《机器学习实战》决策树

《机器学习实战》K近邻（KNN）分类
上一章写了K近邻分类（见上链接），本章将学习决策树的python实现，虽然K近邻在大多数的时候工作很好，但是没有一个直观的认识，而决策树可以将分类视觉化，使人们对其分类一目了然，当然，对于大型的决策树还是很难进行阅读的。本次的实现决策树只生成树，画出树图，不剪枝。

python实现决策树

##function to calculate the Shannon entropy of a datasetfrom math import logimport operatordef calcShannonEnt(dataSet):    numEntries = len(dataSet)    labelCounts = {}    for featVec in dataSet:        currentLabel = featVec[-1]        if currentLabel not in labelCounts.keys():            labelCounts[currentLabel] = 0        labelCounts[currentLabel] += 1    shannonEnt = 0.0    for key in labelCounts:        prob = float(labelCounts[key])/numEntries        shannonEnt -= prob * log(prob,2)#熵的公式-sum pi*log2(pi) i从1到N    return shannonEntdef createDataSet():    dataSet = [[1,1,'yes'],[1,1,'yes'],[1,0,'no'],[0,1,'no'],[0,1,'no']]    labels = ['no surfacing','flippers']    return dataSet, labels## dataset splitting on a given feature    def splitDataSet(dataSet,axis, value):#按某一个特征分割数据    retDataSet = []    for featVec in dataSet:        if featVec[axis] == value:            reducedFeatVec = featVec[:axis]            reducedFeatVec.extend(featVec[axis+1:])#extend见《python小函数（一）》            retDataSet.append(reducedFeatVec)    return retDataSet## choosing the best feature to split on    def chooseFeature(dataSet):    numFeatures = len(dataSet[0]) - 1    baseEntropy = calcShannonEnt(dataSet)#计算经验熵    bestInfoGain = 0.0; bestFeature = -1    for i in range(numFeatures):        featList = [example[i] for example in dataSet]        uniqueVals = set(featList)#set见《python小函数（一）》        newEntropy = 0.0        for value in uniqueVals:            subDataSet = splitDataSet(dataSet, i, value)            prob = len(subDataSet)/float(len(dataSet))            newEntropy += prob * calcShannonEnt(subDataSet)#计算条件经验熵        infoGain = baseEntropy - newEntropy#信息增益        if (infoGain > bestInfoGain):            bestInfoGain = infoGain            bestFeature = i #选择最佳分类特征i    return bestFeaturedef majorityCnt(classList):#多数表决原则    classCount = {}    for vote in classList:        if vote not in classCount.keys(): classCount[vote] = 0 #也可以用classCount.get(vote,0)        classCount[vote] +=1    sortedClassCount = sorted(classCount.iteritems(), key = operator.itemgetter(1), reverse = True)    return sortedClassCount[0][0] ##trees-building code  def createTree(dataSet, labels):    classList = [example[-1] for example in dataSet]#取最后一个，即类    if classList.count(classList[0]) == len(classList):        return classList[0]    if len(dataSet[0]) == 1:        return majorityCnt(classList)    bestFeat = chooseFeature(dataSet)    bestFeatLabel = labels[bestFeat]    myTree = {bestFeatLabel:{}}#字典里面又包含字典，形成树    del(labels[bestFeat])#删除最佳特征标签，然后再从剩下的特征选取最佳特征    featValues = [example[bestFeat] for example in dataSet]    uniqueVals = set(featValues)    for value in uniqueVals:        subLabels = labels[:]        myTree[bestFeatLabel][value] = createTree(splitDataSet(dataSet, bestFeat, value), subLabels)#递归调用    return myTree##Classification function for an existing decision treedef classify(inputTree,featLabels,testVec):    firstStr = inputTree.keys()[0]    secondDict = inputTree[firstStr]    featIndex = featLabels.index(firstStr)    for key in secondDict.keys():        if testVec[featIndex]== key:            if type(secondDict[key]).__name__=='dict':                classLabel = classify(secondDict[key],featLabels,testVec)            else: classLabel = secondDict[key]    return classLabel##methods for persisting the decision tree with pickledef storeTree(inputTree,filename):    import pickle    fw = open(filename,"w")    pickle.dump(inputTree,fw)    fw.close()def grabTree(filename):    import pickle    fr = open(filename)    return pickle.load(fr)##plotting tree nodes with text annotationsimport matplotlib.pyplot as pltdecisionNode = dict(boxstyle="sawtooth",fc="0.8")leafNode = dict(boxstyle="round4", fc="0.8")arrow_args = dict(arrowstyle="<-")def plotNode(nodeTxt,centerPt,parentPt,nodeType):    createPlot.ax1.annotate(nodeTxt,xy=parentPt,xycoords='axes fraction',xytext=centerPt,textcoords='axes fraction',va="center",ha="center",bbox=nodeType,arrowprops=arrow_args)'''def createPlot():    fig = plt.figure(1,facecolor='white')    fig.clf()    createPlot.ax1 = plt.subplot(111,frameon=False)    plotNode('a decision node',(0.5,0.1),(0.1,0.5),decisionNode)    plotNode('a leaf node',(0.8,0.1),(0.3,0.8),leafNode)    plt.show()''' ## identifying the number of leaves in a tree and the depth  def getNumLeafs(myTree):    numLeafs = 0    firstStr = myTree.keys()[0]    secondDict= myTree[firstStr]    for key in secondDict.keys():        if type(secondDict[key]).__name__=='dict':            numLeafs += getNumLeafs(secondDict[key])        else: numLeafs += 1    return numLeafsdef getTreeDepth(myTree):    maxDepth = 0    firstStr = myTree.keys()[0]    secondDict = myTree[firstStr]    for key in secondDict.keys():        if type(secondDict[key]).__name__=='dict':            thisDepth = 1 + getTreeDepth(secondDict[key])        else: thisDepth = 1        if thisDepth > maxDepth: maxDepth = thisDepth    return maxDepthdef retrieveTree(i):    listOfTrees = [{'no surfacing':{0:'no',1:{'flippers':{0:'no',1:'yes'}}}}, {'no surfacing':{0:'no',1:{'flippers':{0:{'head':{0:'no',1:'yes'}},1:'no'}}}}]    return listOfTrees[i]## The plotTree functiondef plotMidText(cntrPt,parentPt,txtString):    xMid = (parentPt[0]-cntrPt[0])/2.0 + cntrPt[0]    yMid = (parentPt[1]-cntrPt[1])/2.0 + cntrPt[1]    createPlot.ax1.text(xMid,yMid,txtString)def plotTree(myTree,parentPt,nodeTxt):    numLeafs = getNumLeafs(myTree)    getTreeDepth(myTree)    firstStr = myTree.keys()[0]    cntrPt = (plotTree.xOff + (1.0 + float(numLeafs))/2.0/plotTree.totalW,plotTree.yOff)    plotMidText(cntrPt,parentPt,nodeTxt)    plotNode(firstStr, cntrPt,parentPt, decisionNode)    secondDict = myTree[firstStr]    plotTree.yOff = plotTree.yOff - 1.0/plotTree.totalD    for key in secondDict.keys():        if type(secondDict[key]).__name__ == 'dict':            plotTree(secondDict[key],cntrPt,str(key))        else:            plotTree.xOff = plotTree.xOff + 1.0/plotTree.totalW            plotNode(secondDict[key],(plotTree.xOff,plotTree.yOff),cntrPt,leafNode)            plotMidText((plotTree.xOff,plotTree.yOff),cntrPt,str(key))    plotTree.yOff = plotTree.yOff + 1.0/plotTree.totalDdef createPlot(inTree):    fig = plt.figure(1,facecolor='white')    fig.clf()    axprops = dict(xticks=[],yticks=[])    createPlot.ax1 = plt.subplot(111,frameon=False,**axprops)    plotTree.totalW = float(getNumLeafs(inTree))    plotTree.totalD = float(getTreeDepth(inTree))    plotTree.xOff = -0.5/plotTree.totalW    plotTree.yOff = 1.0    plotTree(inTree,(0.5,1.0),'')    plt.show()fr = open(r'c:/Users/ll/Documents/lenses.txt')lenses = [inst.strip().split('\t') for inst in fr.readlines()]lensesLabels = ['age','prescript','astigmatic','tearRate']