Python3 ID3决策树判断申请贷款是否成功
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2022-04-28 18:33:12
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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labelCounts
for 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Label
if 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 = 0.0
for key in labelCounts: #遍历每类Label
prob = 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])-1
baseEntropy = calcInfoEnt(dataSet)
bestInfoGain = 0.0; bestFeature = -1
bestSplitDict = {}
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 = 0.0
for 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 = newEntropy
bestSplit = j
bestSplitDict[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 = infoGain
bestFeature = 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] = 0
return 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 += 1
return 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 = thisDepth
return 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