决策树ID3算法python实现 -- 《机器学习实战》

 from math import log
 import numpy as np
 import matplotlib.pyplot as plt
 import operator

 #计算给定数据集的香农熵
 def calcShannonEnt(dataSet):
     numEntries = len(dataSet)
     labelCounts = {}
     for featVec in dataSet:                         #|
         currentLabel = featVec[-1]                  #|
         if currentLabel not in labelCounts.keys():  #|获取标签类别取值空间(key)及出现的次数(value)
             labelCounts[currentLabel] = 0           #|
         labelCounts[currentLabel] += 1              #|
     shannonEnt = 0.0
     for key in labelCounts:                         #|
         prob = float(labelCounts[key])/numEntries   #|计算香农熵
         shannonEnt -= prob * log(prob, 2)           #|
     return shannonEnt

 #创建数据集
 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

 #按照给定特征划分数据集
 def splitDataSet(dataSet, axis, value):
     retDataSet = []
     for featVec in dataSet:                         #|
         if featVec[axis] == value:                  #|
             reducedFeatVec = featVec[:axis]         #|抽取出符合特征的数据
             reducedFeatVec.extend(featVec[axis+1:]) #|
             retDataSet.append(reducedFeatVec)       #|
     return retDataSet

 #选择最好的数据集划分方式
 def chooseBestFeatureToSplit(dataSet):
     numFeatures = len(dataSet[0]) - 1
     basicEntropy = calcShannonEnt(dataSet)
     bestInfoGain = 0.0; bestFeature = -1
     for i in range(numFeatures):        #计算每一个特征的熵增益
         featlist = [example[i] for example in dataSet]
         uniqueVals = set(featlist)
         newEntropy = 0.0
         for value in uniqueVals:        #计算每一个特征的不同取值的熵增益
             subDataSet = splitDataSet(dataSet, i, value)
             prob = len(subDataSet)/float(len(dataSet))
             newEntropy += prob * calcShannonEnt(subDataSet) #不同取值的熵增加起来就是整个特征的熵增益
         infoGain = basicEntropy - newEntropy
         if (infoGain > bestInfoGain):   #选择最高的熵增益作为划分方式
             bestInfoGain = infoGain
             bestFeature = i
     return bestFeature
 #挑选出现次数最多的类别
 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):
     classList = [example[-1] for example in dataSet]
     if classList.count(classList[0]) == len(classList): #停止条件一：判断所有类别标签是否相同，完全相同则停止继续划分
         return classList[0]
     if len(dataSet[0]) == 1:    #停止条件二：遍历完所有特征时返回出现次数最多的
         return majorityCnt(classList)
     bestFeat = chooseBestFeatureToSplit(dataSet)    #得到列表包含的所有属性值
     bestFeatLabel = labels[bestFeat]
     myTree = {bestFeatLabel:{}}
     del(labels[bestFeat])
     featValues = [example[bestFeat] for example in dataSet]
     uniqueVals = set(featValues)
     for value in uniqueVals:
         subLabels = labels[:]
         myTree[bestFeatLabel][value] = createTree(splitDataSet(dataSet, bestFeat, value), subLabels)
     return myTree

 # Simple unit test of func: createDataSet()
 myDat, labels = createDataSet()
 print (myDat)
 #print (labels)
 # Simple unit test of func: splitDataSet()
 splitData = splitDataSet(myDat,0,1)
 print (splitData)
 # Simple unit test of func: chooseBestFeatureToSplit()
 chooseResult = chooseBestFeatureToSplit(myDat)
 print (chooseResult)
 # Simple unit test of func: createTree(
 myDat, labels = createDataSet()
 myTree = createTree(myDat, labels)
 print(myTree)

Output:

[[1, 1, 'yes'], [1, 1, 'yes'], [1, 0, 'no'], [0, 1, 'no'], [0, 1, 'no']]
[[1, 'yes'], [1, 'yes'], [0, 'no']]
0
{'no surfacing': {0: 'no', 1: {'flippers': {0: 'no', 1: 'yes'}}}}

Reference:

《机器学习实战》