这篇文章主要贴本人在决策树算法学习过程中实践的含连续属性的决策树算法。
语言：Python; 数据集：周志华 西瓜数据3.0
大部分与上篇离散属性决策树相同，一下列出主要的不同部分：
#连续属性的最大增益计算 def InfoGainContous(DatSet,Label,k): DatSetk = DatSet[:,k] nk = len(DatSetk) uniqueDatSetk = list(set(DatSetk))#set不能用索引获取值 uniquesortDatSetk = np.sort(uniqueDatSetk) n = len(uniquesortDatSetk) #对于set用len方法,set无序 selectPoint = [] for index in range(n-1): #print index selectPoint.append((uniquesortDatSetk[index] + uniquesortDatSetk[index + 1])/2.0) #print 'selectPoint: ',selectPoint maxinfoEnt = 0.0 bestPoint = -1 bestLabel = [] maxGain = 0 #print 'Label: ',Label for index in range(n-1): Label0 = [] #用于存放小于划分点的值 Label1 = [] #用于存放大于划分点的值 labelCount = 0 infoEnt = 0.0 for datindex in range(nk): if DatSetk[datindex] < selectPoint[index]: labelCount += 1 Label0.append(Label[datindex]) else: Label1.append(Label[datindex]) sumEnt = len(Label0)/(len(Label)*1.0)*InfoEntCalc(Label0) + len(Label1)/(len(Label)*1.0)*InfoEntCalc(Label1) infoEnt = InfoEntCalc(Label) - sumEnt if infoEnt > maxinfoEnt: maxinfoEnt = infoEnt bestPoint = selectPoint[index] #得到最佳划分点 bestLabel = Label0 return maxinfoEnt,bestPoint #计算最大增益 def MaxGain(DatSet,Label,Table): m,n = np.shape(DatSet) #多了一些重复计算 Gain = 0.0 maxGain = -1 bestFeature = -1 bestPoint = -1 for tab in Table: featureNum = list(Table).index(tab) #print "featureNum: ",featureNum try: float(tab) except: Gain = InfoGain(DatSet,Label,featureNum) Point = -1 else: Gain,Point = InfoGainContous(DatSet,Label,featureNum) if Gain > maxGain: bestFeature = featureNum maxGain = Gain bestPoint = Point return bestFeature,bestPoint #完成基本的决策树构建 def TreeGenerate(Dat,DatOri,Table): #输入位np array格式 DatSet = Dat[:,:-1] #取出所有的数据集 Label = Dat[:,-1] #取出样本对应得类别集 Tables = Table[:] m,n = np.shape(DatSet) #当所有数据集的分类相同时： if list(Label).count(Label[0]) == m: return Label[0] #属性集已经遍历完成，但是数据中仍然有多个分类类别时 if n == 1: #n=1表示只剩下了类别 return majorCnt(Label) bestFeature,bestPoint = MaxGain(DatSet,Label,Table) #bestFeature对应特征的编号 bestFeatureTable = Table[bestFeature] del(Table[bestFeature]) #print Table Tree = {bestFeatureTable:{}} try: int(bestFeatureTable)#根据选出的属性是否可以转化为int型确定是否为密度和含糖量 except: for value in set(DatOri[:,bestFeature]): #print (bestFeatureTable,value) subDatSetR = Dat[Dat[:,bestFeature] == value] #选出属性bestFeature，值为value的行 subDatSet = np.concatenate((subDatSetR[:,:bestFeature],subDatSetR[:,bestFeature+1:]),axis=1) #数据集将bestFeature属性去掉 subDatOri = np.concatenate((DatOri[:,:bestFeature],DatOri[:,bestFeature+1:]),axis=1) #数据集将bestFeature属性去掉 subTabel = Table[:] subm,subn = np.shape(subDatSet) #print subm #print "Label:", Label if(subm == 0): #当子集的数据集为空时，说明没有这样的特征样本，根据其父集中样本最多的类 Tree[bestFeatureTable][value] = majorCnt(Label)#return majorCnt(Label) else: Tree[bestFeatureTable][value] = TreeGenerate(subDatSet,subDatOri,subTabel) #Tree[bestFeature][value]两层深度的树 else: for value in [-1,1]: #-1表示小于划分点的情况；1表示大于划分点的情况 if value == -1: subDatSetR = Dat[Dat[:,bestFeature] < bestPoint] #选出属性bestFeature，值为value的行 subDatSet = np.concatenate((subDatSetR[:,:bestFeature],subDatSetR[:,bestFeature+1:]),axis=1) #数据集将bestFeature属性去掉 subDatOri = np.concatenate((DatOri[:,:bestFeature],DatOri[:,bestFeature+1:]),axis=1) #数据集将bestFeature属性去掉 subTabel = Table[:] subm,subn = np.shape(subDatSet) strval = '<' + str(bestPoint) if(subm == 0): #当子集的数据集为空时，说明没有这样的特征样本，根据其父集中样本最多的类 Tree[bestFeatureTable][strval] = majorCnt(Label)#return majorCnt(Label) else: Tree[bestFeatureTable][strval] = TreeGenerate(subDatSet,subDatOri,subTabel) #Tree[bestFeature][value]两层深度的树 if value == 1: subDatSetR = Dat[Dat[:,bestFeature] >= bestPoint] #选出属性bestFeature，值为value的行 subDatSet = np.concatenate((subDatSetR[:,:bestFeature],subDatSetR[:,bestFeature+1:]),axis=1) #数据集将bestFeature属性去掉 subDatOri = np.concatenate((DatOri[:,:bestFeature],DatOri[:,bestFeature+1:]),axis=1) #数据集将bestFeature属性去掉 subTabel = Table[:] subm,subn = np.shape(subDatSet) strval = '>=' + str(bestPoint) if(subm == 0): #当子集的数据集为空时，说明没有这样的特征样本，根据其父集中样本最多的类 Tree[bestFeatureTable][strval] = majorCnt(Label)#return majorCnt(Label) else: Tree[bestFeatureTable][strval] = TreeGenerate(subDatSet,subDatOri,subTabel) #Tree[bestFeature][value]两层深度的树 return Tree