ItKlSqp7I033nAe+/rrr6tszpw5Ktu2bVugtbOysgIdt2jRImfuesgRia9169YqK2iIgOsB/QsvvFBl8+bNi76wQtbjcsstt6js/vvvj6om+Dds2DCVTZ48WWWuASwF7YXevXurLBZDLnbv3u3Mg348riEXM2bMUFmsBnYkmzFjxqhs4cKFgc6tWrWqyq666iqVlSlTJvLC4uCPf/yjyv71r3+p7JVXXgl0vYJez1G8uF6XChqKddttt6ls3bp1Ktu1a5fKgu6b007T92qWLl0a6NyCNGvWTGUNGjRQWb169aJaJxa4kwUAAAAAHtFkAQAAAIBHNFkAAAAA4BFNFgAAAAB4lBSDL1xcDw+KiHTp0iVQFpTrN2l3795dZVdeeaXz/BIlkvY/UdJYsWKFyj7//HOVGWOc57v2ckHHFpZr+MvevXsD1+MSyW+FR/xs3LjR+zX37Nmjsp9++kllJUuW9L52NKZMmaKyyy+/PPaFJCnX61rQ17p27dqprE2bNlHXVJxE8/nx/TUDsVOqVCln3r59+0BZWlpaoHXuu+8+lb3wwguBzo2Vt99+W2WtWrWKQyV5uJMFAAAAAB7RZAEAAACARzRZAAAAAOARTRYAAAAAeMRUhSL25ZdfxrsEFHNbtmxR2TfffBOHSvIcOnRIZW+++abKsrOzA19z8uTJKmvbtm1khSEufvvb36rsgw8+iOqarvP379+vstTU1EDX+/rrr1W2ePFilbkGbhTEtT/XrVunskaNGgW+JgDE0/fff6+yP//5zypzDWMrbkMuXOrUqRPvEv4P7mQBAAAAgEc0WQAAAADgEU0WAAAAAHhEkwUAAAAAHtFkAQAAAIBHTBf06NixYypbtGiRyi677DKVVahQoUhqQnJq165doc999NFHVTZjxoxoypFq1apFdT7iJz09vdDnNmnSxJm/8sorKgs6SdDls88+U1n//v0LfT0Rkd69e6usVatWUV0Twbmmrk6YMCEOlcSX632FiMj48eNV9tprrwW6ZuvWrVV23333RVYYQmnlypUqc+2xTp06xaIc7+rWrRvvEv4P7mQBAAAAgEc0WQAAAADgEU0WAAAAAHhEkwUAAAAAHjH4wqN9+/apbOPGjSobOHCgysqUKVMkNSE53XPPPYGOGzZsmMomTpyospSUlMBrt23bVmWNGjUKfD6KF9d/u+3btwc6d82aNc589OjRKnPtm8WLF6vMtT+ttSozxgQpUUREHnjgAZUx5CK+Lr/8cpX17dtXZa6vp4nENeBCRGTAgAGFvubpp5+uMt6DJJ6DBw+qzDU8pnr16irr2bNnUZSUdLiTBQAAAAAe0WQBAAAAgEc0WQAAAADgEU0WAAAAAHjE4AuPlixZEui4sP4mbRQN10P7OTk5gY4r6NgVK1ao7Omnn1ZZ0CECrjW6dOnirGf69OnOHOFUrVo1lQUdhOLaNyIikydPDpS5uNZ2reM6LjU11XnNjh07BlobKErPP/+8yoYOHRrVNStUqKCy++67L6prIhzS09NV9v7776vM9T7g7LPPLpKakg13sgAAAADAI5osAAAAAPCIJgsAAAAAPKLJAgAAAACPGHzh0fr16wMd16hRoyKuBGFijFFZ0If7Czq2d+/egdaOZohAWlpaoDUQbhs3box3Cf9VuXLlVHbeeeepbMqUKc7zr7rqKt8loZh54403VPbBBx+o7LXXXnOeX6NGjUKvvWXLFpW5hk/s3r1bZceOHXNes3Tp0iorX768yl5//XWVtWzZ0nlNhNPHH3/szJ977jmV3XbbbSrr0aOH95qQhztZAAAAAOARTRYAAAAAeESTBQAAAAAe0WQBAAAAgEcMviikzZs3q2zChAkqa9asWSzKQYhVrFhRZWeccYbKDhw4EIty5MILL1RZnz59VFazZs1YlIM4cz04f/vtt6vMNUSgKLRt21ZlrVq1UlnQ4S8Ij7p166rsnHPOUVlGRobK9u/fHygrisFU1lqVuQYeuVSoUMGZP/HEEyq7//77IysMCWHixInOvGrVqip7+OGHVeYaogI/uJMFAAAAAB7RZAEAAACARzRZAAAAAOARTRYAAAAAeMTgi0Lat2+fylwPsjZu3DgW5SDEunXrprLDhw+rrG/fvrEoRz7//POYrINwqFKlispeeeUVlbmGYaxZsybwOpMnT1ZZtWrVVOYaTJCamhp4HYRXx44dVTZ16lSVLVq0KBblxIRrwIUIQy6S1e7du1Xm+jcgItKrVy+VMYwttriTBQAAAAAe0WQBAAAAgEc0WQAAAADgEU0WAAAAAHjE4ItCWrp0qcpcD1+PHDkyFuUgwfTu3VtlmZmZzmPT0tJUdu6556osPT09+sIAEalVq5bKVq9eHYdKkOxGjx6tshUrVqhs//79sSgnMNfAoz59+qisSZMmsSgHITFhwgSV3Xrrrc5jH3vssaIuB/8Fd7IAAAAAwCOaLAAAAADwiCYLAAAAADyiyQIAAAAAj2iyAAAAAMAjpgt6dOGFF6qsfPnycagEiWjIkCER5QCQ6C6++GKV7du3Lw6VAH7t3btXZa4pwbNmzXKef/bZZ3uvCZHhThYAAAAAeESTBQAAAAAe0WQBAAAAgEc0WQAAAADgEYMvCmns2LHxLgEAAAAJqFevXipzDbq67rrrYlEOCoE7WQAAAADgEU0WAAAAAHhEkwUAAAAAHtFkAQAAAIBHDL4AAAAAipF58+bFuwREiTtZAAAAAOARTRYAAAAAeESTBQAAAAAe0WQBAAAAgEfGWhv8YGMyRWRH0ZWDBFfLWlsllguyZxEl9izChj2LsGHPImwC7dmImiwAAAAAwC/jxwUBAAAAwCOaLAAAAADwiCYLAAAAADyiyQIAAAAAj2iyAAAAAMAjmiwAAAAA8IgmCwAAAAA8oskCAAAAAI9osgAAAADAI5osAAAAAPCIJgsAAAAAPKLJcjDGLDfG3O37XGPMIGPMS9FVB2jsWYQNexZhw55FGLFv4yehmyxjzNfGmBvjXccJ1tqnrLURb3RjTGVjzHxjzCFjzA5jTJeiqA/xlyh79gRjTD1jzFFjzHSfdaH4YM8ibNizCKNE2bfJ9J62RLwLQCAvishxEakqIleIyBJjzGZr7SfxLQv4r14UkbXxLgKIAHsWYcOeRZgkzXvahL6TVRBjTCVjzJvGmExjzL78v1c/5bA6xpg1xpj9xpiFxpjKJ53f1BjzoTEmyxiz2RjTMuC6I058p8kYU9oYM90Yszf/OmuNMVUd55QVkU4iMtRae9Ba+08RWSQi3Qr78SN8wrRnTzr3DhHJEpFlkX/ECDv2LMKGPYswCtO+Tbb3tEnZZEnex/2KiNQSkZoickREXjjlmO4icpeInCsiP4vI8yIixpjzRGSJiDwhIpVF5BERmWuMqRJhDT1E5EwRqSEiZ4lIn/w6TnWhiORYa7edlG0WkUsiXA/hFqY9K8aYCiIyUkQejnANJA72LMKGPYswCtO+Tar3tEnZZFlr91pr51prD1trD4jIkyLS4pTDpllrP7bWHhKRoSLS2RiTIiJdRWSptXaptTbXWvuuiKwTkdYRlvGT5G3EutbaHGvtemtttuO4ciKy/5Rsv4iUj3A9hFjI9qyIyCgRedla+02EayBBsGcRNuxZhFHI9m1SvadNymeyjDFniMizInKLiFTKj8sbY1KstTn5//vkF60dIlJSRFIl7zsFvzfGtD3p/y8pIu9HWMY0yev4ZxljKorIdBEZbK396ZTjDopIhVOyCiJyIML1EGJh2rPGmCtE5EYR+XWE10cCYc8ibNizCKMw7VtJsve0SdlkSd6t9YtE5CprbUb+i9VGETEnHVPjpL/XlLwufY/kbdRp1tpe0RSQv/HSRCTNGFNbRJaKyFYRefmUQ7eJSAljTD1r7fb87FciknAPCOIXhWnPthSR2iKy0xgjkvedqxRjTANrbcNoakCosGcRNuxZhFGY9m1SvadNhh8XLJn/QN6JPyUk77bkERHJyn/4b7jjvK7GmAb53yEYKSJz8r8jMF1E2hpjWhljUvKv2dLxkOEvMsZcZ4y5LP92bbbkbficU4/Lv7U7T0RGGmPKGmOuFZH2kvddAySmUO9ZEUkXkTqSNzXoChGZKHk/890qkvUQKuxZhA17FmEU6n2bbO9pk6HJWip5m+/EnxEi8pyIlJG8Ln61iLzlOG+aiEwRkQwRKS0i/URE8n/2ub2IDBKRTMn7LsCjEvnn8hwRmSN5m/EzEVkheZvd5d78en8QkZki0jcRR13i/wn1ns3/ufCME38k78cDjlprMyNcD+HBnkXYsGcRRqHet/mS5j2tsdbGuwYAAAAASBjJcCcLAAAAAGKGJgsAAAAAPKLJAgAAAACPaLIAAAAAwKOIfk9WamqqrV27dhGVgkS3fv36PdbaKrFckz2LaLBnETbsWYQNexZhE3TPRtRk1a5dW9atW1f4qpDUjDE7Yr0mexbRYM8ibNizCBv2LMIm6J7lxwUBAAAAwCOaLAAAAADwiCYLAAAAADyiyQIAAAAAj2iyAAAAAMAjmiwAAAAA8IgmCwAAAAA8oskCAAAAAI9osgAAAADAI5osAAAAAPCIJgsAAAAAPKLJAgAAAACPaLIAAAAAwCOaLAAAAADwiCYLAAAAADyiyQIAAAAAj2iyAAAAAMAjmiwAAAAA8IgmCwAAAAA8oskCAAAAAI9osgAAAADAI5osAAAAAPCIJgsAAAAAPKLJAgAAAACPSsS7gOJm9erVKtu4caPKxo0bp7Ivv/xSZcuXL1dZixYtClccECejRo1S2bBhw5zHXnrppSobNGiQyu68887oC0OxsXbtWpU1adIkDpX4MWfOHJW5XrurVKkSi3IAIGYyMzNV1qtXL5UtWrQo8DVHjhypsiFDhkRWWMhwJwsAAAAAPKLJAgAAAACPaLIAAAAAwCOaLAAAAADwKCkGX/z4448qu//++53HLlu2TGWuBwBdjDEq69ixo8qqV68e6HoFeeKJJ1R27bXXqqxy5cpRrYPYcA2FuP3221X2q1/9KhblyLFjx1Q2ZsyYwOd//PHHKps0aZLKGHwRXm+//bbKunTporKzzz7bef6WLVtUVrJkyegLK6RZs2aprEePHipr3769ymbPnl0kNQGRevrpp1X25JNPquymm25S2euvv14kNaH4mzBhgspcr/FLlixRWUpKSuB10tLSVHbWWWeprG/fvoGvWdxxJwsAAAAAPKLJAgAAAACPaLIAAAAAwCOaLAAAAADwKCkGX7z33nsqcz3oXBRcQzf27dsX1TVdD1936NBBZTNmzFBZ6dKlo1obwbn+O7t+O7rrodOXX35ZZd9++61znVgMDDh06FCRr4Hi6a233lJZt27dVOZ6rXNlIiLW2ugL86hUqVIqO+00/T3Id999V2Xdu3dX2dSpU/0UhqSXm5vrzF37bubMmSpzDZ8ZPHhw9IWh2Pvwww9V9oc//EFlGRkZKjtw4IDKIhlyEdSAAQNUdvToUZW5htXFc1hSUNzJAgAAAACPaLIAAAAAwCOaLAAAAADwiCYLAAAAADxKuMEXq1atUlmvXr3iUElszZ8/X2V//etfVfbYY4/FohyIyNatW1XWs2fPQl+vuA0LQOJxDTgZNmyYyvbs2aMy16CIvn37OtcpUaJ4felxDQ6qVq2ayr766iuVrV69WmWuh8bLly9fyOqQzDZs2ODMXYOtXEaMGKGyyy+/PJqSUMysWLHCmd9xxx0qc712x5Pra45rGIbLQw895Lsc77iTBQAAAAAe0WQBAAAAgEc0WQAAAADgEU0WAAAAAHhUvJ4+jlB2drbKWrdurbL9+/fHohynNm3aqGzfvn0qc/1m7miNHj1aZffdd5/KypUr531tAOFz//33q2zt2rWBzu3Ro4fKXnjhhahrKu62b9+usrlz56osmqE3KJ7S09NV5hq+9Ze//EVlqampKjt48KDKunXrFrge1x67/fbbA5+PcHINPhMpfkMuouH6t8bgCwAAAABIMjRZAAAAAOARTRYAAAAAeESTBQAAAAAehXrwxd69e1UWqyEXp59+usr69++vsqeeekplP/74o8ref/995zq9evVSWVZWVpASnZ+L3NzcQOcCSGwbNmxQ2Ztvvhno3MqVK6vMNTQDSBSbNm1S2cMPP6yyEiX026qRI0cGWqNLly4q+/zzz53HuoZcPPfccyo788wzA62NcBg1apTKnn/+ee/rWGtVlpOTE7d1XENhPv30U5U1aNDAT2GecCcLAAAAADyiyQIAAAAAj2iyAAAAAMAjmiwAAAAA8IgmCwAAAAA8CvV0waFDh8Zt7YEDB6psxIgRgc51Tebq1KmT89hzzz1XZStXrlTZlClTVLZ161aVLViwQGXdu3d3ro3i5e2333bmbdu2jXElCJv169er7IYbblBZ0OmsEydOVFnDhg0jL6wY+81vfqOyr776KtC5jz/+uMpc0+BQ/BQ0vdc1uc818eyWW25RWY0aNVS2fft2lX3wwQcqq1ixorOeZ599VmVMEkx8w4cPV1lKSor3dVwT/uK5TkZGhspeeukllT3zzDN+CvOEO1kAAAAA4BFNFgAAAAB4RJMFAAAAAB7RZAEAAACAR6EZfLFq1SqVzZkzx/s6ruEVDz74oMrOOOMM72u7XH311YGyf/7znypzDb645557VHbhhReqrGnTpkFLRAFc/02i8fTTTzvz6667TmXlypVT2fz581W2c+dOlS1cuLAQ1aE4W7ZsmcqCDrn49a9/rbI2bdpEXVNx5xrusWXLFpVt2rRJZbm5uUVSE4peQQOsXn31VZWlpqaqbOTIkYHWuf7661XmGroxevRo5/kFDcRA4ti1a5f3a7r2zfHjx1V24MCBQNcrUUK3Ef369XMe63r/uWLFCpX17t070Nquf5MdOnRQmWuIUaxwJwsAAAAAPKLJAgAAAACPaLIAAAAAwCOaLAAAAADwKDSDL8aOHasy18N6LhUqVFBZw4YNncfeddddgc4PK9fnzPW5nTdvXizKSWiLFy/2ej3XA6IiIvXq1VOZ6zem7927V2VHjx6NvrAAhgwZEpN14Pbss88GOq5KlSoqcz14X6ZMmahrKu5cH2OpUqUCnet6nf36669VVrt27UjLgkfp6ekqGz9+vPNY15CLRx55RGVNmjRR2aJFi1T27bffquy2225T2aOPPuqsB4ll8+bNKuvatWtU13QNuZg0aZLKMjMzVda3b99Aa7iGXIwZMybQuSIi27ZtC3zsqbKzs1V2+PDhQl+vKHAnCwAAAAA8oskCAAAAAI9osgAAAADAI5osAAAAAPAoNIMvvvzyy0Kf27x5c5W5HkQNs9tvv11lS5YsCXRuNJ9b5Fm5cqXKNmzYEJO1MzIyYrJONBJpeEwYBd0jTZs2VdnNN9/su5y4Kejz8N133wU6/9ChQ4GOy8rKUlmrVq1UtnXr1kDXQ/Tmzp2rsuHDh6ssNzfXef7VV1+tMmutygYNGqSy559/PkiJMmzYMJWddpr7e+GbNm1S2aeffqqyLl26BFobsbNr1y6VuYZcfP7551Gt8+KLL6qsY8eOgc6tVauWyowxKvvNb34TeWGetG3bVmWNGjWKQyUF404WAAAAAHhEkwUAAAAAHtFkAQAAAIBHNFkAAAAA4FFoBl+4HkZ1PXTqEvS4MHM9NPnJJ5+obPTo0SpLhs9PUatfv77KmjVrprK33norFuXEleu3zLsGAaD4cQ1rGThwoMruv/9+72tv3LhRZTNnzvS6hus1UURky5YtXtdx+eGHH4p8DRRs9uzZKotkaNDixYsDZdFwDRG46qqrnMe69vJjjz3mtR4UDdegrIJem07ler+Wk5PjPDaaIRC33HJLoc+NVkEfz6kWLFigsnvuuUdl8fxYuJMFAAAAAB7RZAEAAACARzRZAAAAAOARTRYAAAAAeBSawReu33ru+u3TLnfeeafvckLB9fkJmiEyVapUUdm0adNUNmvWLJWNGTOmSGo6leuBUFfdAwYMUNmBAwcCr1OhQgWVTZw4UWU333xz4GsiOh06dFDZ/PnzVbZr1y6VufZnrPZsWJUvX15ly5Yti0MlOGHcuHEqa926deDzv/76a5VNnjxZZa5/Q+ecc47KXMOSIvla7HqYv1WrVoHPR2zMmTNHZa7BQSkpKYGu5xoKUdC5kyZNUtnYsWMDrRNPQT8XLsXt/Sx3sgAAAADAI5osAAAAAPCIJgsAAAAAPKLJAgAAAACPQjP4IhquYQNdunSJQyVFJzc3V2VHjx6NQyU4ITU1VWWuB15dWTx99tlnKnv++ecDn79z506VnX/++VHVhOjMmzdPZa6BQK7XykTSvHlzZ96iRYtA5//9739XmWvQQZs2bVTWsGHDQGugaNSoUUNlPXr0CHz+Rx99pLLnnntOZRUrVlSZa+hJgwYNAq+NcFixYoXKevfurbLs7OxCr3HeeeepLCMjw3ns+PHjA11z+PDhKitbtmxkhZ0kKyvLmWdmZqqsV69ega5ZooRuV/r166ey3/zmN4GuFyvcyQIAAAAAj2iyAAAAAMAjmiwAAAAA8IgmCwAAAAA8oskCAAAAAI+SYrrg9u3bVfbFF184j61Tp05Rl1Mkvv32W5W5Jh8B/80NN9ygskimCyIcpk6dqrL09HSVTZgwQWVfffVVVGtfe+21KqtZs6bK1q9fr7K777670OuefvrpzrxUqVKBzn/nnXdU5pouePPNN0dWGIoNa60zd03oPHjwoMrGjh2rMiYJJofDhw+rLJpJgm3btlXZE088obKXXnop8DV//vlnlbkmAtevXz/wNU81bdo0Z96/f3+V5eTkqCwlJUVlrkmCY8aMKUR1scWdLAAAAADwiCYLAAAAADyiyQIAAAAAj2iyAAAAAMCj0Ay+uOSSS1T20UcfBTp369atKmvTpo3z2MWLF6usbt26gdaJp8GDBxf63EsvvdRjJQi7f/7zn/EuATFQsmTJQNmAAQNiUY5T8+bN47a26+vLjh074lAJYsk14EJEZMSIESq7+uqrVfbQQw/5LglJwDXkwjWIKDU1VWXPPPNMkdQUhGvwj6vuSPTp00dlw4cPj+qa8cKdLAAAAADwiCYLAAAAADyiyQIAAAAAj2iyAAAAAMCj0Ay+eOGFF1R27Ngxlc2fPz/Q9VzDMETcDx/ecccdKhs4cKDKSpUqFcXL1M8AAASMSURBVGjtaL311lsqe/fddwOd26lTJ5WNHz8+6pqQOFz/roBkc9lll6msVq1aKsvIyIhFOSgCR44cUdmMGTOcx1asWFFl8Rw4gHDIyckJdJzrtcU15CJWMjMzVdarVy+VLVq0KKp1cnNzozq/uONOFgAAAAB4RJMFAAAAAB7RZAEAAACARzRZAAAAAOBRaAZfVK5cWWWuB1Q7duyoMtegiIK4BmKkpaWp7IsvvlDZvffeq7KmTZsGXttl+fLlKnMN4sjOzg50vZdfflllFSpUiLguJIYffvhBZbNnz45DJUDxd/bZZ6usSZMmKrvxxhtjUQ6iNG7cOJUVNDyrW7duKov26zsSX0pKSqDjVqxYobIHH3xQZc8991zUNQXhGnKxZMkSlbk+vubNmzuv2aFDh+gLCxnuZAEAAACARzRZAAAAAOARTRYAAAAAeESTBQAAAAAehWbwhUvp0qVV5npo9c4771TZggULolp7+vTpKpszZ47KSpYsqbLTTgve2x49elRlx44dU1mNGjVU9tFHH6msfPnygddG4jt+/LjKMjIy4lAJUPylp6er7Oeff1ZZ9erVY1EOojR37lyVud5XiLiHEAAnK1u2rMpcg8Vcg8pc79dc2dKlS1VmjAlaYmDbt29XWdWqVVVWv359lb3++uvOa6ampkZfWMhwJwsAAAAAPKLJAgAAAACPaLIAAAAAwCOaLAAAAADwKNSDL1xKlSqlspdeekll/fv3d56/aNEilc2ePVtlO3fuVJlrSMWRI0dUFu1Diq4HKdPS0gIdB5zMNYSlTJkyKnPt44I0adJEZQMHDoysMKAYOuecc+JdAjz65ptvVNanTx/nsQ0bNizqchByzZs3V5lrWM6SJUtUNm3atEBr/Oc//1FZSkpKoHOjNXjwYJXdf//9MVk7rLiTBQAAAAAe0WQBAAAAgEc0WQAAAADgEU0WAAAAAHiUcIMvXCpXrqyyZs2aOY915b169VLZsmXLVDZr1iyVrVixIkiJBbrllltU9qc//Ullt956a1TrIDmde+65KluwYIHKWrVqFfiaffv2VZlrHwNArLiG9+Tm5qrMNcAKKKxOnTqp7PLLL1dZ0MEXRcE1OM016KVBgwaxKCehcCcLAAAAADyiyQIAAAAAj2iyAAAAAMAjmiwAAADg/2vnjm0chIIoikIPbGwR0Aq1UC09bOwQERF8F4C1YuUHCHNOOLLkCSbwFRYQJLIAAACCbvF2wU91XbdpNgzDEevArvq+X81KKSdsApAxz/Nq1rbtajZN0xHrcGPvfj8uy3LCJuzNkywAAIAgkQUAABAksgAAAIJEFgAAQJAXXwAAX61pmtVsHMcTNgHuwpMsAACAIJEFAAAQJLIAAACCRBYAAECQyAIAAAgSWQAAAEEiCwAAIEhkAQAABIksAACAoLqUsv3Ddf2squp3v3X4co9Sys+RX+hm+ZCb5WrcLFfjZrmaTTf7r8gCAADgb/4uCAAAECSyAAAAgkQWAABAkMgCAAAIElkAAABBIgsAACBIZAEAAASJLAAAgCCRBQAAEPQCEO5+qNedJdkAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 1080x648 with 15 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def getDataSubset( labels ):\n",
    "    subset = np.in1d( yTrain, labels )\n",
    "    return (XTrain[subset][:][:], yTrain[subset])\n",
    "\n",
    "# Create a mini-dataset out of just the zeros and the fours\n",
    "labels = np.array( [0,4] )\n",
    "(X,y) = getDataSubset( labels )\n",
    "\n",
    "# Flatten images for sake of convenience even though it is time consuming and not essential at all\n",
    "n = X.shape[0]\n",
    "d = np.prod( X.shape[1:] )\n",
    "X = X.reshape( n, d )\n",
    "\n",
    "# Display the first few images of this subset dataset\n",
    "fig3, axs3 = pd.getFigList( numRows, numCols )\n",
    "labels = [\"Label is %s\" % y[i] for i in range( numRows * numCols )]\n",
    "pd.showImagesNoAxes( axs3, X[:numRows*numCols], numRows, numCols, resize = True, imShape = imShape, labelList = labels )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 216x216 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x648 with 15 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def fitSingleStandardGaussian( X ):\n",
    "    return np.mean( X, axis = 0 )\n",
    "\n",
    "def truncatePixels( X, low = 0, high = 1 ):\n",
    "    X[X < low] = low\n",
    "    X[X > high] = high\n",
    "    return X\n",
    "\n",
    "# Fit a standard Gaussian to the 0,4 dataset using an MLE\n",
    "mu = fitSingleStandardGaussian( X )\n",
    "fig4, axs4 = pd.getFigList( 1, 1 )\n",
    "labels = [\"Mean image\"]\n",
    "pd.showImagesNoAxes( axs4, mu[np.newaxis,:], 1, 1, resize = True, imShape = imShape, labelList = labels )\n",
    "\n",
    "# Display a few samples taken from this distribution -- you will find these to be extremely noisy\n",
    "fig5, axs5 = pd.getFigList( numRows, numCols )\n",
    "labels = [\"A random image\" for i in range( numRows * numCols )]\n",
    "randSamples = rand.multivariate_normal( mu, np.identity( d ), size = numRows * numCols, check_valid = \"raise\" )\n",
    "randSamples = truncatePixels(randSamples)\n",
    "pd.showImagesNoAxes( axs5, randSamples, numRows, numCols, resize = True, imShape = imShape, labelList = labels )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 216x216 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x648 with 15 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def fitSingleGaussian( X ):\n",
    "    n = X.shape[0]\n",
    "    d = np.prod( X.shape[1:] )\n",
    "    X = X.reshape( n, d )\n",
    "    mu = np.mean( X, axis = 0 )\n",
    "    Xcent = X - mu\n",
    "    cov = 1/n*(Xcent.T).dot(Xcent)\n",
    "    return (mu, cov)\n",
    "\n",
    "# Fit a general Gaussian this time to the same dataset\n",
    "(mu, cov) = fitSingleGaussian( X )\n",
    "\n",
    "fig6, axs6 = pd.getFigList( 1, 1 )\n",
    "labels = [\"Mean image\"]\n",
    "pd.showImagesNoAxes( axs6, mu[np.newaxis,:], 1, 1, resize = True, imShape = imShape, labelList = labels )\n",
    "\n",
    "# The quality of samples is a bit better due to use of a general covariance matrix but not much better\n",
    "fig7, axs7 = pd.getFigList( numRows, numCols )\n",
    "labels = [\"A novel random image\" for i in range( numRows * numCols )]\n",
    "randSamples = rand.multivariate_normal( mu, cov, size = numRows * numCols, check_valid = \"raise\" )\n",
    "randSamples = truncatePixels(randSamples)\n",
    "pd.showImagesNoAxes( axs7, randSamples, numRows, numCols, resize = True, imShape = imShape, labelList = labels )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x432 with 10 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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quYn7vMyfP99lqklw2bJlcQ7RzMweeOABl6k24qR985vflLm6nqvrdM+ePWPtpz4abRGfeu3bsmWLy1Sj3po1a+Q2v/71r7usffv2Lot7rsVVWFgo87KyMpepBm3VYqiOe+TIkS5TrdqqpdFMX3uyaY9W+CQLAAAAABLEJAsAAAAAEsQkCwAAAAASxCQLAAAAABLU6MUXauGZKldQi5APHDjgsvvuuy/WflVxhZkumohLLdaLa/HixTJXx6MW8amyEFXcoJ4zVQIStWD9cLJ7926Z9+/f32UdOnRwWWVlpcuqqqpctnbtWpd17drVZar8xcxs06ZNLlNjUT0eNR5U6Ykq11i0aJE8HqVjx44u6969u8uWL1/uMlVKUpvz9OOPP3aZKmmIWoAPT11bVNlAq1at5P0HDBjgslWrVrnsxBNPdNnbb7/tshNOOMFlarHyzTffLI9n/fr1Lhs2bJjL4hb/lJeXu6ygoMBlahya6etvcy2+iKIW3qviElUEMHPmTJe98847LlOvfaosIIq6VmZTDqXG9quvvipv261bN5dNnjzZZarcQ72GUTrUuFR5lrouKaroysxs3LhxLlOvp6r0JJv3wlHFclFlWTWpEjlVfKHmBbU57oa4zvJJFgAAAAAkiEkWAAAAACSISRYAAAAAJIhJFgAAAAAkqNGLL1q29IeQn58f63YLFy50mVosqxb6HXfccfJ4evToIfP6pr5x20yXFajFg6pQQS2+fuaZZ1x2xRVXuEyVBZhFL2RvjtSiSjNdMqIMHTrUZa+//rrL1KLVe+65x2VqYayZLslQRRVvvvmmy9QC1S5dusTatzr/oqgF3VOmTHFZXl6ey9SCbFWkEbVwO2oR7uFuw4YNLissLHSZGp/vv/++y3bu3Omys88+W+77ggsucNmSJUtcpgo21EL+1157zWXquv/kk0/K4+nXr5/LSkpKXKZKatTxbN++3WXnnHOOy1RxghljNooqvpg6darL7rrrrljbUyVSI0eOlLdVr7vTp093mSphUde1f/3rXy574IEHXKYW/JuZjRkzxmWqyGju3LkuU6VDqrwpW3Hfjx1upk2b5rI1a9a47NRTT3XZxIkTXaZes83MLrroojocXf3p06dPne+rzj9VVqVKlRoTox0AAAAAEsQkCwAAAAASxCQLAAAAABLEJAsAAAAAEtToxRdqEWSnTp1cphYXL1682GVqcZxafJntt5urbapMUYtToxadqoXWTz/9tMvUQunBgwe7TC0QVwtw1e/gcBO34CKKKqRQRQBlZWUumzdvnstmzZqV1fFkQ30jfG2o4gv1/Jx77rkuU4t6o4pZEJ9aUK9KLpQ33njDZcuXL3fZWWedFft4Bg0aFOt2apu//e1vXXbbbbe57Nhjj5XbvPbaa12mrp/qPMj23IDWokULl6kiqJdfftll48aNc5laJD9jxgyXzZw5Ux6PKjNR7zfGjh3rslNOOcVlb731lsvU+5yoc1K95h9zzDEuU+UJCxYscNnll1/uMlVUEFVc0blzZ5ep5xz6fdgrr7ziMlU0tm3bNpepIhMzXYimiuVUoUxU8Vc29u7dW+f7Pv/88y4rKipy2YgRI1w2evRouc2GKHLjkywAAAAASBCTLAAAAABIEJMsAAAAAEgQkywAAAAASFCjF1+ohZGqGGLHjh0uW7duncviLqxT3/ReG2rx5759+1yWSqVcphayRn2r+5w5c1ymFrwOHDjQZTt37ox1jEpUiccnn3ziMrVAGXox6fDhw12mFm8+9NBDLlMLi8304s0ePXq4bOjQoS5T404tylULa++44w55PEpxcbHL4hYTtGzZ6JepnKHOTzN9jqqFzfPnz3fZ5s2bXXbSSSe57L333nPZT3/6U3k8aiHy1q1bXaYWeX/wwQcue+mll+R+arr11ltlrgpX0PR07NjRZV/5yldcpsb7o48+6rIvfelLLosqoVK3Va/FqpTn2WefdZkq9FH7+PKXvyyPZ9KkSS5T57QqW1LbVKUZ6v1UeXm5PB6YVVZWukwVaKlisYKCApepa50aSz//+c/l8ah9Dxs2zGVqzKvSE/VeQ72fjSrNUCVrcamiLPX4os7fuNR79mwKXPgkCwAAAAASxCQLAAAAABLEJAsAAAAAEsQkCwAAAAAS1OgryuOWJqgyjD/+8Y8uKywsdJn6huuoxfRqUacqJlDUIti4RRxRCwVXrlwZaz+q6KBXr14uW716tcvUQt3du3fL41GFH+r5hR6zSklJictUYcCGDRvk/aO+7b2uLrvssli3+/Of/yzzxYsXu+z888932XHHHVe7A8Nnqk3xhTJkyBCX/f73v3fZjBkzXKZ+71GFPvfdd5/L1HVo5MiRLps9e7bcZk39+vVzmVpcbqYLgdRrhLr+1QcKhnSJgCo4ueWWW1z24osvuuzUU0912YABA1zWunVreTzqNXHJkiUuq6iocNmmTZtcpopi1D4WLlwoj0c9PyNGjHDZ6aef7jL1nkY9bpWpMpooSZcINAb1GMrKyuRtVRmbKmspLS11mSpxUNewQYMGuaxbt27yePbv3+8yNT7VWJw2bZrcZmNRrw+qKCvb8ZX0+OSTLAAAAABIEJMsAAAAAEgQkywAAAAASBCTLAAAAABIUKMXX8Q1evRol6mFguobpdU3UkctyFbfaL1161aXHX300fL+NbVp0ybW7aIKMhYtWuQytSh64MCBLlOLaNV+VJaXlyeP5+DBgzLPdepx1WaRu1o4rxZqRo27mtasWeOy9evXy9uqcpQxY8bE2k9cagFtbahva0fyosasGp9RC/xruvrqq2NlO3bscJm6dprpRfuq2EHdf86cOS6rqqpy2ebNm12mFn2bxX8uGsquXbtcpl7vmgN1nTTTv1NVetKpUyeXqTImVfawdOlSl0Vd69Tr5M6dO12myjnqw6WXXuqyM88802Vq3HTu3Nll6vegzpeoki6loYpi6pMqviguLpa33bhxo8vmzZvnMnUNU+Pr+OOPd5kqNIsq2VLXT1UWsWXLFnn/mi655JJYx6Pec5uZ7dmzx2Wq5Eu55pprXKbOVfWYo95fx31/no3cPwMAAAAAoAlhkgUAAAAACWKSBQAAAAAJYpIFAAAAAAlikgUAAAAACcqZdkHVdqcaTD788MNY24u63RlnnOGyhmjU+8tf/iJz1S6ojke13YQQXKba7VQ705FHHimP53CiGr7MdLujarlZvXq1y9Tzqn4nvXv3dllUA9rbb7/tsvvuu89lqm1Sja+vfvWrLlPtlX379pXHs3jxYpdt375d3jZJtTlPm0PrlaLOeTPdHJZ0o54ax3HbNKPceOONLisvL491X9X8litUO15zFXXeqqbfs88+22WFhYUumzt3rstUw5hq3otqQh08eLDLhg0b5rILL7zQZa+99prcZhyXXXaZzL/97W+77OSTT67zftRrk3puG6KRrSmJuqYqQ4YMcZl6f6WaMxV1rVPteaqN2MysZ8+eLlPn2/e//32XqfE+cuRIuZ+aVqxYIfPrrrsu1v27devmMtXorRpp1fOtriUNpXm+0wAAAACARsIkCwAAAAASxCQLAAAAABLEJAsAAAAAEpQzxReq5KJfv36x7qsWt7733nvythUVFS47cOCAy7p06RJr38qWLVtc9uCDD8rbLl261GUnnHCCy9QidvUYR4wY4bIePXq4TJU7mOmFhs2BWtwatVhSPdcFBQUuGzBggMuyKQJQi0HNzL72ta/Fur9aMDtz5kyXqQWmgwYNcpla9G1mNmvWLJepBcFJi1qgXJuFy7ku6vxMpVIuU0UoqmCooSxfvtxljz/+uMtUgcGvfvWrejkm1L+oApY9e/a47Itf/KLLVOmQ2qZ6v1BaWuoy9X7BTJdAlJWVuUxdF9W1d+HChS5TxQA33HCDPB51TU6aeh6ba2lQlNq8fqiCIVXAowop1HtPNWbV8Vx77bXyeEpKSlzWrl07l1VWVrosbsHJtm3bXLZs2TJ5W/V+Vu1n1KhRLlPHqM7JpubwOlsAAAAAoJ4xyQIAAACABDHJAgAAAIAEMckCAAAAgATlTPGFcsopp7jsN7/5jcvUgjm1AM9ML7Tu3r27y4qLi12mFryqRYHqGFUBQZSJEye6TC14V4UWaiGk0lwLLmqjZUt9eqgSAVUUosowGpMqtFDlHMcff7zL1GLbqLGkzreNGzfGOcSsHE4FF7WlFjurBdnqd6ee144dO7os6nyJS5VXbN682WVqzF5//fVZ7bupOZzGsrqemukCCnVbdZ1V1zp1XcvWPffc47LnnnvOZQcPHnTZ0KFDXXbJJZe4rG/fvnU8utpRz6067mzP8+YgqhhMlbWowqoOHTq4TJW6RJWwJK2oqMhl6nev7Nixw2WqqM7MbPDgwS5bu3aty77xjW+47KOPPnKZKr5Q7zV69eolj6ch8EkWAAAAACSISRYAAAAAJIhJFgAAAAAkiEkWAAAAACQop1cwnnzyyS773e9+57KbbrrJZevXr5fbnD59ustU0cTs2bNd9stf/tJlTz75pNxPXO3bt3eZKvxQi2jVgkRoaqF5bRafV1VVxbpd3G9Rrw+q1OCII/z/Z1GPO+4iWDO9qFd9cz0ajlqsrq4tajzUh1//+tcue+CBB2LdVxVkNLWinv3797usVatWjXAkzUvr1q0bbd/q9XTKlCkuGz58uMvUYnw1jlVhR1SJQDbU9VwV4ajrRtS51tTOwfoU9VjV7y+bohD1e6qPa7Qq7FDXMHUOvPPOOy5ThW9mukROPZeqqCJuCUhtSi5UgUnS45hPsgAAAAAgQUyyAAAAACBBTLIAAAAAIEFMsgAAAAAgQTldfJGXl+ey8ePHu6y8vNxlK1askNvcsGGDyx555BGXLV68OM4hxtajRw+ZL1iwwGXq27mVhvq2cOhF7VHfCt8Q1KLVAwcOuKx///6xtqcW23bs2FHedvv27bG2icYVt9hFLYqOuxj/+eefl/nkyZNj3b+kpMRlp59+eqz7NiZKLuLLlefq4osvdpm61pWVlbls1KhRLlOvz126dHHZvn375PGo52337t0uU69DqoxB7UfdrqHKcXJRNiUXinqusy1r2Lt3r8vU+15VUqGKL1KplMt69+4t962O84knnnCZOq9UuVu2KL4AAAAAgBzDJAsAAAAAEsQkCwAAAAASxCQLAAAAABKU08UXqgBCFVqoRdrDhg2T26ysrHTZ448/Xoeji7Z69WqX9evXL9F9oGG1adOmsQ/h36hF0WqBatwCA6Vdu3YyV9+43tSeH8QvvshmjKjSjE/LayotLa3zvpsadf5F/Q7i/m6gCxtU2ZVayK+o12czs6VLl8a6vyoTGjt2rMtUAUFhYWGsfZjFL1ZS5QnqnFbXaFWWxNhsXNkWM6hSLDUW1Xmgbjdo0CCXFRcXy32r6/7cuXNdtnLlSpepc0gVZBQUFLgs6jlr3bq1zJPEJ1kAAAAAkCAmWQAAAACQICZZAAAAAJAgJlkAAAAAkKCcLr5QC4m7devmsvHjx7tsxowZcpt5eXkuu+WWW1x25plnuiybBeJAfevYsWOi23v00Udj35Zil6ZHLUJWi9/Vwvm4ospRrrrqKpepa+/9999f5303poMHD7pMlQg0xMLr5kQ9hyqLWwpRG9dcc43LVDnASSed5LIxY8a4TL1/qQ21mL9lS/+WLm7pkNpeVVVVnbeHpik/P99lAwcOdFl9FJy0b9/eZbfffrvLPvjgg1jb69ChQ6zbqbIPM10QljQ+yQIAAACABDHJAgAAAIAEMckCAAAAgAQxyQIAAACABDHJAgAAAIAE5XS7oGrDUe0lKistLa2XYwIOF/fee6/Me/bs6bLNmze7rHv37i5TTXa0WWVPNZmp5zqbBrxZs2a5bMWKFfK2Y8eOddmll14aaz+5QD23NAlmT7XnqbFdXFwca3vbtm1zmWq5NDO78sorXabOl4qKCpep61/Xrl1jHGHtJH2tLCgoSHR7aJp27drlMtVCWB+OPvroWFlc+/btc5maKzQUPskCAAAAgAQxyQIAAACABDHJAgAAAIAEMckCAAAAgATldPEFgMbTtm1bmd96660u2717t8vUIm1VGID6EUKIdTtVLKAMGTLEZf369ZO3VeUoce3fv99lrVq1qvP26oN6zj755BOXqSIH1E42v/vCwsIEjyRNjW11rsU9/xqKGrNxz33ktoYquWgITa1giHc0AAAAAJAgJlkAAAAAkCAmWQAAAACQICZZAAAAAJAgVt0CqHd5eXmNfQiHNbXIPukFwu3bt4+VZauplVwo6vmm5OLwkKvlPWrMtmjRohGOBGg+cvNqAAAAAABNFJMsAAAAAEgQkywAAAAASBCTLAAAAABIUKjNN3qHELaY2Zr6Oxw0c71TqVSnhtwhYxZZYswi1zBmkWsYs8g1scZsrSZZAAAAAIBPxz8XBAAAAIAEMckCAAAAgAQxyQIAAACABDHJAgAAAIAEMckCAAAAgAQxyQIAAACABDHJAgAAAIAEMckCAAAAgAQxyQIAAACABP1fi+1Hdg030pgAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 1080x648 with 15 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Perform the k-means++ initialization\n",
    "def doKMPPInitGreedy( X, C ):\n",
    "    init = np.zeros( (C, X.shape[1]) )\n",
    "    n = X.shape[0]\n",
    "    # Choose a random data point and make it a centroid\n",
    "    i = random.randint( 0, n-1 )\n",
    "    init[0,:] = X[i,:]\n",
    "    for t in range( 1, C ):\n",
    "        # For all data points, find the squared Euclidean distance to the closest centroid\n",
    "        # Python is funny: init[0,:] generates a vector but init[0:1,:] generates a matrix with one row :)\n",
    "        dist = np.min( utils.getAllPairsDistances( X, init[0:t,:] ), axis = 1 )\n",
    "        i = np.argmax( dist )\n",
    "        init[t,:] = X[i,:]\n",
    "    return init\n",
    "\n",
    "def getSigmaInit( C, d ):\n",
    "    iden = np.identity( d )\n",
    "    init = np.zeros( (C, d, d) )\n",
    "    for i in range( C ):\n",
    "        init[i] = iden\n",
    "    return init\n",
    "\n",
    "# Obtain probability of data point x^i belonging to component N(\\mu^c, S^c)\n",
    "# The proper way of computing this is 1/\\sqrt((2\\pi)^d*|S^c|)*exp( - (x^i - \\mu^c)'(S^c)^{-1}(x^i - \\mu^c))\n",
    "# However, this can be very expensive due to all the inverses involved\n",
    "# Cheaper shortcut: approximate S^c \\approx I_d\n",
    "def doEStep( X, muVals, SigmaVals ):\n",
    "    qVals = np.exp( -utils.getAllPairsDistances( X, muVals ) / 2 )        \n",
    "    rowSum = qVals.sum( axis = 1 )\n",
    "    qVals = qVals / rowSum[:, np.newaxis]\n",
    "    return qVals\n",
    "\n",
    "# Update the models by optimizing the Q function given by the E Step\n",
    "# Ideally, both means and covariances for all components should be updated\n",
    "# The solution to the weighted MLE for the covariance matrix update can be shown to be\n",
    "# S^c = 1/Q_c * \\sum_{i=1}^n q^i_c (x^i - \\mu^c)(x^i - \\mu^c)^T where Q_c = \\sum_{i=1}^n q^i_c\n",
    "# Cheaper shortcut: do not update covariance matrix at every M step (update only means every time)\n",
    "# Update covariance only at the end (we are anyway not using SigmaVals to compute the E step)\n",
    "def doMStep( X, qVals, C, prevMuVals, prevSigmaVals ):\n",
    "    d = X.shape[1]\n",
    "    muVals = np.zeros( (C, d) )\n",
    "    SigmaVals = np.zeros( (C, d, d) )\n",
    "    \n",
    "    # Process every component\n",
    "    for c in range( C ):\n",
    "        # Get hold of the weights different data points have given to this component\n",
    "        q = qVals[:, c]\n",
    "        amountData = sum(q)\n",
    "        # If there is enough data for this component, do weighted MLE estimation\n",
    "        if amountData > 1:\n",
    "            muVals[c] = (X.T).dot( q )/amountData\n",
    "        # If some cluster is almost empty, return the old value of its centroid\n",
    "        else:\n",
    "            muVals[c] = prevMuVals[c]\n",
    "    return (muVals, SigmaVals)\n",
    "\n",
    "# Execute EM algorithm for jointly learning a mixture of general (not standard) Gaussians\n",
    "def doEMGMM( X, C, initMu, initSigma, niter ):\n",
    "    muVals = initMu\n",
    "    SigmaVals = initSigma\n",
    "    # Perform the EM algorithm for niter steps\n",
    "    for t in range( niter ):\n",
    "        qVals = doEStep( X, muVals, SigmaVals )\n",
    "        (muVals, SigmaVals) = doMStep( X, qVals, C, muVals, SigmaVals )\n",
    "    # Cheaper shortcut we employed -- doing costly S^c updates only once at the end\n",
    "    for c in range( C ):\n",
    "        q = qVals[:, c]\n",
    "        amountData = sum(q)\n",
    "        if amountData > 1:\n",
    "            Xcent = X - muVals[c]\n",
    "            wXCent = (Xcent.T * q).T\n",
    "            SigmaVals[c] = 1 / amountData * (wXCent.T).dot( Xcent )\n",
    "    return (muVals, SigmaVals, qVals)\n",
    "\n",
    "# Number of components in the Gaussian mixture model (GMM)\n",
    "C = 10\n",
    "niter = 5\n",
    "\n",
    "initMu = doKMPPInitGreedy( X, C )\n",
    "initSigma = getSigmaInit( C, X.shape[1] )\n",
    "(muVals, SigmaVals, qVals) = doEMGMM( X, C, initMu, initSigma, niter )\n",
    "        \n",
    "numRows = 2\n",
    "numCols = C//2\n",
    "\n",
    "# Visualize the means/modes of the various components the EM algorithm returned\n",
    "# Notice how the various components do not just capture the different digits but also\n",
    "# different ways/styles of writing each digit e.g. slanted 0 vs fat round 0 etc\n",
    "fig8, axs8 = pd.getFigList( numRows, numCols )\n",
    "labels = [\"Component number %s\" % (i+1) for i in range( numRows * numCols )]\n",
    "pd.showImagesNoAxes( axs8, muVals, numRows, numCols, resize = True, imShape = imShape, labelList = labels )\n",
    "\n",
    "numRows = 3\n",
    "numCols = 5\n",
    "\n",
    "fig9, axs9 = pd.getFigList( numRows, numCols )\n",
    "labels = [\"A novel random image\" for i in range( numRows * numCols )]\n",
    "randSamples = np.zeros( (numRows * numCols, d) )\n",
    "for i in range( numRows * numCols ):\n",
    "    # Choose a random component of the GMM from which to sample\n",
    "    # It should be noted here that we have not used the label information in the data at all\n",
    "    # All these results are being achieved in a completely \"unsupervised\" setting\n",
    "    # Also note that all of these are novel images -- that never appeared in the training set\n",
    "    # Notice the significantly improved quality of the novel images compared to previous attempts\n",
    "    idx = random.randint( 0, C - 1 )\n",
    "    randSamples[i] = rand.multivariate_normal( muVals[idx], SigmaVals[idx], check_valid = \"raise\" )\n",
    "\n",
    "randSamples = truncatePixels(randSamples)\n",
    "pd.showImagesNoAxes( axs9, randSamples, numRows, numCols, resize = True, imShape = imShape, labelList = labels )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x432 with 10 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Create a dataset of upright and inverted 7s. Notice that an upight 7 means that there are black pixels\n",
    "# in the top, right regions and the top-right corner. An inverted 7, on the other hand means that there are\n",
    "# black pixels in the bottom, left regions and the bottom-left corner.\n",
    "labels = np.array( [7] )\n",
    "(X,y) = getDataSubset( labels )\n",
    "Xinv = X[:,::-1,::-1]\n",
    "n = X.shape[0]\n",
    "d = np.prod( X.shape[1:] )\n",
    "X = X.reshape( n, d )\n",
    "Xinv = Xinv.reshape( n, d )\n",
    "\n",
    "Xcomb = np.zeros( (2 * n, d) )\n",
    "Xcomb[::2] = X\n",
    "Xcomb[1::2] = Xinv\n",
    "\n",
    "n = 2 * n\n",
    "\n",
    "numRows = 2\n",
    "numCols = 5\n",
    "\n",
    "fig10, axs10 = pd.getFigList( numRows, numCols )\n",
    "labels = [\"\" for i in range( numRows * numCols )]\n",
    "labels1 = [\"Label is %s\" % y[i] for i in range( (numRows * numCols) // 2 )]\n",
    "labels2 = [\"Label is inverted %s\" % y[i] for i in range( (numRows * numCols) // 2 )]\n",
    "labels[::2] = labels1\n",
    "labels[1::2] = labels2\n",
    "\n",
    "pd.showImagesNoAxes( axs10, Xcomb[:numRows*numCols], numRows, numCols, resize = True, imShape = imShape, labelList = labels )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 216x216 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x432 with 10 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Fitting a \"spherical\" Gaussian i.e. whose covariance matrix is a multiple of the identity matrix\n",
    "# gives very poor samples since such a distribution is incapable of storing the fact that in the \n",
    "# current dataset, if there are black pixels in the top-right region, then the bottom-left region\n",
    "# is largely vacant and vice versa. Only covariance among different pixels can allow a distribution\n",
    "# to store such information about correlated behavior among pixels\n",
    "mu = fitSingleStandardGaussian( Xcomb )\n",
    "sigmaSq = np.square( lin.norm( Xcomb - mu, 'fro' ) ) / (n * d)\n",
    "\n",
    "fig11, axs11 = pd.getFigList( 1, 1 )\n",
    "labels = [\"Mean image\"]\n",
    "pd.showImagesNoAxes( axs11, mu[np.newaxis,:], 1, 1, resize = True, imShape = imShape, labelList = labels )\n",
    "\n",
    "fig12, axs12 = pd.getFigList( numRows, numCols )\n",
    "labels = [\"Standard Gaussian\" for i in range( numRows * numCols )]\n",
    "randSamples = rand.multivariate_normal( mu, sigmaSq*np.identity( d ), size = numRows * numCols, check_valid = \"raise\" )\n",
    "randSamples = truncatePixels(randSamples)\n",
    "pd.showImagesNoAxes( axs12, randSamples, numRows, numCols, resize = True, imShape = imShape, labelList = labels )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x864 with 20 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Using a proper Gaussian with a general covariance allows even a single Gaussian to capture\n",
    "# the fact that there exist upright and inverted 7s in this dataset and give much better samples\n",
    "(mu, cov) = fitSingleGaussian( Xcomb )\n",
    "\n",
    "numRows = 4\n",
    "numCols = 5\n",
    "\n",
    "fig13, axs13 = pd.getFigList( numRows, numCols )\n",
    "labels = [\"General Gaussian\" for i in range( numRows * numCols )]\n",
    "randSamples = rand.multivariate_normal( mu, cov, size = numRows * numCols, check_valid = \"raise\" )\n",
    "randSamples = truncatePixels(randSamples)\n",
    "pd.showImagesNoAxes( axs13, randSamples, numRows, numCols, resize = True, imShape = imShape, labelList = labels )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "author": {
   "email": "purushot@cse.iitk.ac.in",
   "institution": "IIT Kanpur",
   "name": "Puru"
  },
  "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": "3.7.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}