Parametric Classification.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The data is the given in the form of (x^t, r^t) where x is the input and r is class code (1 or 2). The code builds a classifier assuming Gaussian densities:\n",
    "\n",
    "- Estimate parameters of the fitted Gaussians p(x | C_i) and the priors p(C_i) where i is the index of class code\n",
    "- Plot p(x | C_i) and p(C_i | x) \n",
    "- Use the trained model on the test data and calculate the total number of misclassifications"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## read training data from .txt file"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "fileID = fopen('trainingdata.txt','r');\n",
    "trainingData = fscanf(fileID,'%e %e',[2 inf]);\n",
    "trainingData = trainingData';\n",
    "fclose(fileID);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## read test data from .txt file"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "fileID2 = fopen('testdata.txt','r');\n",
    "testdata = fscanf(fileID2,'%e %e',[2 inf]);\n",
    "testdata = testdata';\n",
    "fclose(fileID2);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## classify into two classes:class1 & class2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "trn = trainingData(:,1);\n",
    "class1_index = find(trainingData(:,2)==1);\n",
    "class1 = trn(class1_index);\n",
    "class2_index = find(trainingData(:,2)==2);\n",
    "class2 = trn(class2_index);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Training Phase"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "% compute parameters of fitted gaussians\n",
    "[meanClass1,sigmaClass1] = normfit(class1);\n",
    "[meanClass2,sigmaClass2] = normfit(class2);\n",
    "%sigmaClass2 = sigmaClass1;\n",
    "\n",
    "% compute likelihood P(x|C_i)\n",
    "Range = 0:0.0001:10;\n",
    "likelihood1 = normpdf(Range,meanClass1,sigmaClass1);\n",
    "likelihood2 = normpdf(Range,meanClass2,sigmaClass2);\n",
    "% likelihoodClass1 = normpdf(class1,meanClass1,sigmaClass1);\n",
    "% likelihoodClass2 = normpdf(class2,meanClass2,sigmaClass2);\n",
    "\n",
    "% compute priors P(C_i)\n",
    "priorClass1 = length(class1)/length(trainingData(:,2));\n",
    "priorClass2 = length(class2)/length(trainingData(:,2));\n",
    "\n",
    "evidence = likelihood1*priorClass1 + likelihood2*priorClass2;\n",
    "\n",
    "% compute posterior  P(C_i|x)\n",
    "posteriorClass1 = likelihood1 .* priorClass1./evidence;\n",
    "posteriorClass2 = likelihood2 .* priorClass2./evidence;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAjAAAAGkCAIAAACgjIjwAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA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\n8StqMIZMAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "col = 'brgm';\n",
    "f=figure('Name','Prior and Posterior Probability','NumberTitle','off');\n",
    "plot(Range,likelihood1,col(1),Range,likelihood2,col(2),...\n",
    "    Range,posteriorClass1,col(3),Range,posteriorClass2,col(4));\n",
    "title('Prior and Posterior Probability');\n",
    "hleg = legend('Likelihood1','Likelihood2','Posterior1','Posterior2');\n",
    "set(hleg,'FontAngle','italic','TextColor',[.3,.2,.1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Testing phase"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "testresult = testdata;\n",
    "\n",
    "for i=1:length(testdata(:,1))\n",
    "    \n",
    "    p1 = normpdf(testdata(i,1),meanClass1,sigmaClass1)*priorClass1./evidence;\n",
    "    p2 = normpdf(testdata(i,1),meanClass2,sigmaClass2)*priorClass2./evidence;\n",
    "    if p1>p2\n",
    "        testresult(i,3) = 1;\n",
    "    else\n",
    "        testresult(i,3) = 2;\n",
    "    end\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## computation of misclassification"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "dat = zeros(2,2);\n",
    "for i=1:length(testresult(:,2))\n",
    "    if testresult(i,2)== 1\n",
    "        if testresult(i,3) == 1\n",
    "            dat(1,1) = dat(1,1) + 1;\n",
    "        else\n",
    "            dat(2,1) = dat(2,1) +1;\n",
    "        end\n",
    "    else\n",
    "        if testresult(i,3) == 1\n",
    "            dat(1,2) = dat(1,2) + 1;\n",
    "        else\n",
    "            dat(2,2) = dat(2,2) +1;\n",
    "        end\n",
    "    end\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "dat =\n",
      "\n",
      "    16     3\n",
      "     4    27\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "dat"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Matlab",
   "language": "matlab",
   "name": "matlab"
  },
  "language_info": {
   "codemirror_mode": "octave",
   "file_extension": ".m",
   "help_links": [
    {
     "text": "MetaKernel Magics",
     "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md"
    }
   ],
   "mimetype": "text/x-octave",
   "name": "matlab",
   "version": "0.15.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}