ID3

# -*- coding: utf-8 -*-
import copy
from numpy import *
import math
class ID3DTree(object):
    def __init__(self):
        self.tree = {}
        self.dataSet = []
        self.labels = []

    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() for row in rowlist if row.strip()]
        #print(recordlist)
        self.dataSet = recordlist
        self.labels = labels

    def train(self):
        #labels = copy.deepcopy(self.labels)
        labels=self.labels
        self.tree = self.buildTree(self.dataSet, labels)

        # 创建决策树主程序

    def buildTree(self, dataSet, labels):
        #print('zhesh1',dataSet,'
')
        cateList = [data[-1] for data in dataSet]  # 抽取源数据集的决策标签列
        #print(cateList)
        # 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 返回这个决策标签
        #print(len(dataSet[0]))
        if len(dataSet[0]) == 1:
            return self.maxCate(cateList)
        # 算法核心：
        bestFeat = self.getBestFeat(dataSet)  # 返回数据集的最优特征轴：
        bestFeatLabel = labels[bestFeat]
        tree = {bestFeatLabel: {}}
        del (labels[bestFeat])#删除当前最优的特征轴，然后继续进行
        # 抽取最优特征轴的列向量
        uniqueVals = set([data[bestFeat] for data in dataSet])  # 去重
        for value in uniqueVals:
            subLabels = labels[:]  # 将删除后的特征类别集建立子类别集
            splitDataset = self.splitDataSet(dataSet, bestFeat, value)  # 按最优特征列和值分割数据集
            subTree = self.buildTree(splitDataset, subLabels)  # 构建子树
            tree[bestFeatLabel][value] = subTree
        return tree

    def maxCate(self, catelist):  # 计算出现最多的类别标签
        items = dict([(catelist.count(i), i) for i in catelist])
        return items[max(items.keys())]
#计算最优特征子函数，就是根据求出来的信息增益去比较，谁的大，谁的就最优，然后就可以作为根节点，不断的循环下去
    def getBestFeat(self, dataSet):
        # 计算特征向量维，其中最后一列用于类别标签，因此要减去
        numFeatures = len(dataSet[0]) - 1  # 特征向量维数= 行向量维度-1
        baseEntropy = self.computeEntropy(dataSet)  # 基础熵：源数据的香农熵，这是总的信息熵
        bestInfoGain = 0.0;  # 初始化最优的信息增益
        bestFeature = -1  # 初始化最优的特征轴
        # 外循环：遍历数据集各列,计算最优特征轴
        # i 为数据集列索引：取值范围 0~(numFeatures-1)
        for i in range(numFeatures):  # 抽取第i列的列向量
            uniqueVals = set([data[i] for data in dataSet])  # 去重：该列的唯一值集
            newEntropy = 0.0  # 初始化该列的香农熵
            for value in uniqueVals:  # 内循环：按列和唯一值计算香农熵
                subDataSet = self.splitDataSet(dataSet, i, value)  # 按选定列i和唯一值分隔数据集,这是除了类别标签外的类别。
                #print('长度',len(subDataSet))
                #print(subDataSet)
                prob = len(subDataSet) / float(len(dataSet))
                newEntropy += prob * self.computeEntropy(subDataSet)
            infoGain = baseEntropy - newEntropy  # 计算最大增益
            if (infoGain > bestInfoGain):  # 如果信息增益>0;
                bestInfoGain = infoGain  # 用当前信息增益值替代之前的最优增益值
                bestFeature = i  # 重置最优特征为当前列
        return bestFeature

#计算总的信息熵
    def computeEntropy(self, dataSet):  # 计算香农熵
        datalen = float(len(dataSet))
        cateList = [data[-1] for data in dataSet]  # 从数据集中得到类别标签
        items = dict([(i, cateList.count(i)) for i in cateList])  # 得到类别为key，出现次数value的字典
        infoEntropy = 0.0  # 初始化香农熵
        for key in items:  # 计算香农熵
            prob = float(items[key]) / datalen
            infoEntropy -= prob * math.log(prob, 2)  # 香农熵：= - p*log2(p) --infoEntropy = -prob * log(prob,2)
        return infoEntropy

    # 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:
            #print('what',featVec)
            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

    def predict(self, inputTree, featLabels, testVec):  # 分类器
        root = 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

    # 存储树到文件
    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)
dtree=ID3DTree()
dtree.loadDataSet("F:python数据挖掘DesktopMLBookchapter03dataset.dat",['age','revenue','student','credit'])
dtree.train()
print(dtree.tree)

 结果输出为：

{'age': {b'1': b'yes', b'0': {'student': {b'1': b'yes', b'0': b'no'}}, b'2': {'credit': {b'1': b'no', b'0': b'yes'}}}}