C4.5决策树算法（Python实现）

C4.5算法使用信息增益率来代替ID3的信息增益进行特征的选择，克服了信息增益选择特征时偏向于特征值个数较多的不足。信息增益率的定义如下：

# -*- coding: utf-8 -*-from numpy import *import mathimport copyimport cPickle as pickleclass C45DTree(object):    def __init__(self):  # 构造方法        self.tree = {}  # 生成树        self.dataSet = []  # 数据集        self.labels = []  # 标签集    # 数据导入函数    def loadDataSet(self, path, labels):        recordList = []        fp = open(path, "rb")  # 读取文件内容        content = fp.read()        fp.close()        rowList = content.splitlines()  # 按行转换为一维表        recordList = [row.split("\t") for row in rowList if row.strip()]  # strip()函数删除空格、Tab等        self.dataSet = recordList        self.labels = labels    # 执行决策树函数    def train(self):        labels = copy.deepcopy(self.labels)        self.tree = self.buildTree(self.dataSet, labels)    # 构件决策树：穿件决策树主程序    def buildTree(self, dataSet, lables):        cateList = [data[-1] for data in dataSet]  # 抽取源数据集中的决策标签列        # 程序终止条件1：如果classList只有一种决策标签，停止划分，返回这个决策标签        if cateList.count(cateList[0]) == len(cateList):            return cateList[0]        # 程序终止条件2：如果数据集的第一个决策标签只有一个，返回这个标签        if len(dataSet[0]) == 1:            return self.maxCate(cateList)        # 核心部分        bestFeat, featValueList= self.getBestFeat(dataSet)  # 返回数据集的最优特征轴        bestFeatLabel = lables[bestFeat]        tree = {bestFeatLabel: {}}        del (lables[bestFeat])        for value in featValueList:  # 决策树递归生长            subLables = lables[:]  # 将删除后的特征类别集建立子类别集            # 按最优特征列和值分隔数据集            splitDataset = self.splitDataSet(dataSet, bestFeat, value)            subTree = self.buildTree(splitDataset, subLables)  # 构建子树            tree[bestFeatLabel][value] = subTree        return tree    # 计算出现次数最多的类别标签    def maxCate(self, cateList):        items = dict([(cateList.count(i), i) for i in cateList])        return items[max(items.keys())]    # 计算最优特征    def getBestFeat(self, dataSet):        Num_Feats = len(dataSet[0][:-1])        totality = len(dataSet)        BaseEntropy = self.computeEntropy(dataSet)        ConditionEntropy = []     # 初始化条件熵        slpitInfo = []    # for C4.5,caculate gain ratio        allFeatVList = []        for f in xrange(Num_Feats):            featList = [example[f] for example in dataSet]            [splitI, featureValueList] = self.computeSplitInfo(featList)            allFeatVList.append(featureValueList)            slpitInfo.append(splitI)            resultGain = 0.0            for value in featureValueList:                subSet = self.splitDataSet(dataSet, f, value)                appearNum = float(len(subSet))                subEntropy = self.computeEntropy(subSet)                resultGain += (appearNum/totality)*subEntropy            ConditionEntropy.append(resultGain)    # 总条件熵        infoGainArray = BaseEntropy*ones(Num_Feats)-array(ConditionEntropy)        infoGainRatio = infoGainArray/array(slpitInfo)  # C4.5信息增益的计算        bestFeatureIndex = argsort(-infoGainRatio)[0]        return bestFeatureIndex, allFeatVList[bestFeatureIndex]    # 计算划分信息    def computeSplitInfo(self, featureVList):        numEntries = len(featureVList)        featureVauleSetList = list(set(featureVList))        valueCounts = [featureVList.count(featVec) for featVec in featureVauleSetList]        pList = [float(item)/numEntries for item in valueCounts]        lList = [item*math.log(item, 2) for item in pList]        splitInfo = -sum(lList)        return splitInfo, featureVauleSetList # 计算信息熵    # @staticmethod    def computeEntropy(self, dataSet):        dataLen = float(len(dataSet))        cateList = [data[-1] for data in dataSet]  # 从数据集中得到类别标签        # 得到类别为key、 出现次数value的字典        items = dict([(i, cateList.count(i)) for i in cateList])        infoEntropy = 0.0        for key in items:  # 香农熵： = -p*log2(p) --infoEntropy = -prob * log(prob, 2)            prob = float(items[key]) / dataLen            infoEntropy -= prob * math.log(prob, 2)        return infoEntropy    # 划分数据集： 分割数据集； 删除特征轴所在的数据列，返回剩余的数据集    # dataSet : 数据集； axis: 特征轴； value: 特征轴的取值    def splitDataSet(self, dataSet, axis, value):        rtnList = []        for featVec in dataSet:            if featVec[axis] == value:                rFeatVec = featVec[:axis]  # list操作：提取0~（axis-1）的元素                rFeatVec.extend(featVec[axis + 1:])   # 将特征轴之后的元素加回                rtnList.append(rFeatVec)        return rtnList    # 存取树到文件    def storetree(self, inputTree, filename):        fw = open(filename,'w')        pickle.dump(inputTree, fw)        fw.close()    # 从文件抓取树    def grabTree(self, filename):        fr = open(filename)        return pickle.load(fr)

调用代码

# -*- coding: utf-8 -*-from numpy import *from C45DTree import *dtree = C45DTree()dtree.loadDataSet("dataset.dat",["age", "revenue", "student", "credit"])dtree.train()dtree.storetree(dtree.tree, "data.tree")mytree = dtree.grabTree("data.tree")print mytree

代码测试所用资源下载：
链接：http://pan.baidu.com/s/1geLP5qb 密码：m6go