自己造轮子是理解算法的好办法，今天写了一个ID3的，对决策树理解更加深刻了

from math import log
import operator

#计算信息熵，Ent(D)
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


#按照给定特征划分数据集,axis是特征，value是特征的值，返回的是DV
def splitDataSet(dataSet, axis, value):
    retDataSet = []
    for featVec in dataSet:
        if featVec[axis] == value:
            reducedFeatVec = featVec[:axis]
            reducedFeatVec.extend(featVec[axis+1:])
            retDataSet.append(reducedFeatVec)
    return retDataSet

#计算信息增益
def chooseBestFeatureToSplit(dataSet):
    numFeatures = len(dataSet[0]) - 1      
    baseEntropy = calcShannonEnt(dataSet)
    bestInfoGain = 0.0  #初始化增益和最佳特征
    bestFeature = -1
    for i in range(numFeatures):       
        featList = [example[i] for example in dataSet] #获得属性的各种取值
        uniqueVals = set(featList)       
        newEntropy = 0.0
        for value in uniqueVals:
            subDataSet = splitDataSet(dataSet, i, value)
            prob = len(subDataSet)/float(len(dataSet))
            newEntropy += prob * calcShannonEnt(subDataSet)     
        infoGain = baseEntropy - newEntropy     
        if (infoGain > bestInfoGain):       
            bestInfoGain = infoGain         
            bestFeature = i
    return bestFeature     

#终止条件，属性用光的情况下，不同标签选择数量最多的当做叶节点标签
def majorityCht(classList):
    classCount = {}
    for vote in classList:
        if vote not in classList.keys():
            classCount[vote] = 0
        classCount[vote] += 1
    sortedClassCount = sorted(classCount.items(), key = operator.itemgetter(1), \
                              reverse = True)
    return sortedClassCount[0][0]

#生成树,labels是所有特征组成的列表
def createTree(dataSet, labels):
    classList = [example[-1] for example in dataSet]
    if classList.count(classList[0]) == len(classList):  #终止条件一：如果标签都一样没必要划分
        return classList[0]
    if len(dataSet[0]) == 1: #终止条件二：如果没有属性了，无法划分，返回最多的标签
        return majorityCht(classList)
    bestFeat = chooseBestFeatureToSplit(dataSet)
    bestFeatLabel = labels[bestFeat]
    myTree = {bestFeatLabel:{}}
    del(labels[bestFeat])
    featValues = [example[bestFeat] for example in dataSet]
    uniqueVals = set(featValues)
    for value in uniqueVals:  #树的递归调用
        subLabels = labels[:]
        myTree[bestFeatLabel][value] = createTree(splitDataSet(dataSet, bestFeat, value)\
              ,subLabels)
    return myTree


#测试部分：使用决策树的分类函数
def 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