AdaBoost.ipynb

{
 "metadata": {
  "name": ""
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def loadSimpData():\n",
      "    datMat = matrix([[ 1. , 2.1],\n",
      "    [ 2. , 1.1],\n",
      "    [ 1.3, 1. ],\n",
      "    [ 1. , 1. ],\n",
      "    [ 2. , 1. ]])\n",
      "    classLabels = [1.0, 1.0, -1.0, -1.0, 1.0]\n",
      "    return datMat,classLabels\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "datMat,label = loadSimpData()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def stumpClassify(dataset, dim, threashold, threshIneq):\n",
      "    retArray = ones((shape(dataset)[0],1))\n",
      "    if threshIneq == 'lt':\n",
      "        retArray[dataset[:,dim]<=threashold] = -1\n",
      "    else:\n",
      "        retArray[dataset[:,dim]>threashold] = -1\n",
      "    return retArray"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def buildStump(dataset, classifyLabel, D):\n",
      "    m,n = shape(dataset);classifyLabel = mat(classifyLabel).T\n",
      "    numsteps = 10\n",
      "    bestStump = {}\n",
      "    minError = inf\n",
      "    for i in range(n):\n",
      "        rangeMax = dataset[:,i].max()\n",
      "        rangeMin = dataset[:,i].min()\n",
      "        stepsize = (rangeMax - rangeMin)/float(numsteps)\n",
      "        for j in range(-1, int(numsteps)+1):\n",
      "            for inequality in ['lt','gt']:\n",
      "                predictVal = \\\n",
      "                    stumpClassify(dataset, i, float(j)*stepsize+ rangeMin, inequality)\n",
      "                errArr =  mat(ones((m,1)))\n",
      "                errArr[classifyLabel==predictVal] = 0\n",
      "                weightedError = D.T*errArr\n",
      "                print \"split: dim %d, thresh %.2f, thresh ineqal: \\\n",
      "                    %s, the weighted error is %.3f\" %(i, float(j)*stepsize+ rangeMin, inequality, weightedError)\n",
      "                if weightedError < minError:\n",
      "                    minError = weightedError\n",
      "                    bestClasEst = predictVal.copy()\n",
      "                    bestStump['dim'] = i\n",
      "                    bestStump['thresh'] = float(j)*stepsize+ rangeMin\n",
      "                    bestStump['ineq'] = inequality\n",
      "    return bestStump, minError, bestClasEst\n",
      "\n",
      "                "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 36
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "D = mat(ones((5,1))/5)\n",
      "buildStump(datMat,label,D)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "split: dim 0, thresh 0.90, thresh ineqal:                     lt, the weighted error is 0.400\n",
        "split: dim 0, thresh 0.90, thresh ineqal:                     gt, the weighted error is 0.600\n",
        "split: dim 0, thresh 1.00, thresh ineqal:                     lt, the weighted error is 0.400\n",
        "split: dim 0, thresh 1.00, thresh ineqal:                     gt, the weighted error is 0.600\n",
        "split: dim 0, thresh 1.10, thresh ineqal:                     lt, the weighted error is 0.400\n",
        "split: dim 0, thresh 1.10, thresh ineqal:                     gt, the weighted error is 0.600\n",
        "split: dim 0, thresh 1.20, thresh ineqal:                     lt, the weighted error is 0.400\n",
        "split: dim 0, thresh 1.20, thresh ineqal:                     gt, the weighted error is 0.600\n",
        "split: dim 0, thresh 1.30, thresh ineqal:                     lt, the weighted error is 0.200\n",
        "split: dim 0, thresh 1.30, thresh ineqal:                     gt, the weighted error is 0.800\n",
        "split: dim 0, thresh 1.40, thresh ineqal:                     lt, the weighted error is 0.200\n",
        "split: dim 0, thresh 1.40, thresh ineqal:                     gt, the weighted error is 0.800\n",
        "split: dim 0, thresh 1.50, thresh ineqal:                     lt, the weighted error is 0.200\n",
        "split: dim 0, thresh 1.50, thresh ineqal:                     gt, the weighted error is 0.800\n",
        "split: dim 0, thresh 1.60, thresh ineqal:                     lt, the weighted error is 0.200\n",
        "split: dim 0, thresh 1.60, thresh ineqal:                     gt, the weighted error is 0.800\n",
        "split: dim 0, thresh 1.70, thresh ineqal:                     lt, the weighted error is 0.200\n",
        "split: dim 0, thresh 1.70, thresh ineqal:                     gt, the weighted error is 0.800\n",
        "split: dim 0, thresh 1.80, thresh ineqal:                     lt, the weighted error is 0.200\n",
        "split: dim 0, thresh 1.80, thresh ineqal:                     gt, the weighted error is 0.800\n",
        "split: dim 0, thresh 1.90, thresh ineqal:                     lt, the weighted error is 0.200\n",
        "split: dim 0, thresh 1.90, thresh ineqal:                     gt, the weighted error is 0.800\n",
        "split: dim 0, thresh 2.00, thresh ineqal:                     lt, the weighted error is 0.600\n",
        "split: dim 0, thresh 2.00, thresh ineqal:                     gt, the weighted error is 0.400\n",
        "split: dim 1, thresh 0.89, thresh ineqal:                     lt, the weighted error is 0.400\n",
        "split: dim 1, thresh 0.89, thresh ineqal:                     gt, the weighted error is 0.600\n",
        "split: dim 1, thresh 1.00, thresh ineqal:                     lt, the weighted error is 0.200\n",
        "split: dim 1, thresh 1.00, thresh ineqal:                     gt, the weighted error is 0.800\n",
        "split: dim 1, thresh 1.11, thresh ineqal:                     lt, the weighted error is 0.400\n",
        "split: dim 1, thresh 1.11, thresh ineqal:                     gt, the weighted error is 0.600\n",
        "split: dim 1, thresh 1.22, thresh ineqal:                     lt, the weighted error is 0.400\n",
        "split: dim 1, thresh 1.22, thresh ineqal:                     gt, the weighted error is 0.600\n",
        "split: dim 1, thresh 1.33, thresh ineqal:                     lt, the weighted error is 0.400\n",
        "split: dim 1, thresh 1.33, thresh ineqal:                     gt, the weighted error is 0.600\n",
        "split: dim 1, thresh 1.44, thresh ineqal:                     lt, the weighted error is 0.400\n",
        "split: dim 1, thresh 1.44, thresh ineqal:                     gt, the weighted error is 0.600\n",
        "split: dim 1, thresh 1.55, thresh ineqal:                     lt, the weighted error is 0.400\n",
        "split: dim 1, thresh 1.55, thresh ineqal:                     gt, the weighted error is 0.600\n",
        "split: dim 1, thresh 1.66, thresh ineqal:                     lt, the weighted error is 0.400\n",
        "split: dim 1, thresh 1.66, thresh ineqal:                     gt, the weighted error is 0.600\n",
        "split: dim 1, thresh 1.77, thresh ineqal:                     lt, the weighted error is 0.400\n",
        "split: dim 1, thresh 1.77, thresh ineqal:                     gt, the weighted error is 0.600\n",
        "split: dim 1, thresh 1.88, thresh ineqal:                     lt, the weighted error is 0.400\n",
        "split: dim 1, thresh 1.88, thresh ineqal:                     gt, the weighted error is 0.600\n",
        "split: dim 1, thresh 1.99, thresh ineqal:                     lt, the weighted error is 0.400\n",
        "split: dim 1, thresh 1.99, thresh ineqal:                     gt, the weighted error is 0.600\n",
        "split: dim 1, thresh 2.10, thresh ineqal:                     lt, the weighted error is 0.600\n",
        "split: dim 1, thresh 2.10, thresh ineqal:                     gt, the weighted error is 0.400\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 37,
       "text": [
        "({'dim': 0, 'ineq': 'lt', 'thresh': 1.3},\n",
        " matrix([[ 0.2]]),\n",
        " array([[-1.],\n",
        "       [ 1.],\n",
        "       [-1.],\n",
        "       [-1.],\n",
        "       [ 1.]]))"
       ]
      }
     ],
     "prompt_number": 37
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def adaBoostTrainDS(dataArr,classLabels,numIt=40):\n",
      "    weakClassArr = []\n",
      "    m = shape(dataArr)[0]\n",
      "    D = mat(ones((m,1))/m)   #init D to all equal\n",
      "    aggClassEst = mat(zeros((m,1)))\n",
      "    for i in range(numIt):\n",
      "        bestStump,error,classEst = buildStump(dataArr,classLabels,D)#build Stump\n",
      "        #print \"D:\",D.T\n",
      "        alpha = float(0.5*log((1.0-error)/max(error,1e-16)))#calc alpha, throw in max(error,eps) to account for error=0\n",
      "        bestStump['alpha'] = alpha  \n",
      "        weakClassArr.append(bestStump)                  #store Stump Params in Array\n",
      "        #print \"classEst: \",classEst.T\n",
      "        expon = multiply(-1*alpha*mat(classLabels).T,classEst) #exponent for D calc, getting messy\n",
      "        D = multiply(D,exp(expon))                              #Calc New D for next iteration\n",
      "        D = D/D.sum()\n",
      "        #calc training error of all classifiers, if this is 0 quit for loop early (use break)\n",
      "        aggClassEst += alpha*classEst\n",
      "        #print \"aggClassEst: \",aggClassEst.T\n",
      "        aggErrors = multiply(sign(aggClassEst) != mat(classLabels).T,ones((m,1)))\n",
      "        errorRate = aggErrors.sum()/m\n",
      "        print \"total error: \",errorRate\n",
      "        if errorRate == 0.0: break\n",
      "    return weakClassArr,aggClassEst"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 52
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def adaClassify(datToClass,classifierArr):\n",
      "    dataMatrix = mat(datToClass)#do stuff similar to last aggClassEst in adaBoostTrainDS\n",
      "    m = shape(dataMatrix)[0]\n",
      "    aggClassEst = mat(zeros((m,1)))\n",
      "    for i in range(len(classifierArr)):\n",
      "        classEst = stumpClassify(dataMatrix,classifierArr[i]['dim'],\\\n",
      "                                 classifierArr[i]['thresh'],\\\n",
      "                                 classifierArr[i]['ineq'])#call stump classify\n",
      "        aggClassEst += classifierArr[i]['alpha']*classEst\n",
      "        print aggClassEst\n",
      "    return sign(aggClassEst)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def plotROC(predStrengths, classLabels):\n",
      "    import matplotlib.pyplot as plt\n",
      "    cur = (1.0,1.0) #cursor\n",
      "    ySum = 0.0 #variable to calculate AUC\n",
      "    numPosClas = sum(array(classLabels)==1.0)\n",
      "    yStep = 1/float(numPosClas); xStep = 1/float(len(classLabels)-numPosClas)\n",
      "    sortedIndicies = predStrengths.argsort()#get sorted index, it's reverse\n",
      "    fig = plt.figure()\n",
      "    fig.clf()\n",
      "    ax = plt.subplot(111)\n",
      "    #loop through all the values, drawing a line segment at each point\n",
      "    for index in sortedIndicies.tolist()[0]:\n",
      "        if classLabels[index] == 1.0:\n",
      "            delX = 0; delY = yStep;\n",
      "        else:\n",
      "            delX = xStep; delY = 0;\n",
      "            ySum += cur[1]\n",
      "        #draw line from cur to (cur[0]-delX,cur[1]-delY)\n",
      "        ax.plot([cur[0],cur[0]-delX],[cur[1],cur[1]-delY], c='b')\n",
      "        cur = (cur[0]-delX,cur[1]-delY)\n",
      "    ax.plot([0,1],[0,1],'b--')\n",
      "    plt.xlabel('False positive rate'); plt.ylabel('True positive rate')\n",
      "    plt.title('ROC curve for AdaBoost horse colic detection system')\n",
      "    ax.axis([0,1,0,1])\n",
      "    plt.show()\n",
      "    print \"the Area Under the Curve is: \",ySum*xStep"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a = array([1,2,3])\n",
      "a.argsort()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 41,
       "text": [
        "array([0, 1, 2])"
       ]
      }
     ],
     "prompt_number": 41
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def loadDataSet(fileName):      #general function to parse tab -delimited floats\n",
      "    numFeat = len(open(fileName).readline().split('\\t')) #get number of fields \n",
      "    dataMat = []; labelMat = []\n",
      "    fr = open(fileName)\n",
      "    for line in fr.readlines():\n",
      "        lineArr =[]\n",
      "        curLine = line.strip().split('\\t')\n",
      "        for i in range(numFeat-1):\n",
      "            lineArr.append(float(curLine[i]))\n",
      "        dataMat.append(lineArr)\n",
      "        labelMat.append(float(curLine[-1]))\n",
      "    return dataMat,labelMat"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 43
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "datArr,labelArr = loadDataSet('machinelearninginaction/Ch07/horseColicTraining2.txt')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 46
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "classifierArray,aggClassEst = adaBoostTrainDS(datArr,labelArr,40)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "total error:  0.284280936455\n",
        "total error: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 0.284280936455\n",
        "total error: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 0.247491638796\n",
        "total error: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 0.247491638796\n",
        "total error: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 0.254180602007\n",
        "total error: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 0.240802675585\n",
        "total error: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 0.240802675585\n",
        "total error: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 0.220735785953\n",
        "total error: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 0.247491638796\n",
        "total error: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 0.230769230769\n",
        "total error: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 0.240802675585\n",
        "total error: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 0.214046822742\n",
        "total error: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 0.227424749164\n",
        "total error: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 0.217391304348\n",
        "total error: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 0.220735785953\n",
        "total error: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 0.217391304348\n",
        "total error: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 0.224080267559\n",
        "total error: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 0.224080267559\n",
        "total error: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 0.230769230769\n",
        "total error: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 0.224080267559\n",
        "total error: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 0.214046822742\n",
        "total error: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 0.207357859532\n",
        "total error: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 0.224080267559\n",
        "total error: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 0.224080267559\n",
        "total error: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 0.214046822742\n",
        "total error: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 0.220735785953\n",
        "total error: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 0.204013377926\n",
        "total error: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 0.207357859532\n",
        "total error: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 0.210702341137\n",
        "total error: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 0.217391304348\n",
        "total error: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 0.210702341137\n",
        "total error: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 0.217391304348\n",
        "total error: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 0.207357859532\n",
        "total error: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 0.210702341137\n",
        "total error: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 0.207357859532\n",
        "total error: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 0.207357859532\n",
        "total error: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 0.197324414716\n",
        "total error: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 0.190635451505\n",
        "total error: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 0.200668896321\n",
        "total error: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 0.197324414716\n"
       ]
      }
     ],
     "prompt_number": 53
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def plotROC(predStrengths, classLabels):\n",
      "    import matplotlib.pyplot as plt\n",
      "    cur = (1.0,1.0) #cursor\n",
      "    ySum = 0.0 #variable to calculate AUC\n",
      "    numPosClas = sum(array(classLabels)==1.0)\n",
      "    yStep = 1/float(numPosClas); xStep = 1/float(len(classLabels)-numPosClas)\n",
      "    sortedIndicies = predStrengths.argsort()#get sorted index, it's reverse\n",
      "    fig = plt.figure()\n",
      "    fig.clf()\n",
      "    ax = plt.subplot(111)\n",
      "    #loop through all the values, drawing a line segment at each point\n",
      "    for index in sortedIndicies.tolist()[0]:\n",
      "        if classLabels[index] == 1.0:\n",
      "            delX = 0; delY = yStep;\n",
      "        else:\n",
      "            delX = xStep; delY = 0;\n",
      "            ySum += cur[1]\n",
      "        #draw line from cur to (cur[0]-delX,cur[1]-delY)\n",
      "        ax.plot([cur[0],cur[0]-delX],[cur[1],cur[1]-delY], c='b')\n",
      "        cur = (cur[0]-delX,cur[1]-delY)\n",
      "    ax.plot([0,1],[0,1],'b--')\n",
      "    plt.xlabel('False positive rate'); plt.ylabel('True positive rate')\n",
      "    plt.title('ROC curve for AdaBoost horse colic detection system')\n",
      "    ax.axis([0,1,0,1])\n",
      "    plt.show()\n",
      "    print \"the Area Under the Curve is: \",ySum*xStep"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 50
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plotROC(aggClassEst.T,labelArr)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAYYAAAEZCAYAAACTsIJzAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x38f6a10>"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "the Area Under the Curve is:  0.89181911041\n"
       ]
      }
     ],
     "prompt_number": 54
    }
   ],
   "metadata": {}
  }
 ]
}