决策树ID3算法

一、构造决策树步骤：

1.数据准备

数据离散化

2.划分数据

• 计算数据集香农熵
• 计算特征值信息增量，最大的为最好划分

3.递归构造决策树

二、代码模块

1.计算香农熵：

def calcShannonEnt(dataSet):    numEntries = len(dataSet)    labelCounts = {}    for featVec in dataSet: #the the number of unique elements and their occurance        currentLabel = featVec[-1]        if currentLabel not in labelCounts.keys(): labelCounts[currentLabel] = 0        labelCounts[currentLabel] += 1    shannonEnt = 0.0    for key in labelCounts:#公式：H=-∑（n）（i-1）p(xi)log2p(xi)        prob = float(labelCounts[key])/numEntries #选择该分类概率p(xi)        shannonEnt -= prob * log(prob,2) #log base 2    return shannonEnt

2.划分数据集（按给定特征值划分）

def splitDataSet(dataSet, axis, value):    retDataSet = []    for featVec in dataSet:        if featVec[axis] == value:            reducedFeatVec = featVec[:axis]     #chop out axis used for splitting            reducedFeatVec.extend(featVec[axis+1:])            retDataSet.append(reducedFeatVec)    return retDataSet

3.选择最好的数据集划分方式

• 选取特征值
• 划分数据
• 计算最好的划分数据特征

def chooseBestFeatureToSplit(dataSet):    numFeatures = len(dataSet[0]) - 1      #the last column is used for the labels    baseEntropy = calcShannonEnt(dataSet)    bestInfoGain = 0.0; bestFeature = -1    for i in range(numFeatures):        #iterate over all the features        featList = [example[i] for example in dataSet]#create a list of all the examples of this feature        uniqueVals = set(featList)       #get a set of unique values        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     #calculate the info gain; ie reduction in entropy        if (infoGain > bestInfoGain):       #compare this to the best gain so far            bestInfoGain = infoGain         #if better than current best, set to best            bestFeature = i    return bestFeature                      #returns an integer

4.递归构造决策树

递归退出条件：

• 所有的类标签完全相同，直接返回该类标签
• 使用完了所有特征，但是还是不能将数据集划分成只包含唯一类别的分组（返回值:挑出出现次数最多的类别）

def createTree(dataSet,labels):    classList = [example[-1] for example in dataSet] #all labels    if classList.count(classList[0]) == len(classList):         return classList[0]#stop splitting when all of the classes are equal    if len(dataSet[0]) == 1: #stop splitting when there are no more features in dataSet        return majorityCnt(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:        subLabels = labels[:]       #copy all of labels, so trees don't mess up existing labels        myTree[bestFeatLabel][value] = createTree(splitDataSet(dataSet, bestFeat, value),subLabels)    return myTree