# -*- coding: utf-8 -*-#生成樹的函數(shù)from numpy import * import numpy as npimport pandas as pdfrom math import log import operator # 計(jì)算數(shù)據(jù)集的信息熵(Information Gain)增益函數(shù)(機(jī)器學(xué)習(xí)實(shí)戰(zhàn)中信息熵叫香農(nóng)熵)def calcInfoEnt(dataSet):#本題中Label即好or壞瓜 #dataSet每一列是一個(gè)屬性(列末是Label) numEntries = len(dataSet) #每一行是一個(gè)樣本 labelCounts = {} #給所有可能的分類創(chuàng)建字典labelCounts for featVec in dataSet: #按行循環(huán)：即rowVev取遍了數(shù)據(jù)集中的每一行 currentLabel = featVec[-1] #故featVec[-1]取遍每行最后一個(gè)值即Label if currentLabel not in labelCounts.keys(): #如果當(dāng)前的Label在字典中還沒有 labelCounts[currentLabel] = 0 #則先賦值0來創(chuàng)建這個(gè)詞 labelCounts[currentLabel] += 1 #計(jì)數(shù), 統(tǒng)計(jì)每類Label數(shù)量(這行不受if限制) InfoEnt = 0.0 for key in labelCounts: #遍歷每類Label prob = float(labelCounts[key])/numEntries #各類Label熵累加 InfoEnt -= prob * log(prob,2) #ID3用的信息熵增益公式 return InfoEnt### 對于離散特征: 取出該特征取值為value的所有樣本def splitDiscreteDataSet(dataSet, axis, value): #dataSet是當(dāng)前結(jié)點(diǎn)(待劃分)集合,axis指示劃分所依據(jù)的屬性,value該屬性用于劃分的取值 retDataSet = [] #為return Data Set分配一個(gè)列表用來儲(chǔ)存 for featVec in dataSet: if featVec[axis] == value: reducedFeatVec = featVec[:axis] #該特征之前的特征仍保留在樣本dataSet中 reducedFeatVec.extend(featVec[axis+1:]) #該特征之后的特征仍保留在樣本dataSet中 retDataSet.append(reducedFeatVec) #把這個(gè)樣本加到list中 return retDataSet### 對于連續(xù)特征: 返回特征取值大于value的所有樣本(以value為閾值將集合分成兩部分)def splitContinuousDataSet(dataSet, axis, value): retDataSetG = [] #將儲(chǔ)存取值大于value的樣本 retDataSetL = [] #將儲(chǔ)存取值小于value的樣本 for featVec in dataSet: if featVec[axis] > value: reducedFeatVecG = featVec[:axis] reducedFeatVecG.extend(featVec[axis+1:]) retDataSetG.append(reducedFeatVecG) else: reducedFeatVecL = featVec[:axis] reducedFeatVecL.extend(featVec[axis+1:]) retDataSetL.append(reducedFeatVecL) return retDataSetG,retDataSetL #返回兩個(gè)集合, 是含2個(gè)元素的tuple形式### 根據(jù)InfoGain選擇當(dāng)前最好的劃分特征(以及對于連續(xù)變量還要選擇以什么值劃分)def chooseBestFeatureToSplit(dataSet,labels): numFeatures = len(dataSet[0])-1 baseEntropy = calcInfoEnt(dataSet) bestInfoGain = 0.0; bestFeature = -1 bestSplitDict = {} for i in range(numFeatures): #遍歷所有特征：下面這句是取每一行的第i個(gè), 即得當(dāng)前集合所有樣本第i個(gè)feature的值 featList = [example[i] for example in dataSet] #判斷是否為離散特征 if not (type(featList[0]).__name__==’float’ or type(featList[0]).__name__==’int’): # 對于離散特征：求若以該特征劃分的熵增 uniqueVals = set(featList) #從列表中創(chuàng)建集合set(得列表唯一元素值) newEntropy = 0.0 for value in uniqueVals: #遍歷該離散特征每個(gè)取值 subDataSet = splitDiscreteDataSet(dataSet, i, value)#計(jì)算每個(gè)取值的信息熵 prob = len(subDataSet)/float(len(dataSet)) newEntropy += prob * calcInfoEnt(subDataSet)#各取值的熵累加 infoGain = baseEntropy - newEntropy #得到以該特征劃分的熵增 # 對于連續(xù)特征：求若以該特征劃分的熵增(區(qū)別：n個(gè)數(shù)據(jù)則需添n-1個(gè)候選劃分點(diǎn), 并選最佳劃分點(diǎn)) else: #產(chǎn)生n-1個(gè)候選劃分點(diǎn) sortfeatList=sorted(featList) splitList=[] for j in range(len(sortfeatList)-1): #產(chǎn)生n-1個(gè)候選劃分點(diǎn) splitList.append((sortfeatList[j] + sortfeatList[j+1])/2.0) bestSplitEntropy = 10000 #設(shè)定一個(gè)很大的熵值(之后用) #遍歷n-1個(gè)候選劃分點(diǎn): 求選第j個(gè)候選劃分點(diǎn)劃分時(shí)的熵增, 并選出最佳劃分點(diǎn) for j in range(len(splitList)): value = splitList[j] newEntropy = 0.0 DataSet = splitContinuousDataSet(dataSet, i, value) subDataSetG = DataSet[0] subDataSetL = DataSet[1] probG = len(subDataSetG) / float(len(dataSet)) newEntropy += probG * calcInfoEnt(subDataSetG) probL = len(subDataSetL) / float(len(dataSet)) newEntropy += probL * calcInfoEnt(subDataSetL) if newEntropy < bestSplitEntropy: bestSplitEntropy = newEntropy bestSplit = j bestSplitDict[labels[i]] = splitList[bestSplit]#字典記錄當(dāng)前連續(xù)屬性的最佳劃分點(diǎn) infoGain = baseEntropy - bestSplitEntropy #計(jì)算以該節(jié)點(diǎn)劃分的熵增# 在所有屬性(包括連續(xù)和離散)中選擇可以獲得最大熵增的屬性 if infoGain > bestInfoGain: bestInfoGain = infoGain bestFeature = i #若當(dāng)前節(jié)點(diǎn)的最佳劃分特征為連續(xù)特征，則需根據(jù)“是否小于等于其最佳劃分點(diǎn)”進(jìn)行二值化處理 #即將該特征改為“是否小于等于bestSplitValue”, 例如將“密度”變?yōu)椤懊芏?lt;=0.3815” #注意：以下這段直接操作了原dataSet數(shù)據(jù), 之前的那些float型的值相應(yīng)變?yōu)?和1 #【為何這樣做?】在函數(shù)createTree()末尾將看到解釋 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 # 若特征已經(jīng)劃分完，節(jié)點(diǎn)下的樣本還沒有統(tǒng)一取值，則需要進(jìn)行投票：計(jì)算每類Label個(gè)數(shù), 取max者def majorityCnt(classList): classCount = {} #將創(chuàng)建鍵值為Label類型的字典 for vote in classList: if vote not in classCount.keys(): classCount[vote] = 0 #第一次出現(xiàn)的Label加入字典 classCount[vote] += 1 #計(jì)數(shù) return max(classCount)2. 遞歸產(chǎn)生決策樹

# 主程序：遞歸產(chǎn)生決策樹 # dataSet：當(dāng)前用于構(gòu)建樹的數(shù)據(jù)集, 最開始就是data_full，然后隨著劃分的進(jìn)行越來越小。這是因?yàn)檫M(jìn)行到到樹分叉點(diǎn)上了. 第一次劃分之前17個(gè)瓜的數(shù)據(jù)在根節(jié)點(diǎn)，然后選擇第一個(gè)bestFeat是紋理. 紋理的取值有清晰、模糊、稍糊三種；將瓜分成了清晰（9個(gè)），稍糊（5個(gè)），模糊（3個(gè)）,這時(shí)應(yīng)該將劃分的類別減少1以便于下次劃分。 # labels：當(dāng)前數(shù)據(jù)集中有的用于劃分的類別(這是因?yàn)橛行㎜abel當(dāng)前數(shù)據(jù)集沒了, 比如假如到某個(gè)點(diǎn)上西瓜都是淺白沒有深綠了) # data_full：全部的數(shù)據(jù) # label_full:全部的類別 numLine = numColumn = 2 #這句是因?yàn)橹笠胓lobal numLine……至于為什么我一定要用global# 我也不完全理解。如果我只定義local變量總報(bào)錯(cuò)，我只好在那里的if里用global變量了。求解。def createTree(dataSet,labels,data_full,labels_full): classList = [example[-1] for example in dataSet] #遞歸停止條件1：當(dāng)前節(jié)點(diǎn)所有樣本屬于同一類；(注：count()方法統(tǒng)計(jì)某元素在列表中出現(xiàn)的次數(shù)) if classList.count(classList[0]) == len(classList): return classList[0] #遞歸停止條件2：當(dāng)前節(jié)點(diǎn)上樣本集合為空集(即特征的某個(gè)取值上已經(jīng)沒有樣本了)： global numLine,numColumn (numLine,numColumn) = shape(dataSet) if float(numLine) == 0: return ’empty’ #遞歸停止條件3：所有可用于劃分的特征均使用過了，則調(diào)用majorityCnt()投票定Label； if float(numColumn) == 1: return majorityCnt(classList) #不停止時(shí)繼續(xù)劃分： bestFeat = chooseBestFeatureToSplit(dataSet,labels)#調(diào)用函數(shù)找出當(dāng)前最佳劃分特征是第幾個(gè) bestFeatLabel = labels[bestFeat] #當(dāng)前最佳劃分特征 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]) #劃分完后, 即當(dāng)前特征已經(jīng)使用過了, 故將其從“待劃分特征集”中刪去 #【遞歸調(diào)用】針對當(dāng)前用于劃分的特征(beatFeat)的每個(gè)取值，劃分出一個(gè)子樹。 for value in uniqueVals: #遍歷該特征【現(xiàn)存的】取值 subLabels = labels[:] if type(dataSet[0][bestFeat]).__name__==’str’: uniqueValsFull.remove(value) #劃分后刪去(從uniqueValsFull中刪!) myTree[bestFeatLabel][value] = createTree(splitDiscreteDataSet(dataSet,bestFeat,value),subLabels,data_full,labels_full)#用splitDiscreteDataSet() #是由于, 所有的連續(xù)特征在劃分后都被我們定義的chooseBestFeatureToSplit()處理成離散取值了。 if type(dataSet[0][bestFeat]).__name__==’str’: #若該特征離散【更詳見后注】 for value in uniqueValsFull:#則可能有些取值已經(jīng)不在【現(xiàn)存的】取值中了 #這就是上面為何從“uniqueValsFull”中刪去 #因?yàn)槟切┈F(xiàn)有數(shù)據(jù)集中沒取到的該特征的值，保留在了其中 myTree[bestFeatLabel][value] = majorityCnt(classList) return myTree 3. 調(diào)用生成樹

#生成樹調(diào)用的語句df = pd.read_excel(r’E:BaiduNetdiskDownloadspss數(shù)據(jù)實(shí)驗(yàn)data銀行貸款.xlsx’) 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)

查看數(shù)據(jù)

data

labels

#繪決策樹的函數(shù)import matplotlib.pyplot as plt decisionNode = dict(boxstyle = 'sawtooth',fc = '0.8') #定義分支點(diǎn)的樣式leafNode = dict(boxstyle = 'round4',fc = '0.8') #定義葉節(jié)點(diǎn)的樣式arrow_args = dict(arrowstyle = '<-') #定義箭頭標(biāo)識(shí)樣式# 計(jì)算樹的葉子節(jié)點(diǎn)數(shù)量 def getNumLeafs(myTree): numLeafs = 0 firstStr = list(myTree.keys())[0] secondDict = myTree[firstStr] for key in secondDict.keys(): if type(secondDict[key]).__name__==’dict’: numLeafs += getNumLeafs(secondDict[key]) else: numLeafs += 1 return numLeafs# 計(jì)算樹的最大深度def getTreeDepth(myTree): maxDepth = 0 firstStr = list(myTree.keys())[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 # 畫出節(jié)點(diǎn) 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) # 標(biāo)箭頭上的文字 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) firstStr = list(myTree.keys())[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.totalD def 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()5. 調(diào)用函數(shù)

#命令繪決策樹的圖createPlot(myTree)

myTree

總結(jié)

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