id3算法python实现

import numpy as np
import operator

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

#计算给定数据集的香浓熵
def calcShannonEnt(dataSet):
    numEntries = len(dataSet)  #计算机数据有多少行

    labelCounts = {}        #创建一个空字典
    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 = labelCounts[key]/numEntries
        shannonEnt = shannonEnt - prob*np.log2(prob)
    return shannonEnt

def splitDataSet(dataSet,axis,value):
    retDataSet = []
    for featVec in dataSet:
        if featVec[axis]==value:
            reduceFeatVec = featVec[:axis]
            reduceFeatVec.extend(featVec[axis+1:])
            retDataSet.append(reduceFeatVec)
    return retDataSet

# 循环计算香农熵和splitDataSet()函数，找到最好的特征划分方式
def chooseBestFeatureToSplit(dataSet):
    numFeatures = len(dataSet[0])-1
    baseEntropy = calcShannonEnt(dataSet)
    bestInfoGain = 0.0
    bestFeature = -1

    for i in range(numFeatures):
        featList = [example[i] for example in dataSet]
        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

def majorityCnt(classList):
    classCount = {}
    for vote in classList:
        if vote not in classCount.keys():
            classCount = 0
        classCount[vote] += 1
    sortedClassCount = sorted(classCount.iteritems(), key=operator.itemgetter(1), reverse=True)
    return sortedClassCount[0][0]

# 参数：数据集和标签列表
def createTree(dataSet,labels):
    classList = [example[-1] for example in dataSet]        # 包含了数据集的所有类标签
    if classList.count(classList[0]) == len(classList):     # 当所有的类都相等时停止分裂
        return classList[0]
    if len(dataSet[0]) == 1:                                    # 使用完了所有特征，仍然不能将数据集划分成仅包含唯一类别的分组
        return majorityCnt(classList)                           # 采用多数多数原则选出分组
    bestFeat = chooseBestFeatureToSplit(dataSet)                # 选出最佳的特征值
    bestFeatLabel = labels[bestFeat]                            # 获取该特征的名称

    # 这里直接使用字典变量来存储树信息，这对于绘制树形图很重要。
    myTree = {bestFeatLabel:{}}                                 # 当前数据集选取最好的特征存储在bestFeat中
    del(labels[bestFeat])                                       # 删除已经在选取的特征
    featValues = [example[bestFeat] for example in dataSet]
    uniqueVlas = set(featValues)
    for value in uniqueVlas:
        subLabels = labels[:]                                   # 复制所有标签，这样树就不会破坏现有的标签
        myTree[bestFeatLabel][value] = createTree(splitDataSet(dataSet, bestFeat, value),subLabels)
    return myTree
myDat,labels = createDataSet()
print("myDat:",myDat)

print(len(myDat[0]) -1 )
c = chooseBestFeatureToSplit(myDat)

MyTree = createTree(myDat,labels)
print(MyTree)