机器学习——决策树

 什么是决策树？

        分类决策树模型是一种描述对实例进行分类的树形结构。 决策树由结点和有向边组成。结点有两种类型：内部结点和叶 节点。内部结点表示一个特征或属性，叶节点表示一个类

# 相亲角
#
# ID    白	富	美
# 1	    0	0	0
# 2	    0	0	1
# 3	    0	1	0
# 4	    0	1	1
# 5	    1	0	0
# 6	    1	0	1
# 7	    1	1	0
# 8	    1	1	1

from math import log
import operator

def calcShannonEnt(dataSet):
    numEntries=len(dataSet)
    labelCounts={}
    for featVec in dataSet:
        currentLabel=featVec[-1]                     #提取标签信息
        if currentLabel not in labelCounts.keys():   #如果标签没有放入统计次数的字典，添加进去
            labelCounts[currentLabel]=0
        labelCounts[currentLabel]+=1                 #label计数

    shannonEnt=0.0                                   #经验熵

    for key in labelCounts:
        prob=float(labelCounts[key])/numEntries      #选择该标签的概率
        shannonEnt-=prob*log(prob,2)                 #利用公式计算
    return shannonEnt                                #返回经验熵


def createDataSet():

    dataSet=[[0, 0, 0, 'no'],
             [0, 0, 1, 'maybe'],
             [0, 1, 0, 'yes'],
             [0, 1, 1, 'yes'],
             [1, 0, 0, 'maybe'],
             [1, 0, 1, 'maybe'],
             [1, 1, 0, 'yes'],
             [1, 1, 1, 'yes']]
    labels=['白','富','美','去否']

    return dataSet,labels

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

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

        print("第%d个特征的增益为%.3f" % (i, infoGain))

        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.items(),key=operator.itemgetter(1),reverse=True)
        return sortedClassCount[0][0]


def createTree(dataSet,labels,featLabels):

    classList=[example[-1] for example in dataSet]

    if classList.count(classList[0])==len(classList):
        return classList[0]

    if len(dataSet[0])==1:
        return majorityCnt(classList)

    bestFeat=chooseBestFeatureToSplit(dataSet)

    bestFeatLabel=labels[bestFeat]
    featLabels.append(bestFeatLabel)

    myTree={bestFeatLabel:{}}

    del(labels[bestFeat])

    featValues=[example[bestFeat] for example in dataSet]

    uniqueVls=set(featValues)

    for value in uniqueVls:
        myTree[bestFeatLabel][value]=createTree(splitDataSet(dataSet,bestFeat,value),
                                               labels,featLabels)
    return myTree

if __name__=='__main__':
    dataSet,labels=createDataSet()
    featLabels=[]
    myTree=createTree(dataSet,labels,featLabels)
    print(myTree)

运行输出

第0个特征的增益为0.156
第1个特征的增益为1.000
第2个特征的增益为0.156
第0个特征的增益为0.311
第1个特征的增益为0.311
第0个特征的增益为1.000
{'富': {0: {'白': {0: {'美': {0: 'no', 1: 'maybe'}}, 1: 'maybe'}}, 1: 'yes'}}

Process finished with exit code 0