Assignment4/AviKhandelwal_204102301_Assignment-4.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#-----------------------------------------------------Q1 (a)----------------------------------------------------------\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "x1 = np.random.normal(0,1,100)\n",
    "x2 = np.random.normal(3,np.sqrt(2),100)\n",
    "bins = np.arange(-10,10)\n",
    "plt.figure(1)\n",
    "plt.hist(x1,bins,histtype='bar',linewidth=2)\n",
    "plt.xlabel(\"x\")\n",
    "plt.ylabel(\"pdf\")\n",
    "plt.title(\"N(0,1)\")\n",
    "plt.figure(2)\n",
    "plt.hist(x2,bins,histtype='bar',linewidth=2)\n",
    "plt.xlabel(\"x\")\n",
    "plt.ylabel(\"pdf\")\n",
    "plt.title(\"N(3,2)\")\n",
    "plt.show()\n",
    "\n",
    "# Looking at the plots for N(0,1) and N(3,2) we can comment that standard deviation gives a sense of spread of a normal\n",
    "# curve, since N(3,2) has higher SD hence it is more spread out in comparison. The peak of normal curve is inversely related\n",
    "# to SD hence N(3,2) is having lower peak in comaprison. Mu tells us about the point where the curve is centred hence N(0,1)\n",
    "# is centred around 0 whereas N(3,2) is centered around 3\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#-----------------------------------------------------Q1 (b)----------------------------------------------------------\n",
    "#-----------------------------------------------SURFACE AND CONTOUR PLOT----------------------------------------------------------\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "from matplotlib import cm\n",
    "from matplotlib.ticker import LinearLocator, FormatStrFormatter\n",
    "\n",
    "fig = plt.figure()\n",
    "ax = fig.gca(projection='3d')\n",
    "mean = np.matrix([0, 0]) # Mean vector\n",
    "cov = np.matrix([[1, 0.6], [0.6, 2]]) # Covarince matrix\n",
    "arr = []\n",
    "\n",
    "# 2D normal density function at x = [x1,x2]\n",
    "def normal_2D(x,mu,co):\n",
    "    co_inv = np.linalg.inv(co)\n",
    "    x_mu_t = (x-mu).transpose()\n",
    "    \n",
    "    a1 = 1/(2*np.pi)\n",
    "    a2 = 1/((np.linalg.det(cov))**0.5)\n",
    "    a3 = (x-mu)*co_inv*(x_mu_t)*(-0.5)\n",
    "    a = np.linalg.det(a3)\n",
    "    p = a1*a2*(np.e**a)\n",
    "    return p \n",
    "\n",
    "\n",
    "\n",
    "x1 = np.linspace(-10,10,100)\n",
    "x2 = np.linspace(-10,10,100)\n",
    "\n",
    "\n",
    "for i in range(100):\n",
    "    for j in range(100):\n",
    "        x = np.mat([x1[i],x2[j]])\n",
    "        p = normal_2D(x,mean,cov)\n",
    "        arr = np.append(arr,p)\n",
    "        \n",
    "# arr contains 100*100 points of probability values computed at x = [x1,x2]\n",
    "\n",
    "arr = arr.reshape(100,100)    \n",
    "x1,x2 = np.meshgrid(x1,x2)\n",
    "surf = ax.plot_surface(x1,x2,arr, cmap=cm.coolwarm,linewidth=0, antialiased=False)\n",
    "plt.figure(1)\n",
    "fig.colorbar(surf, shrink=0.5, aspect=5)\n",
    "plt.xlabel(\"x1\")\n",
    "plt.ylabel(\"x2\")\n",
    "plt.title(\"Surface plot\")\n",
    "\n",
    "#Contour plot\n",
    "fig,ax=plt.subplots(1,1)\n",
    "cp = ax.contourf(x1,x2,arr)\n",
    "fig.colorbar(cp)\n",
    "plt.ylim((-3,3))\n",
    "plt.xlim((-3,3))\n",
    "plt.xlabel(\"x1\")\n",
    "plt.ylabel(\"x2\")\n",
    "plt.title(\"Contour plot\")\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[5.1 3.5 1.4 0.2]\n",
      " [4.9 3.  1.4 0.2]\n",
      " [4.7 3.2 1.3 0.2]\n",
      " [4.6 3.1 1.5 0.2]\n",
      " [5.  3.6 1.4 0.2]\n",
      " [5.4 3.9 1.7 0.4]\n",
      " [4.6 3.4 1.4 0.3]\n",
      " [5.  3.4 1.5 0.2]\n",
      " [4.4 2.9 1.4 0.2]\n",
      " [4.9 3.1 1.5 0.1]\n",
      " [5.4 3.7 1.5 0.2]\n",
      " [4.8 3.4 1.6 0.2]\n",
      " [4.8 3.  1.4 0.1]\n",
      " [4.3 3.  1.1 0.1]\n",
      " [5.8 4.  1.2 0.2]\n",
      " [5.7 4.4 1.5 0.4]\n",
      " [5.4 3.9 1.3 0.4]\n",
      " [5.1 3.5 1.4 0.3]\n",
      " [5.7 3.8 1.7 0.3]\n",
      " [5.1 3.8 1.5 0.3]\n",
      " [5.4 3.4 1.7 0.2]\n",
      " [5.1 3.7 1.5 0.4]\n",
      " [4.6 3.6 1.  0.2]\n",
      " [5.1 3.3 1.7 0.5]\n",
      " [4.8 3.4 1.9 0.2]\n",
      " [5.  3.  1.6 0.2]\n",
      " [5.  3.4 1.6 0.4]\n",
      " [5.2 3.5 1.5 0.2]\n",
      " [5.2 3.4 1.4 0.2]\n",
      " [4.7 3.2 1.6 0.2]\n",
      " [4.8 3.1 1.6 0.2]\n",
      " [5.4 3.4 1.5 0.4]\n",
      " [5.2 4.1 1.5 0.1]\n",
      " [5.5 4.2 1.4 0.2]\n",
      " [4.9 3.1 1.5 0.1]\n",
      " [5.  3.2 1.2 0.2]\n",
      " [5.5 3.5 1.3 0.2]\n",
      " [4.9 3.1 1.5 0.1]\n",
      " [4.4 3.  1.3 0.2]\n",
      " [5.1 3.4 1.5 0.2]\n",
      " [5.  3.5 1.3 0.3]\n",
      " [4.5 2.3 1.3 0.3]\n",
      " [4.4 3.2 1.3 0.2]\n",
      " [5.  3.5 1.6 0.6]\n",
      " [5.1 3.8 1.9 0.4]\n",
      " [4.8 3.  1.4 0.3]\n",
      " [5.1 3.8 1.6 0.2]\n",
      " [4.6 3.2 1.4 0.2]\n",
      " [5.3 3.7 1.5 0.2]\n",
      " [5.  3.3 1.4 0.2]\n",
      " [7.  3.2 4.7 1.4]\n",
      " [6.4 3.2 4.5 1.5]\n",
      " [6.9 3.1 4.9 1.5]\n",
      " [5.5 2.3 4.  1.3]\n",
      " [6.5 2.8 4.6 1.5]\n",
      " [5.7 2.8 4.5 1.3]\n",
      " [6.3 3.3 4.7 1.6]\n",
      " [4.9 2.4 3.3 1. ]\n",
      " [6.6 2.9 4.6 1.3]\n",
      " [5.2 2.7 3.9 1.4]\n",
      " [5.  2.  3.5 1. ]\n",
      " [5.9 3.  4.2 1.5]\n",
      " [6.  2.2 4.  1. ]\n",
      " [6.1 2.9 4.7 1.4]\n",
      " [5.6 2.9 3.6 1.3]\n",
      " [6.7 3.1 4.4 1.4]\n",
      " [5.6 3.  4.5 1.5]\n",
      " [5.8 2.7 4.1 1. ]\n",
      " [6.2 2.2 4.5 1.5]\n",
      " [5.6 2.5 3.9 1.1]\n",
      " [5.9 3.2 4.8 1.8]\n",
      " [6.1 2.8 4.  1.3]\n",
      " [6.3 2.5 4.9 1.5]\n",
      " [6.1 2.8 4.7 1.2]\n",
      " [6.4 2.9 4.3 1.3]\n",
      " [6.6 3.  4.4 1.4]\n",
      " [6.8 2.8 4.8 1.4]\n",
      " [6.7 3.  5.  1.7]\n",
      " [6.  2.9 4.5 1.5]\n",
      " [5.7 2.6 3.5 1. ]\n",
      " [5.5 2.4 3.8 1.1]\n",
      " [5.5 2.4 3.7 1. ]\n",
      " [5.8 2.7 3.9 1.2]\n",
      " [6.  2.7 5.1 1.6]\n",
      " [5.4 3.  4.5 1.5]\n",
      " [6.  3.4 4.5 1.6]\n",
      " [6.7 3.1 4.7 1.5]\n",
      " [6.3 2.3 4.4 1.3]\n",
      " [5.6 3.  4.1 1.3]\n",
      " [5.5 2.5 4.  1.3]\n",
      " [5.5 2.6 4.4 1.2]\n",
      " [6.1 3.  4.6 1.4]\n",
      " [5.8 2.6 4.  1.2]\n",
      " [5.  2.3 3.3 1. ]\n",
      " [5.6 2.7 4.2 1.3]\n",
      " [5.7 3.  4.2 1.2]\n",
      " [5.7 2.9 4.2 1.3]\n",
      " [6.2 2.9 4.3 1.3]\n",
      " [5.1 2.5 3.  1.1]\n",
      " [5.7 2.8 4.1 1.3]\n",
      " [6.3 3.3 6.  2.5]\n",
      " [5.8 2.7 5.1 1.9]\n",
      " [7.1 3.  5.9 2.1]\n",
      " [6.3 2.9 5.6 1.8]\n",
      " [6.5 3.  5.8 2.2]\n",
      " [7.6 3.  6.6 2.1]\n",
      " [4.9 2.5 4.5 1.7]\n",
      " [7.3 2.9 6.3 1.8]\n",
      " [6.7 2.5 5.8 1.8]\n",
      " [7.2 3.6 6.1 2.5]\n",
      " [6.5 3.2 5.1 2. ]\n",
      " [6.4 2.7 5.3 1.9]\n",
      " [6.8 3.  5.5 2.1]\n",
      " [5.7 2.5 5.  2. ]\n",
      " [5.8 2.8 5.1 2.4]\n",
      " [6.4 3.2 5.3 2.3]\n",
      " [6.5 3.  5.5 1.8]\n",
      " [7.7 3.8 6.7 2.2]\n",
      " [7.7 2.6 6.9 2.3]\n",
      " [6.  2.2 5.  1.5]\n",
      " [6.9 3.2 5.7 2.3]\n",
      " [5.6 2.8 4.9 2. ]\n",
      " [7.7 2.8 6.7 2. ]\n",
      " [6.3 2.7 4.9 1.8]\n",
      " [6.7 3.3 5.7 2.1]\n",
      " [7.2 3.2 6.  1.8]\n",
      " [6.2 2.8 4.8 1.8]\n",
      " [6.1 3.  4.9 1.8]\n",
      " [6.4 2.8 5.6 2.1]\n",
      " [7.2 3.  5.8 1.6]\n",
      " [7.4 2.8 6.1 1.9]\n",
      " [7.9 3.8 6.4 2. ]\n",
      " [6.4 2.8 5.6 2.2]\n",
      " [6.3 2.8 5.1 1.5]\n",
      " [6.1 2.6 5.6 1.4]\n",
      " [7.7 3.  6.1 2.3]\n",
      " [6.3 3.4 5.6 2.4]\n",
      " [6.4 3.1 5.5 1.8]\n",
      " [6.  3.  4.8 1.8]\n",
      " [6.9 3.1 5.4 2.1]\n",
      " [6.7 3.1 5.6 2.4]\n",
      " [6.9 3.1 5.1 2.3]\n",
      " [5.8 2.7 5.1 1.9]\n",
      " [6.8 3.2 5.9 2.3]\n",
      " [6.7 3.3 5.7 2.5]\n",
      " [6.7 3.  5.2 2.3]\n",
      " [6.3 2.5 5.  1.9]\n",
      " [6.5 3.  5.2 2. ]\n",
      " [6.2 3.4 5.4 2.3]\n",
      " [5.9 3.  5.1 1.8]]\n"
     ]
    }
   ],
   "source": [
    "#-----------------------------------------------------Q2----------------------------------------------------------\n",
    "#--------------------------------------PART-1: EXTRACTING DATA FROM DATASET---------------------------------------\n",
    "\n",
    "import numpy as np\n",
    "import csv\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.metrics import confusion_matrix\n",
    "\n",
    "\n",
    "opened_csv_file = open(\"C:/Users/avikh/Desktop/SPML_Sem1/ML/Lab/iris.data\", 'r') # File handling operation\n",
    "reader = csv.reader(opened_csv_file) # Read the data given in the data set in the form of lists\n",
    "features = []\n",
    "for row in reader:\n",
    "        features.append(row)\n",
    "opened_csv_file.close()\n",
    "\n",
    "features.pop() # Removing the last element which was an empty space in data \n",
    "# Now we will be having features which will be a 2D list but having all entries in string format \n",
    "\n",
    "\n",
    "data_set = []\n",
    "\n",
    "for i in range(len(features)):\n",
    "    lst = []\n",
    "    for j in range(4): # Excluding the class label for now for computational convinience \n",
    "        lst.append(float(features[i][j]))\n",
    "    data_set.append(lst)\n",
    "\n",
    "data_set = np.matrix(data_set)\n",
    "\n",
    "# Finally we would have convered the 2D feature vector we had before into our desired data set format which is having all \n",
    "# entries in float and can be realised as a 2D matrix\n",
    "\n",
    "print(data_set)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[5.6 3.  4.1 1.3]\n",
      " [5.9 3.  4.2 1.5]\n",
      " [5.7 2.9 4.2 1.3]\n",
      " [6.7 3.1 4.4 1.4]\n",
      " [7.  3.2 4.7 1.4]\n",
      " [5.7 3.  4.2 1.2]\n",
      " [5.  2.3 3.3 1. ]\n",
      " [6.8 2.8 4.8 1.4]\n",
      " [6.4 2.9 4.3 1.3]\n",
      " [5.5 2.5 4.  1.3]\n",
      " [6.9 3.1 4.9 1.5]\n",
      " [5.7 2.8 4.1 1.3]\n",
      " [5.8 2.7 4.1 1. ]\n",
      " [6.4 3.2 4.5 1.5]\n",
      " [6.5 2.8 4.6 1.5]\n",
      " [6.2 2.9 4.3 1.3]\n",
      " [5.8 2.7 3.9 1.2]\n",
      " [5.6 2.7 4.2 1.3]\n",
      " [5.  2.  3.5 1. ]\n",
      " [5.7 2.8 4.5 1.3]\n",
      " [5.5 2.6 4.4 1.2]\n",
      " [6.3 3.3 4.7 1.6]\n",
      " [6.3 2.5 4.9 1.5]\n",
      " [5.7 2.6 3.5 1. ]\n",
      " [6.  2.7 5.1 1.6]\n",
      " [5.2 2.7 3.9 1.4]\n",
      " [6.  2.9 4.5 1.5]\n",
      " [6.1 3.  4.6 1.4]\n",
      " [5.6 2.9 3.6 1.3]\n",
      " [6.2 2.2 4.5 1.5]\n",
      " [6.3 2.3 4.4 1.3]\n",
      " [6.7 3.  5.  1.7]\n",
      " [5.5 2.4 3.7 1. ]\n",
      " [6.  3.4 4.5 1.6]\n",
      " [5.5 2.4 3.8 1.1]]\n"
     ]
    }
   ],
   "source": [
    "#-----------------------------------------------------Q2----------------------------------------------------------\n",
    "#--------------------------------------PART-2: COMING UP WITH TRAINING DATA SET---------------------------------------\n",
    "\n",
    "# Our data set is having 150 elements, with 50 elements from each class\n",
    "\n",
    "setosa = data_set[0:50] # First 50 elements from Setosa class \n",
    "np.random.shuffle(setosa) # Since we want to make a random selection of training examples from setosa data-set\n",
    "setosa_train = setosa[0:35] # Taking 70% as training examples hence taking 35 randomly selected samples as training set\n",
    "\n",
    "\n",
    "versicolor = data_set[50:100] #  51-100 elements from Versicolor class \n",
    "np.random.shuffle(versicolor) # Since we want to make a random selection of training examples from Versicolor data-set\n",
    "versicolor_train = versicolor[0:35] # Taking 70% as training examples hence taking 35 randomly selected samples as training set\n",
    "\n",
    "virginica = data_set[100:150] #  101-150 elements \n",
    "np.random.shuffle(virginica)\n",
    "virginica_train = virginica[0:35]\n",
    "\n",
    "print(versicolor_train) # Just for understanding\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mu1 = [[5.05142857 3.44       1.47428571 0.24285714]] \n",
      "\n",
      "Cov1 = [[0.12992653 0.10137143 0.01732245 0.01322449]\n",
      " [0.10137143 0.14068571 0.01417143 0.01628571]\n",
      " [0.01732245 0.01417143 0.03505306 0.00653061]\n",
      " [0.01322449 0.01628571 0.00653061 0.01159184]] \n",
      "\n",
      "\n",
      "mu2 = [[5.96571429 2.78       4.28285714 1.33428571]] \n",
      "\n",
      "Cov2= [[0.25653878 0.08474286 0.1745551  0.0608898 ]\n",
      " [0.08474286 0.09931429 0.06594286 0.03411429]\n",
      " [0.1745551  0.06594286 0.19342041 0.06773061]\n",
      " [0.0608898  0.03411429 0.06773061 0.03539592]] \n",
      "\n",
      "\n",
      "mu3= [[6.59714286 3.00285714 5.54857143 2.05714286]] \n",
      "\n",
      "Cov3= [[0.43970612 0.10972245 0.33213878 0.06302041]\n",
      " [0.10972245 0.12313469 0.09471837 0.04926531]\n",
      " [0.33213878 0.09471837 0.3333551  0.06522449]\n",
      " [0.06302041 0.04926531 0.06522449 0.06530612]] \n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "#-----------------------------------------------------Q2----------------------------------------------------------\n",
    "#--------------------------------------PART-3: CALCULATING MEAN AND COVARIANCE MATRIX-----------------------------\n",
    "\n",
    "mu1 = setosa_train.sum(0)/35     # sum(0) will compute sum along columns of the 2D matrix and dividing by 35 gives the mean \n",
    "mu2 = versicolor_train.sum(0)/35 # Similary calculating mu2 and mu3\n",
    "mu3 = virginica_train.sum(0)/35\n",
    "\n",
    "#Initialising the covariance matrices for each class\n",
    "cov1 = 0\n",
    "cov2 = 0\n",
    "cov3 = 0\n",
    "\n",
    "# We have used the formula that mu = E(x) and cov = E[(x-u)*(x-u)']\n",
    "for i in range(35):\n",
    "    x = setosa_train[i]-mu1\n",
    "    y = versicolor_train[i]-mu2\n",
    "    z = virginica_train[i]-mu3\n",
    "    cov1 += x.getT()*x # (x-u)*(x-u)'\n",
    "    cov2 += y.getT()*y\n",
    "    cov3 += z.getT()*z\n",
    "    \n",
    "#Dividing by 35 to get the average \n",
    "cov1 = cov1/35\n",
    "cov2 = cov2/35\n",
    "cov3 = cov3/35\n",
    "\n",
    "#Just for understanding\n",
    "print(\"mu1 =\",mu1,\"\\n\")\n",
    "print(\"Cov1 =\",cov1,\"\\n\\n\")\n",
    "\n",
    "print('mu2 =',mu2,'\\n')\n",
    "print('Cov2=',cov2,'\\n\\n')\n",
    "\n",
    "print('mu3=',mu3,'\\n')\n",
    "print('Cov3=',cov3,'\\n\\n')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True class: Iris-setosa \tPredicted class: Iris-setosa\n",
      "True class: Iris-setosa \tPredicted class: Iris-setosa\n",
      "True class: Iris-setosa \tPredicted class: Iris-setosa\n",
      "True class: Iris-setosa \tPredicted class: Iris-setosa\n",
      "True class: Iris-setosa \tPredicted class: Iris-setosa\n",
      "True class: Iris-setosa \tPredicted class: Iris-setosa\n",
      "True class: Iris-setosa \tPredicted class: Iris-setosa\n",
      "True class: Iris-setosa \tPredicted class: Iris-setosa\n",
      "True class: Iris-setosa \tPredicted class: Iris-setosa\n",
      "True class: Iris-setosa \tPredicted class: Iris-setosa\n",
      "True class: Iris-setosa \tPredicted class: Iris-setosa\n",
      "True class: Iris-setosa \tPredicted class: Iris-setosa\n",
      "True class: Iris-setosa \tPredicted class: Iris-setosa\n",
      "True class: Iris-setosa \tPredicted class: Iris-setosa\n",
      "True class: Iris-setosa \tPredicted class: Iris-setosa\n",
      "True class: Iris-setosa \tPredicted class: Iris-setosa\n",
      "True class: Iris-setosa \tPredicted class: Iris-setosa\n",
      "True class: Iris-setosa \tPredicted class: Iris-setosa\n",
      "True class: Iris-setosa \tPredicted class: Iris-setosa\n",
      "True class: Iris-setosa \tPredicted class: Iris-setosa\n",
      "True class: Iris-setosa \tPredicted class: Iris-setosa\n",
      "True class: Iris-setosa \tPredicted class: Iris-setosa\n",
      "True class: Iris-setosa \tPredicted class: Iris-setosa\n",
      "True class: Iris-setosa \tPredicted class: Iris-setosa\n",
      "True class: Iris-setosa \tPredicted class: Iris-setosa\n",
      "True class: Iris-setosa \tPredicted class: Iris-setosa\n",
      "True class: Iris-setosa \tPredicted class: Iris-setosa\n",
      "True class: Iris-setosa \tPredicted class: Iris-setosa\n",
      "True class: Iris-setosa \tPredicted class: Iris-setosa\n",
      "True class: Iris-setosa \tPredicted class: Iris-setosa\n",
      "True class: Iris-setosa \tPredicted class: Iris-setosa\n",
      "True class: Iris-setosa \tPredicted class: Iris-setosa\n",
      "True class: Iris-setosa \tPredicted class: Iris-setosa\n",
      "True class: Iris-setosa \tPredicted class: Iris-setosa\n",
      "True class: Iris-setosa \tPredicted class: Iris-setosa\n",
      "True class: Iris-setosa \tPredicted class: Iris-setosa\n",
      "True class: Iris-setosa \tPredicted class: Iris-setosa\n",
      "True class: Iris-setosa \tPredicted class: Iris-setosa\n",
      "True class: Iris-setosa \tPredicted class: Iris-setosa\n",
      "True class: Iris-setosa \tPredicted class: Iris-setosa\n",
      "True class: Iris-setosa \tPredicted class: Iris-setosa\n",
      "True class: Iris-setosa \tPredicted class: Iris-setosa\n",
      "True class: Iris-setosa \tPredicted class: Iris-setosa\n",
      "True class: Iris-setosa \tPredicted class: Iris-setosa\n",
      "True class: Iris-setosa \tPredicted class: Iris-setosa\n",
      "True class: Iris-setosa \tPredicted class: Iris-setosa\n",
      "True class: Iris-setosa \tPredicted class: Iris-setosa\n",
      "True class: Iris-setosa \tPredicted class: Iris-setosa\n",
      "True class: Iris-setosa \tPredicted class: Iris-setosa\n",
      "True class: Iris-setosa \tPredicted class: Iris-setosa\n",
      "True class: Iris-versicolor \tPredicted class: Iris-versicolor\n",
      "True class: Iris-versicolor \tPredicted class: Iris-versicolor\n",
      "True class: Iris-versicolor \tPredicted class: Iris-versicolor\n",
      "True class: Iris-versicolor \tPredicted class: Iris-versicolor\n",
      "True class: Iris-versicolor \tPredicted class: Iris-versicolor\n",
      "True class: Iris-versicolor \tPredicted class: Iris-versicolor\n",
      "True class: Iris-versicolor \tPredicted class: Iris-versicolor\n",
      "True class: Iris-versicolor \tPredicted class: Iris-versicolor\n",
      "True class: Iris-versicolor \tPredicted class: Iris-versicolor\n",
      "True class: Iris-versicolor \tPredicted class: Iris-versicolor\n",
      "True class: Iris-versicolor \tPredicted class: Iris-versicolor\n",
      "True class: Iris-versicolor \tPredicted class: Iris-versicolor\n",
      "True class: Iris-versicolor \tPredicted class: Iris-versicolor\n",
      "True class: Iris-versicolor \tPredicted class: Iris-versicolor\n",
      "True class: Iris-versicolor \tPredicted class: Iris-versicolor\n",
      "True class: Iris-versicolor \tPredicted class: Iris-versicolor\n",
      "True class: Iris-versicolor \tPredicted class: Iris-versicolor\n",
      "True class: Iris-versicolor \tPredicted class: Iris-versicolor\n",
      "True class: Iris-versicolor \tPredicted class: Iris-versicolor\n",
      "True class: Iris-versicolor \tPredicted class: Iris-versicolor\n",
      "True class: Iris-versicolor \tPredicted class: Iris-versicolor\n",
      "True class: Iris-versicolor \tPredicted class: Iris-versicolor\n",
      "True class: Iris-versicolor \tPredicted class: Iris-versicolor\n",
      "True class: Iris-versicolor \tPredicted class: Iris-versicolor\n",
      "True class: Iris-versicolor \tPredicted class: Iris-virginica\n",
      "True class: Iris-versicolor \tPredicted class: Iris-versicolor\n",
      "True class: Iris-versicolor \tPredicted class: Iris-versicolor\n",
      "True class: Iris-versicolor \tPredicted class: Iris-versicolor\n",
      "True class: Iris-versicolor \tPredicted class: Iris-versicolor\n",
      "True class: Iris-versicolor \tPredicted class: Iris-versicolor\n",
      "True class: Iris-versicolor \tPredicted class: Iris-versicolor\n",
      "True class: Iris-versicolor \tPredicted class: Iris-versicolor\n",
      "True class: Iris-versicolor \tPredicted class: Iris-versicolor\n",
      "True class: Iris-versicolor \tPredicted class: Iris-versicolor\n",
      "True class: Iris-versicolor \tPredicted class: Iris-versicolor\n",
      "True class: Iris-versicolor \tPredicted class: Iris-versicolor\n",
      "True class: Iris-versicolor \tPredicted class: Iris-versicolor\n",
      "True class: Iris-versicolor \tPredicted class: Iris-versicolor\n",
      "True class: Iris-versicolor \tPredicted class: Iris-versicolor\n",
      "True class: Iris-versicolor \tPredicted class: Iris-versicolor\n",
      "True class: Iris-versicolor \tPredicted class: Iris-versicolor\n",
      "True class: Iris-versicolor \tPredicted class: Iris-versicolor\n",
      "True class: Iris-versicolor \tPredicted class: Iris-versicolor\n",
      "True class: Iris-versicolor \tPredicted class: Iris-versicolor\n",
      "True class: Iris-versicolor \tPredicted class: Iris-versicolor\n",
      "True class: Iris-versicolor \tPredicted class: Iris-versicolor\n",
      "True class: Iris-versicolor \tPredicted class: Iris-virginica\n",
      "True class: Iris-versicolor \tPredicted class: Iris-versicolor\n",
      "True class: Iris-versicolor \tPredicted class: Iris-versicolor\n",
      "True class: Iris-versicolor \tPredicted class: Iris-versicolor\n",
      "True class: Iris-virginica \tPredicted class: Iris-virginica\n",
      "True class: Iris-virginica \tPredicted class: Iris-virginica\n",
      "True class: Iris-virginica \tPredicted class: Iris-virginica\n",
      "True class: Iris-virginica \tPredicted class: Iris-virginica\n",
      "True class: Iris-virginica \tPredicted class: Iris-virginica\n",
      "True class: Iris-virginica \tPredicted class: Iris-virginica\n",
      "True class: Iris-virginica \tPredicted class: Iris-virginica\n",
      "True class: Iris-virginica \tPredicted class: Iris-virginica\n",
      "True class: Iris-virginica \tPredicted class: Iris-virginica\n",
      "True class: Iris-virginica \tPredicted class: Iris-virginica\n",
      "True class: Iris-virginica \tPredicted class: Iris-virginica\n",
      "True class: Iris-virginica \tPredicted class: Iris-virginica\n",
      "True class: Iris-virginica \tPredicted class: Iris-virginica\n",
      "True class: Iris-virginica \tPredicted class: Iris-virginica\n",
      "True class: Iris-virginica \tPredicted class: Iris-virginica\n",
      "True class: Iris-virginica \tPredicted class: Iris-virginica\n",
      "True class: Iris-virginica \tPredicted class: Iris-virginica\n",
      "True class: Iris-virginica \tPredicted class: Iris-virginica\n",
      "True class: Iris-virginica \tPredicted class: Iris-virginica\n",
      "True class: Iris-virginica \tPredicted class: Iris-virginica\n",
      "True class: Iris-virginica \tPredicted class: Iris-virginica\n",
      "True class: Iris-virginica \tPredicted class: Iris-virginica\n",
      "True class: Iris-virginica \tPredicted class: Iris-virginica\n",
      "True class: Iris-virginica \tPredicted class: Iris-virginica\n",
      "True class: Iris-virginica \tPredicted class: Iris-virginica\n",
      "True class: Iris-virginica \tPredicted class: Iris-virginica\n",
      "True class: Iris-virginica \tPredicted class: Iris-virginica\n",
      "True class: Iris-virginica \tPredicted class: Iris-virginica\n",
      "True class: Iris-virginica \tPredicted class: Iris-virginica\n",
      "True class: Iris-virginica \tPredicted class: Iris-virginica\n",
      "True class: Iris-virginica \tPredicted class: Iris-virginica\n",
      "True class: Iris-virginica \tPredicted class: Iris-virginica\n",
      "True class: Iris-virginica \tPredicted class: Iris-virginica\n",
      "True class: Iris-virginica \tPredicted class: Iris-virginica\n",
      "True class: Iris-virginica \tPredicted class: Iris-virginica\n",
      "True class: Iris-virginica \tPredicted class: Iris-virginica\n",
      "True class: Iris-virginica \tPredicted class: Iris-virginica\n",
      "True class: Iris-virginica \tPredicted class: Iris-virginica\n",
      "True class: Iris-virginica \tPredicted class: Iris-virginica\n",
      "True class: Iris-virginica \tPredicted class: Iris-virginica\n",
      "True class: Iris-virginica \tPredicted class: Iris-virginica\n",
      "True class: Iris-virginica \tPredicted class: Iris-virginica\n",
      "True class: Iris-virginica \tPredicted class: Iris-versicolor\n",
      "True class: Iris-virginica \tPredicted class: Iris-virginica\n",
      "True class: Iris-virginica \tPredicted class: Iris-virginica\n",
      "True class: Iris-virginica \tPredicted class: Iris-virginica\n",
      "True class: Iris-virginica \tPredicted class: Iris-virginica\n",
      "True class: Iris-virginica \tPredicted class: Iris-virginica\n",
      "True class: Iris-virginica \tPredicted class: Iris-virginica\n",
      "True class: Iris-virginica \tPredicted class: Iris-virginica\n"
     ]
    }
   ],
   "source": [
    "#-----------------------------------------------------Q2----------------------------------------------------------\n",
    "#------------------PART-4: DEFINING DISCRIMINANT FUNCTIONS AND DEVELOPING A MINIMUM ERROR RATE CLASSIFIER---------\n",
    "\n",
    "#Ignoring the apriori probability in all gi(X) since it is constant for all classes which is 1/3\n",
    "\n",
    "def g1(X): # Discriminant Function corresponding to Setosa class\n",
    "\n",
    "    cov1_inv = np.linalg.inv(cov1)\n",
    "    cov1_det = np.linalg.det(cov1)\n",
    "    p = (X-mu1)*cov1_inv*(X-mu1).transpose()*(-0.5) + (-0.5)*(np.log(cov1_det)) \n",
    "    return p\n",
    "    \n",
    "def g2(X): # Discriminant Function corresponding to Versicolor class\n",
    "\n",
    "    cov2_inv = np.linalg.inv(cov2)\n",
    "    cov2_det = np.linalg.det(cov2)\n",
    "    p = (X-mu2)*cov2_inv*(X-mu2).transpose()*(-0.5) + (-0.5)*(np.log(cov2_det))\n",
    "    return p\n",
    "    \n",
    "def g3(X): # Discriminant Function corresponding to Virginica class\n",
    "\n",
    "    cov3_inv = np.linalg.inv(cov3)\n",
    "    cov3_det = np.linalg.det(cov3)\n",
    "    p = (X-mu3)*cov3_inv*(X-mu3).transpose()*(-0.5) + (-0.5)*(np.log(cov3_det))\n",
    "    return p\n",
    "\n",
    "# Minimum error rate classifier which will select the maximum value from the 3 discriminant functions output and classify \n",
    "# the data point into the corresponding class\n",
    "\n",
    "def classifier(x):\n",
    "    if (g1(x)>g2(x) and g1(x)>g3(x)):\n",
    "        return \"Iris-setosa\"\n",
    "    if (g2(x)>g1(x) and g2(x) >g3(x)):\n",
    "        return \"Iris-versicolor\"\n",
    "    if (g3(x)>g1(x) and g3(x)>g2(x)):\n",
    "        return \"Iris-virginica\"\n",
    "\n",
    "# Displaying the 'True class' label and 'Predicted class' label of a given data point with the help of classifier\n",
    "\n",
    "for i in range(150):\n",
    "    print(\"True class:\",features[i][4],\"\\tPredicted class:\",classifier(data_set[i]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Actual Confusion Matrix\n",
      " [[50  0  0]\n",
      " [ 0 48  2]\n",
      " [ 0  1 49]] \n",
      "\n",
      "Normalised Confusion Matrix\n",
      " [[1.   0.   0.  ]\n",
      " [0.   0.96 0.04]\n",
      " [0.   0.02 0.98]]\n"
     ]
    }
   ],
   "source": [
    "#-----------------------------------------------------Q2----------------------------------------------------------\n",
    "#-------------------------------PART-5: CONSTRUCTING CONFUSION MATRIX---------------------------------------------\n",
    "\n",
    "#Initialising the arrays containing True and Predicted labels\n",
    "true = np.array([])\n",
    "predicted = np.array([])\n",
    "\n",
    "for i in range(150):\n",
    "    true = np.append(true,features[i][4])\n",
    "    predicted = np.append(predicted, classifier(data_set[i]))\n",
    "\n",
    "\n",
    "# Matrix 1 shows the actual number of data points classified \n",
    "matrix1 = confusion_matrix(true, predicted,labels=[\"Iris-setosa\", \"Iris-versicolor\", \"Iris-virginica\"]) \n",
    "\n",
    "\n",
    "# Matrix 2 gives the normalised values and also the probability of making a correct/wrong classification decision\n",
    "matrix2 = confusion_matrix(true, predicted,labels=[\"Iris-setosa\", \"Iris-versicolor\", \"Iris-virginica\"],normalize='true')\n",
    "\n",
    "\n",
    "print(\"Actual Confusion Matrix\\n\",matrix1,'\\n')\n",
    "print(\"Normalised Confusion Matrix\\n\",matrix2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [],
   "source": [
    "#-----------------------------------------------------Q2----------------------------------------------------------\n",
    "#---------------------------------------------PART-6: CONCLUSION---------------------------------------------\n",
    "\n",
    "# Looking at the Confusion Matrix we can conclude that-\n",
    "\n",
    "#1. All data points belonging to Setosa class (50/50) have been correctly classified and hence the accuracy of prediction \n",
    "# is 100%  for setosa data points\n",
    "\n",
    "#2. While for Versicolor class 48/50 samples have been correctly classified while 2 samples have been wrongly classified \n",
    "# into Vergininca class and hence accuracy of prediction for data points in Versicolor class is 96%\n",
    "\n",
    "#3. While for Virginica class 49/50 samples have been correctly classified while 1 sample has been wrongly classified into \n",
    "# Versicolor class and hence accuracy of prediction for data points in Virginica class is 98%\n",
    "\n",
    "#4. Hence overall accuracy of classification using a Naive Bayes Classifier is (1+0.96+0.98)/3 = 0.98, Hence any random \n",
    "# sample selected from the dataset will be correctly classified 98% times."
   ]
  }
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