#coding:utf-8from numpy import *
import math
import copy
import cPickle as pickle# 定义一个ID3DTree的类来封装算法：
class ID3DTree(object):def __init__(self):        #构造方法self.tree    = {}      #生成的树self.dataSet = []      #数据集self.label   = []      #标签集#数据导入函数def loadDataSet(self,path,labels):recordlist   = []fp           = open(path,"rb")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()]self.dataSet = recordlistself.labels  = labels#执行决策树函数def train(self):labels    = copy.deepcopy(self.labels)self.tree = self.buildTree(self.dataSet,labels)# 3.2.3 决策树主方法# （1）构建决策树：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#程序的终止条件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]#程序的终止条件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# uniqueVals = set([data[bestFeat] for data in dataSet]) #去重for value in featValueLis:  #决策树递归生长subLabels = labels[:]  #将删除后的特征类别接建立子类别集#按最优特征列和值分割数据集splitDataset = self.splitDataSet(dataSet,bestFeat,value)subTree      = self.buildTree(splitDataset,subLabels)tree[bestFeatLabel][value] = subTreereturn 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):#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=行向量维数-1Num_Feats    = len(dataSet[0][:-1])totality     = len(dataSet)BaseEntropy  = self.computeEntropy(dataSet)  #基础熵：源数据香农熵ConditionEntropy = []                        #初始化条件熵slpitInfo    = []                            #for C4.5,calculate gain ratooallFeatVList = []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 = 0.0for value in featureValueList:subSet     = self.splitDataSet(dataSet,f,value)appearNum  = float(len(subSet))subEntropy = self.computeEntropy(subSet)resultGain += (appearNum/totality)*subEntropyConditionEntropy.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bastFeatureIndex = argsort(-infoGainArray)[0]return bastFeatureIndex ,allFeatVList[bastFeatureIndex]#计算信息熵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#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 = 0.0for key in items: #香农熵：=-p*log2(p) --infoEntropy = -prob*log(prob,2)prob = float(items[key])/dataleninfoEntropy -= prob*math.log(prob,2)return infoEntropy#（5）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:])#lsit操作：将特征轴（列）之后的元素加回
                rtnList.append(rFeatVec)return rtnList                          #剔除已选择的一列#计算划分信息def computeSplitInfo(self,featureVList):numEntries = len(featureVList)featureValueSetList = list(set(featureVList))valueCount = [featureVList.count(featVec) for featVec in featureValueSetList]#caclulate shannonEntpList = [float(item)/numEntries from item in valueCount]lList [item*math.log(item,2) for item in pList]splitInfo = -sum(lList)return splitInfo,featureValueSetList