python实现决策树C4.5算法详解(在ID3基础上改进)

from numpy import *from scipy import *from math import logimport operator#计算给定数据的香浓熵：def calcShannonEnt(dataSet): numEntries = len(dataSet)  labelCounts = {} #类别字典（类别的名称为键，该类别的个数为值） for featVec in dataSet:  currentLabel = featVec[-1]   if currentLabel not in labelCounts.keys(): #还没添加到字典里的类型   labelCounts[currentLabel] = 0;  labelCounts[currentLabel] += 1; shannonEnt = 0.0  for key in labelCounts: #求出每种类型的熵  prob = float(labelCounts[key])/numEntries #每种类型个数占所有的比值  shannonEnt -= prob * log(prob, 2) return shannonEnt; #返回熵#按照给定的特征划分数据集def splitDataSet(dataSet, axis, value): retDataSet = []  for featVec in dataSet: #按dataSet矩阵中的第axis列的值等于value的分数据集  if featVec[axis] == value:  #值等于value的，每一行为新的列表（去除第axis个数据）   reducedFeatVec = featVec[:axis]   reducedFeatVec.extend(featVec[axis+1:])    retDataSet.append(reducedFeatVec)  return retDataSet #返回分类后的新矩阵#选择最好的数据集划分方式def chooseBestFeatureToSplit(dataSet):  numFeatures = len(dataSet[0])-1 #求属性的个数 baseEntropy = calcShannonEnt(dataSet) bestInfoGain = 0.0; bestFeature = -1  for i in range(numFeatures): #求所有属性的信息增益  featList = [example[i] for example in dataSet]   uniqueVals = set(featList) #第i列属性的取值（不同值）数集合  newEntropy = 0.0   splitInfo = 0.0;  for value in uniqueVals: #求第i列属性每个不同值的熵*他们的概率   subDataSet = splitDataSet(dataSet, i , value)    prob = len(subDataSet)/float(len(dataSet)) #求出该值在i列属性中的概率   newEntropy += prob * calcShannonEnt(subDataSet) #求i列属性各值对于的熵求和   splitInfo -= prob * log(prob, 2);  infoGain = (baseEntropy - newEntropy) / splitInfo; #求出第i列属性的信息增益率  print infoGain;   if(infoGain > bestInfoGain): #保存信息增益率最大的信息增益率值以及所在的下表（列值i）   bestInfoGain = infoGain    bestFeature = i  return bestFeature #找出出现次数最多的分类名称def majorityCnt(classList):  classCount = {}  for vote in classList:   if vote not in classCount.keys(): classCount[vote] = 0   classCount[vote] += 1  sortedClassCount = sorted(classCount.iteritems(), key = operator.itemgetter(1), reverse=True) return sortedClassCount[0][0] #创建树def createTree(dataSet, labels):  classList = [example[-1] for example in dataSet]; #创建需要创建树的训练数据的结果列表（例如最外层的列表是[N, N, Y, Y, Y, N, Y]） if classList.count(classList[0]) == len(classList): #如果所有的训练数据都是属于一个类别，则返回该类别  return classList[0];  if (len(dataSet[0]) == 1): #训练数据只给出类别数据（没给任何属性值数据），返回出现次数最多的分类名称  return majorityCnt(classList); bestFeat = chooseBestFeatureToSplit(dataSet); #选择信息增益最大的属性进行分（返回值是属性类型列表的下标） bestFeatLabel = labels[bestFeat] #根据下表找属性名称当树的根节点 myTree = {bestFeatLabel:{}} #以bestFeatLabel为根节点建一个空树 del(labels[bestFeat]) #从属性列表中删掉已经被选出来当根节点的属性 featValues = [example[bestFeat] for example in dataSet] #找出该属性所有训练数据的值（创建列表） uniqueVals = set(featValues) #求出该属性的所有值得集合（集合的元素不能重复） for value in uniqueVals: #根据该属性的值求树的各个分支  subLabels = labels[:]   myTree[bestFeatLabel][value] = createTree(splitDataSet(dataSet, bestFeat, value), subLabels) #根据各个分支递归创建树 return myTree #生成的树#实用决策树进行分类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 #读取数据文档中的训练数据（生成二维列表）def createTrainData(): lines_set = open('../data/ID3/Dataset.txt').readlines() labelLine = lines_set[2]; labels = labelLine.strip().split() lines_set = lines_set[4:11] dataSet = []; for line in lines_set:  data = line.split();  dataSet.append(data); return dataSet, labels#读取数据文档中的测试数据（生成二维列表）def createTestData(): lines_set = open('../data/ID3/Dataset.txt').readlines() lines_set = lines_set[15:22] dataSet = []; for line in lines_set:  data = line.strip().split();  dataSet.append(data); return dataSetmyDat, labels = createTrainData() myTree = createTree(myDat,labels) print myTreebootList = ['outlook','temperature', 'humidity', 'windy'];testList = createTestData();for testData in testList: dic = classify(myTree, bootList, testData) print dic

训练集: outlook temperature humidity windy  --------------------------------------------------------- sunny  hot    high   false   N sunny  hot    high   true   N overcast hot    high   false   Y rain  mild   high   false   Y rain  cool   normal  false   Y rain  cool   normal  true   N overcast cool   normal  true   Y测试集 outlook temperature humidity windy  -----------------------------------------------   sunny  mild   high   false    sunny  cool   normal  false    rain   mild   normal  false   sunny  mild   normal  true    overcast mild   high   true    overcast hot    normal  false    rain   mild   high   true