机器学习-决策树-C4.5决策树

针对ID3算法存在的一些问题，1993年，Quinlan将ID3算法改进为C4.5算法。该算法成功地解决了ID3算法遇到的诸多问题，发展成为机器学习的十大算法之一。

C4.5并没有改变ID3的算法逻辑，基本的程序结构仍与ID3相同，但在节点的划分标准上做了改进。C4.5使用信息增益率（GainRatio）来替代信息增益（Gain）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：

GainRatio(S,A) = Gain(S,A) / SplitInfo(S,A)

其中Gain(S,A)就是ID3算法中的信息增益，而划分信息SplitInfo(S,A)代表了按照特征A划分样本集S的广度和均匀性。

 

其中Si到Sc时特征A的C个不同值构成的样本子集。

代码

 

# C4.5决策树，使用信息增益率确定最优特征
from numpy import *
import math
import copy
import pickle

class C45DTree(object):
    def __init__(self): # 构造方法
        self.tree = {}  # 生成的树
        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, "r")  # 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()]
        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)

        # 创建决策树主程序

    def buildTree(self, dataSet, labels):
        cateList = [data[-1] for data in dataSet]  # 抽取源数据集的决策标签列
        # 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，则返回这个决策标签
        if len(dataSet[0]) == 1:
            return self.maxCate(cateList)
        # 算法核心：
        bestFeat,featValueList = self.getBestFeat(dataSet)  # 返回数据集的最优特征轴
        bestFeatLabel = labels[bestFeat]
        tree = {bestFeatLabel: {}}
        del (labels[bestFeat])
        # 抽取最优特征轴的列向量
        for value in featValueList:  # 决策树递归生长
            subLabels = labels[:]  # 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, subLabels)  # 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())]

    # 计算信息熵
    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  # 初始化香农熵
        for key in items:  # 香农熵：
            prob = float(items[key]) / datalen
            infoEntropy -= prob * math.log(prob, 2)
        return infoEntropy

    # 划分数据集；分隔数据集；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:])  # list操作：将特征轴（列）之后的元素加回
                rtnList.append(rFeatVec)
        return rtnList

    # 计算划分信息（SpilitInfo）
    def computeSplitInfo(self, featureVList):
        numEntries = len(featureVList)
        featureValueListSetList = list(set(featureVList))
        valueCounts = [featureVList.count(featVec) for featVec in featureValueListSetList]
        # 计算香农熵
        pList = [float(item) / numEntries for item in valueCounts]
        lList = [item * math.log(item, 2) for item in pList]
        splitInfo = -sum(lList)
        return splitInfo, featureValueListSetList

    # 使用信息增益率划分最优节点
    def getBestFeat(self, dataSet):
        Num_feats = len(dataSet[0][:-1])
        totality = len(dataSet)
        BaseEntropy = self.computeEntropy(dataSet)
        ConditionEntropy = []   # 初始化条件熵
        splitInfo = []  # 计算信息增益率
        allFeatVList = []
        for f in range(Num_feats):
            featList = [example[f] for example in dataSet]
            [splitI, featureValueList] = self.computeSplitInfo(featList)
            allFeatVList.append(featureValueList)
            splitInfo.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(splitInfo)    # C4.5信息增益的计算
        bestFeatureIndex = argsort(-infoGainRatio)[0]
        return bestFeatureIndex, allFeatVList[bestFeatureIndex]

    # 分类
    def predict(self, inputTree, featLabels, testVec):
        root = list(inputTree.keys())[0]  # 树根节点
        secondDict = inputTree[root]  # value-子树结构或分类标签
        featIndex = featLabels.index(root)  # 根节点在分类标签集中的位置
        key = testVec[featIndex]  # 测试集数组取值
        valueOfFeat = secondDict[key]
        if isinstance(valueOfFeat, dict):
            classLabel = self.predict(valueOfFeat, featLabels, testVec)  # 递归分类
        else:
            classLabel = valueOfFeat
        return classLabel


    # 持久化
    def storeTree(self, inputTree, filename):
        fw = open(filename, 'wb')
        pickle.dump(inputTree, fw)
        fw.close()

    # 从文件抓取树
    def grabTree(self, filename):
        fr = open(filename, 'rb')
        return pickle.load(fr)

#训练
dtree = C45DTree()
dtree.loadDataSet("/Users/FengZhen/Desktop/accumulate/机器学习/决策树/决策树训练集.txt", ["age", "revenue", "student", "credit"])
dtree.train()
print(dtree.tree)

#持久化
dtree.storeTree(dtree.tree, "/Users/FengZhen/Desktop/accumulate/机器学习/决策树/决策树C45.tree")
mytree = dtree.grabTree("/Users/FengZhen/Desktop/accumulate/机器学习/决策树/决策树C45.tree")
print(mytree)

#测试
labels = ["age", "revenue", "student", "credit"]
vector = ['0','1','0','0']
print(dtree.predict(mytree, labels, vector))