决策树在机器学习中的实现-优快云博客

本文介绍了如何使用Python实现决策树算法，包括计算信息熵、创建数据集、选择最佳特征进行分割，以及构建递归决策树的过程。通过示例展示了如何通过特征选择和概率计算来构建决策树模型。

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from math import log

#以决策为标准计算信息熵
def 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)
    return shannonEnt

def creatDataSet():
    dataSet = [[1,1,'yes'],[1,1,'yes'],[1,0,'no'],[0,1,'no'],[0,1,'no']]
    labels = ['no surfacing','flippers']
    return dataSet,labels

def splitDataSet(dataSet,axis,value):
    retDataSet = []#根据特征新建链表
    for featVec in dataSet:
        if featVec[axis] == value:
            reducedFeatVec = featVec[:axis]
            reducedFeatVec.extend(featVec[axis+1:])
            retDataSet.append(reducedFeatVec)
    return retDataSet

#选择信息熵最小的最佳特征
def chooseBestFeatureToSplit(dataSet):
    numFeatures = len(dataSet[0])-1
    baseEntropy = calcShannonEnt(dataSet)#比较标准为最末尾的特征
    bestInfoGain =0.0;bestFeature =-1
    for i in range(numFeatures):
        featList = [example[i] for example in dataSet]#建立特征i的链表
        uniqueVals = set(featList)#set不允许重复
        newEntropy =0.0
        for value in uniqueVals:
            subDataSet = splitDataSet(dataSet,i,value)
            prob = len(subDataSet)/float(len(dataSet))#计算满足特征i为value的概率
            newEntropy += prob*calcShannonEnt(subDataSet)
        infoGain = baseEntropy - newEntropy
        if(infoGain > bestInfoGain):
            bestInfoGain = infoGain
            bestFeature = i
    return bestFeature
#
def majorityCnt(classList):
    classCount ={}
    for vote in classList:
        if vote not in classCount.keys():classCount[vote] = 0
        classCount[vote] += 1
    sortedClassCount = sorted(classCount.iteritems(),key = operator.itemgetter(1),reverse = True)
    return sortedClassCount[0][0]

#构建递归决策树
def createTree(dataSet,labels):
    classList = [example[-1] for example in dataSet]
    if classList.count(classList[0])==len(classList):#如果决策全相同，则停止分割
        return classList[0]
    if len(dataSet[0])==1:#没有特征了，则返回出现次数多的
        return majorityCnt(classList)
    bestFeat = chooseBestFeatureToSplit(dataSet)#选择最佳的特征的下坐标
    bestFeatLabel = labels[bestFeat]
    myTree = {bestFeatLabel:{}}
    del(labels[bestFeat])#删除这个特征
    featValues = [example[bestFeat] for example in dataSet]
    uniqueVals = set(featValues)#最佳特征的值set
    for value in uniqueVals:
        subLabels = labels[:]
        myTree[bestFeatLabel][value] = createTree(splitDataSet(dataSet,bestFeat,value),subLabels)
    return myTree