基于ID3决策树算法的实现(Python版)

# -*- coding:utf-8 -*-from numpy import *import numpy as npimport pandas as pdfrom math import logimport operator#计算数据集的香农熵def calcShannonEnt(dataSet):  numEntries=len(dataSet)  labelCounts={}  #给所有可能分类创建字典  for featVec in dataSet:    currentLabel=featVec[-1]    if currentLabel not in labelCounts.keys():      labelCounts[currentLabel]=0    labelCounts[currentLabel]+=1  shannonEnt=0.0  #以2为底数计算香农熵  for key in labelCounts:    prob = float(labelCounts[key])/numEntries    shannonEnt-=prob*log(prob,2)  return shannonEnt#对离散变量划分数据集，取出该特征取值为value的所有样本def splitDataSet(dataSet,axis,value):  retDataSet=[]  for featVec in dataSet:    if featVec[axis]==value:      reducedFeatVec=featVec[:axis]      reducedFeatVec.extend(featVec[axis+1:])      retDataSet.append(reducedFeatVec)  return retDataSet#对连续变量划分数据集，direction规定划分的方向，#决定是划分出小于value的数据样本还是大于value的数据样本集def splitContinuousDataSet(dataSet,axis,value,direction):  retDataSet=[]  for featVec in dataSet:    if direction==0:      if featVec[axis]>value:        reducedFeatVec=featVec[:axis]        reducedFeatVec.extend(featVec[axis+1:])        retDataSet.append(reducedFeatVec)    else:      if featVec[axis]<=value:        reducedFeatVec=featVec[:axis]        reducedFeatVec.extend(featVec[axis+1:])        retDataSet.append(reducedFeatVec)  return retDataSet#选择最好的数据集划分方式def chooseBestFeatureToSplit(dataSet,labels):  numFeatures=len(dataSet[0])-1  baseEntropy=calcShannonEnt(dataSet)  bestInfoGain=0.0  bestFeature=-1  bestSplitDict={}  for i in range(numFeatures):    featList=[example[i] for example in dataSet]    #对连续型特征进行处理    if type(featList[0]).__name__=='float' or type(featList[0]).__name__=='int':      #产生n-1个候选划分点      sortfeatList=sorted(featList)      splitList=[]      for j in range(len(sortfeatList)-1):        splitList.append((sortfeatList[j]+sortfeatList[j+1])/2.0)      bestSplitEntropy=10000      slen=len(splitList)      #求用第j个候选划分点划分时，得到的信息熵，并记录最佳划分点      for j in range(slen):        value=splitList[j]        newEntropy=0.0        subDataSet0=splitContinuousDataSet(dataSet,i,value,0)        subDataSet1=splitContinuousDataSet(dataSet,i,value,1)        prob0=len(subDataSet0)/float(len(dataSet))        newEntropy+=prob0*calcShannonEnt(subDataSet0)        prob1=len(subDataSet1)/float(len(dataSet))        newEntropy+=prob1*calcShannonEnt(subDataSet1)        if newEntropy<bestSplitEntropy:          bestSplitEntropy=newEntropy          bestSplit=j      #用字典记录当前特征的最佳划分点      bestSplitDict[labels[i]]=splitList[bestSplit]      infoGain=baseEntropy-bestSplitEntropy    #对离散型特征进行处理    else:      uniqueVals=set(featList)      newEntropy=0.0      #计算该特征下每种划分的信息熵      for value in uniqueVals:        subDataSet=splitDataSet(dataSet,i,value)        prob=len(subDataSet)/float(len(dataSet))        newEntropy+=prob*calcShannonEnt(subDataSet)      infoGain=baseEntropy-newEntropy    if infoGain>bestInfoGain:      bestInfoGain=infoGain      bestFeature=i  #若当前节点的最佳划分特征为连续特征，则将其以之前记录的划分点为界进行二值化处理  #即是否小于等于bestSplitValue  if type(dataSet[0][bestFeature]).__name__=='float' or type(dataSet[0][bestFeature]).__name__=='int':    bestSplitValue=bestSplitDict[labels[bestFeature]]    labels[bestFeature]=labels[bestFeature]+'<='+str(bestSplitValue)    for i in range(shape(dataSet)[0]):      if dataSet[i][bestFeature]<=bestSplitValue:        dataSet[i][bestFeature]=1      else:        dataSet[i][bestFeature]=0  return bestFeature#特征若已经划分完，节点下的样本还没有统一取值，则需要进行投票def majorityCnt(classList):  classCount={}  for vote in classList:    if vote not in classCount.keys():      classCount[vote]=0    classCount[vote]+=1  return max(classCount)#主程序，递归产生决策树def createTree(dataSet,labels,data_full,labels_full):  classList=[example[-1] for example in dataSet]  if classList.count(classList[0])==len(classList):    return classList[0]  if len(dataSet[0])==1:    return majorityCnt(classList)  bestFeat=chooseBestFeatureToSplit(dataSet,labels)  bestFeatLabel=labels[bestFeat]  myTree={bestFeatLabel:{}}  featValues=[example[bestFeat] for example in dataSet]  uniqueVals=set(featValues)  if type(dataSet[0][bestFeat]).__name__=='str':    currentlabel=labels_full.index(labels[bestFeat])    featValuesFull=[example[currentlabel] for example in data_full]    uniqueValsFull=set(featValuesFull)  del(labels[bestFeat])  #针对bestFeat的每个取值，划分出一个子树。  for value in uniqueVals:    subLabels=labels[:]    if type(dataSet[0][bestFeat]).__name__=='str':      uniqueValsFull.remove(value)    myTree[bestFeatLabel][value]=createTree(splitDataSet/     (dataSet,bestFeat,value),subLabels,data_full,labels_full)  if type(dataSet[0][bestFeat]).__name__=='str':    for value in uniqueValsFull:      myTree[bestFeatLabel][value]=majorityCnt(classList)  return myTreeimport matplotlib.pyplot as pltdecisionNode=dict(boxstyle="sawtooth",fc="0.8")leafNode=dict(boxstyle="round4",fc="0.8")arrow_args=dict(arrowstyle="<-")#计算树的叶子节点数量def getNumLeafs(myTree):  numLeafs=0  firstSides = list(myTree.keys())  firstStr=firstSides[0]  secondDict=myTree[firstStr]  for key in secondDict.keys():    if type(secondDict[key]).__name__=='dict':      numLeafs+=getNumLeafs(secondDict[key])    else: numLeafs+=1  return numLeafs#计算树的最大深度def getTreeDepth(myTree):  maxDepth=0  firstSides = list(myTree.keys())  firstStr=firstSides[0]  secondDict=myTree[firstStr]  for key in secondDict.keys():    if type(secondDict[key]).__name__=='dict':      thisDepth=1+getTreeDepth(secondDict[key])    else: thisDepth=1    if thisDepth>maxDepth:      maxDepth=thisDepth  return maxDepth#画节点def plotNode(nodeTxt,centerPt,parentPt,nodeType):  createPlot.ax1.annotate(nodeTxt,xy=parentPt,xycoords='axes fraction',/  xytext=centerPt,textcoords='axes fraction',va="center", ha="center",/  bbox=nodeType,arrowprops=arrow_args)#画箭头上的文字def plotMidText(cntrPt,parentPt,txtString):  lens=len(txtString)  xMid=(parentPt[0]+cntrPt[0])/2.0-lens*0.002  yMid=(parentPt[1]+cntrPt[1])/2.0  createPlot.ax1.text(xMid,yMid,txtString)def plotTree(myTree,parentPt,nodeTxt):  numLeafs=getNumLeafs(myTree)  depth=getTreeDepth(myTree)  firstSides = list(myTree.keys())  firstStr=firstSides[0]  cntrPt=(plotTree.x0ff+(1.0+float(numLeafs))/2.0/plotTree.totalW,plotTree.y0ff)  plotMidText(cntrPt,parentPt,nodeTxt)  plotNode(firstStr,cntrPt,parentPt,decisionNode)  secondDict=myTree[firstStr]  plotTree.y0ff=plotTree.y0ff-1.0/plotTree.totalD  for key in secondDict.keys():    if type(secondDict[key]).__name__=='dict':      plotTree(secondDict[key],cntrPt,str(key))    else:      plotTree.x0ff=plotTree.x0ff+1.0/plotTree.totalW      plotNode(secondDict[key],(plotTree.x0ff,plotTree.y0ff),cntrPt,leafNode)      plotMidText((plotTree.x0ff,plotTree.y0ff),cntrPt,str(key))  plotTree.y0ff=plotTree.y0ff+1.0/plotTree.totalDdef createPlot(inTree):  fig=plt.figure(1,facecolor='white')  fig.clf()  axprops=dict(xticks=[],yticks=[])  createPlot.ax1=plt.subplot(111,frameon=False,**axprops)  plotTree.totalW=float(getNumLeafs(inTree))  plotTree.totalD=float(getTreeDepth(inTree))  plotTree.x0ff=-0.5/plotTree.totalW  plotTree.y0ff=1.0  plotTree(inTree,(0.5,1.0),'')  plt.show()df=pd.read_csv('watermelon_4_3.csv')data=df.values[:,1:].tolist()data_full=data[:]labels=df.columns.values[1:-1].tolist()labels_full=labels[:]myTree=createTree(data,labels,data_full,labels_full)print(myTree)createPlot(myTree)