1. 定义生成树

# -*- coding: utf-8 -*-
#生成树的函数from numpy import *  
import numpy as np
import pandas as pd
from math import log  
import operator  # 计算数据集的信息熵(Information Gain)增益函数(机器学习实战中信息熵叫香农熵)
def calcInfoEnt(dataSet):#本题中Label即好or坏瓜 #dataSet每一列是一个属性(列末是Label)numEntries = len(dataSet)    #每一行是一个样本labelCounts = {} #给所有可能的分类创建字典labelCountsfor featVec in dataSet:    #按行循环：即rowVev取遍了数据集中的每一行currentLabel = featVec[-1]    #故featVec[-1]取遍每行最后一个值即Labelif currentLabel not in labelCounts.keys():    #如果当前的Label在字典中还没有labelCounts[currentLabel] = 0    #则先赋值0来创建这个词labelCounts[currentLabel] += 1    #计数, 统计每类Label数量(这行不受if限制)InfoEnt = 0.0for key in labelCounts:    #遍历每类Labelprob = float(labelCounts[key])/numEntries   #各类Label熵累加InfoEnt -= prob * log(prob,2)    #ID3用的信息熵增益公式return InfoEnt### 对于离散特征: 取出该特征取值为value的所有样本
def splitDiscreteDataSet(dataSet, axis, value):    #dataSet是当前结点(待划分)集合,axis指示划分所依据的属性,value该属性用于划分的取值retDataSet = []     #为return Data Set分配一个列表用来储存for featVec in dataSet:if featVec[axis] == value:reducedFeatVec = featVec[:axis]         #该特征之前的特征仍保留在样本dataSet中reducedFeatVec.extend(featVec[axis+1:]) #该特征之后的特征仍保留在样本dataSet中retDataSet.append(reducedFeatVec)        #把这个样本加到list中return retDataSet### 对于连续特征: 返回特征取值大于value的所有样本(以value为阈值将集合分成两部分)
def splitContinuousDataSet(dataSet, axis, value): retDataSetG = []        #将储存取值大于value的样本retDataSetL = []        #将储存取值小于value的样本  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        #返回两个集合, 是含2个元素的tuple形式### 根据InfoGain选择当前最好的划分特征(以及对于连续变量还要选择以什么值划分)
def chooseBestFeatureToSplit(dataSet,labels):  numFeatures = len(dataSet[0])-1baseEntropy = calcInfoEnt(dataSet) bestInfoGain = 0.0; bestFeature = -1bestSplitDict = {}for i in range(numFeatures):#遍历所有特征：下面这句是取每一行的第i个, 即得当前集合所有样本第i个feature的值featList = [example[i] for example in dataSet]#判断是否为离散特征if not (type(featList[0]).__name__=='float' or type(featList[0]).__name__=='int'): 
# 对于离散特征：求若以该特征划分的熵增uniqueVals = set(featList)        #从列表中创建集合set(得列表唯一元素值)newEntropy = 0.0for value in uniqueVals:        #遍历该离散特征每个取值subDataSet = splitDiscreteDataSet(dataSet, i, value)#计算每个取值的信息熵prob = len(subDataSet)/float(len(dataSet))newEntropy += prob * calcInfoEnt(subDataSet)#各取值的熵累加infoGain = baseEntropy - newEntropy    #得到以该特征划分的熵增 
# 对于连续特征：求若以该特征划分的熵增(区别：n个数据则需添n-1个候选划分点, 并选最佳划分点) else:  #产生n-1个候选划分点  sortfeatList=sorted(featList)  splitList=[]  for j in range(len(sortfeatList)-1):  #产生n-1个候选划分点splitList.append((sortfeatList[j] + sortfeatList[j+1])/2.0)  bestSplitEntropy = 10000                  #设定一个很大的熵值(之后用)#遍历n-1个候选划分点: 求选第j个候选划分点划分时的熵增, 并选出最佳划分点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 = newEntropybestSplit = jbestSplitDict[labels[i]] = splitList[bestSplit]#字典记录当前连续属性的最佳划分点infoGain = baseEntropy - bestSplitEntropy       #计算以该节点划分的熵增
# 在所有属性(包括连续和离散)中选择可以获得最大熵增的属性if infoGain > bestInfoGain:  bestInfoGain = infoGainbestFeature = i#若当前节点的最佳划分特征为连续特征，则需根据“是否小于等于其最佳划分点”进行二值化处理#即将该特征改为“是否小于等于bestSplitValue”, 例如将“密度”变为“密度<=0.3815”#注意：以下这段直接操作了原dataSet数据, 之前的那些float型的值相应变为0和1#【为何这样做?】在函数createTree()末尾将看到解释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] = 0return bestFeature      # 若特征已经划分完，节点下的样本还没有统一取值，则需要进行投票：计算每类Label个数, 取max者
def majorityCnt(classList):  classCount = {}      #将创建键值为Label类型的字典for vote in classList:  if vote not in classCount.keys():  classCount[vote] = 0      #第一次出现的Label加入字典classCount[vote] += 1      #计数return max(classCount)

2. 递归产生决策树

# 主程序：递归产生决策树# dataSet：当前用于构建树的数据集, 最开始就是data_full，然后随着划分的进行越来越小。这是因为进行到到树分叉点上了. 第一次划分之前17个瓜的数据在根节点，然后选择第一个bestFeat是纹理. 纹理的取值有清晰、模糊、稍糊三种；将瓜分成了清晰（9个），稍糊（5个），模糊（3个）,这时应该将划分的类别减少1以便于下次划分。 # labels：当前数据集中有的用于划分的类别(这是因为有些Label当前数据集没了, 比如假如到某个点上西瓜都是浅白没有深绿了)# data_full：全部的数据 # label_full:全部的类别 numLine = numColumn = 2 #这句是因为之后要用global numLine……至于为什么我一定要用global# 我也不完全理解。如果我只定义local变量总报错，我只好在那里的if里用global变量了。求解。def createTree(dataSet,labels,data_full,labels_full):  classList = [example[-1] for example in dataSet] #递归停止条件1：当前节点所有样本属于同一类；(注：count()方法统计某元素在列表中出现的次数)if classList.count(classList[0]) == len(classList):  return classList[0]#递归停止条件2：当前节点上样本集合为空集(即特征的某个取值上已经没有样本了)：global numLine,numColumn(numLine,numColumn) = shape(dataSet)if float(numLine) == 0:  return 'empty'#递归停止条件3：所有可用于划分的特征均使用过了，则调用majorityCnt()投票定Label；if float(numColumn) == 1:  return majorityCnt(classList) #不停止时继续划分：bestFeat = chooseBestFeatureToSplit(dataSet,labels)#调用函数找出当前最佳划分特征是第几个bestFeatLabel = labels[bestFeat]      #当前最佳划分特征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]) #划分完后, 即当前特征已经使用过了, 故将其从“待划分特征集”中删去#【递归调用】针对当前用于划分的特征(beatFeat)的每个取值，划分出一个子树。  for value in uniqueVals:    #遍历该特征【现存的】取值subLabels = labels[:]  if type(dataSet[0][bestFeat]).__name__=='str':  uniqueValsFull.remove(value)      #划分后删去(从uniqueValsFull中删!)myTree[bestFeatLabel][value] = createTree(splitDiscreteDataSet(dataSet,bestFeat,value),subLabels,data_full,labels_full)#用splitDiscreteDataSet()#是由于, 所有的连续特征在划分后都被我们定义的chooseBestFeatureToSplit()处理成离散取值了。if type(dataSet[0][bestFeat]).__name__=='str':  #若该特征离散【更详见后注】for value in uniqueValsFull:#则可能有些取值已经不在【现存的】取值中了#这就是上面为何从“uniqueValsFull”中删去#因为那些现有数据集中没取到的该特征的值，保留在了其中myTree[bestFeatLabel][value] = majorityCnt(classList)  return myTree 

3. 调用生成树

#生成树调用的语句
df = pd.read_excel(r'E:\BaiduNetdiskDownload\spss\数据\实验data\银行贷款.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)  

查看数据

data

labels

4. 绘制决策树

#绘决策树的函数
import matplotlib.pyplot as plt  
decisionNode = dict(boxstyle = "sawtooth",fc = "0.8")  #定义分支点的样式
leafNode = dict(boxstyle = "round4",fc = "0.8")  #定义叶节点的样式
arrow_args = dict(arrowstyle = "<-") #定义箭头标识样式# 计算树的叶子节点数量  
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 += 1return numLeafs# 计算树的最大深度
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 = thisDepthreturn maxDepth  # 画出节点  
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)  # 标箭头上的文字  
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)  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. 调用函数

#命令绘决策树的图
createPlot(myTree)

myTree