实例如下：
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# -*- 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) |
最终结果如下：
{'texture': {'blur': 0, 'little_blur': {'touch': {'soft_stick': 1, 'hard_smooth': 0}}, 'distinct': {'density<=0.38149999999999995': {0: 1, 1: 0}}}}
得到的决策树如下：
参考资料：
《机器学习实战》
《机器学习》周志华著
以上这篇基于ID3决策树算法的实现(Python版)就是小编分享给大家的全部内容了，希望能给大家一个参考，也希望大家多多支持服务器之家。
