Decision Tree.py

# -*- coding: UTF-8 -*-
from matplotlib.font_manager import FontProperties
import matplotlib.pyplot as plt
from math import log
import operator
import pickle

"""
函数说明:计算给定数据集的经验熵(香农熵)

Parameters:
	dataSet - 数据集
Returns:
	shannonEnt - 经验熵(香农熵)
Author:
	Jack Cui
Blog:
	http://blog.csdn.net/c406495762
Modify:
	2017-07-24
"""
def calcShannonEnt(dataSet):
	numEntires = len(dataSet)						#返回数据集的行数
	labelCounts = {}								#保存每个标签(Label)出现次数的字典
	for featVec in dataSet:							#对每组特征向量进行统计
		currentLabel = featVec[-1]					#提取标签(Label)信息
		if currentLabel not in labelCounts.keys():	#如果标签(Label)没有放入统计次数的字典,添加进去
			labelCounts[currentLabel] = 0
		labelCounts[currentLabel] += 1				#Label计数
	shannonEnt = 0.0								#经验熵(香农熵)
	for key in labelCounts:							#计算香农熵
		prob = float(labelCounts[key]) / numEntires	#选择该标签(Label)的概率
		shannonEnt -= prob * log(prob, 2)			#利用公式计算
	return shannonEnt								#返回经验熵(香农熵)

"""
函数说明:创建测试数据集

Parameters:
	无
Returns:
	dataSet - 数据集
	labels - 特征标签
Author:
	Jack Cui
Blog:
	http://blog.csdn.net/c406495762
Modify:
	2017-07-20
"""
def createDataSet():
	dataSet = [[0, 0, 0, 0, 'no'],						#数据集
			[0, 0, 0, 1, 'no'],
			[0, 1, 0, 1, 'yes'],
			[0, 1, 1, 0, 'yes'],
			[0, 0, 0, 0, 'no'],
			[1, 0, 0, 0, 'no'],
			[1, 0, 0, 1, 'no'],
			[1, 1, 1, 1, 'yes'],
			[1, 0, 1, 2, 'yes'],
			[1, 0, 1, 2, 'yes'],
			[2, 0, 1, 2, 'yes'],
			[2, 0, 1, 1, 'yes'],
			[2, 1, 0, 1, 'yes'],
			[2, 1, 0, 2, 'yes'],
			[2, 0, 0, 0, 'no']]
	labels = ['年龄', '有工作', '有自己的房子', '信贷情况']		#特征标签
	return dataSet, labels 							#返回数据集和分类属性

"""
函数说明:按照给定特征划分数据集

Parameters:
	dataSet - 待划分的数据集
	axis - 划分数据集的特征
	value - 需要返回的特征的值
Returns:
	无
Author:
	Jack Cui
Blog:
	http://blog.csdn.net/c406495762
Modify:
	2017-07-24
"""
def splitDataSet(dataSet, axis, value):		
	retDataSet = []										#创建返回的数据集列表
	for featVec in dataSet: 							#遍历数据集
		if featVec[axis] == value:
			reducedFeatVec = featVec[:axis]				#去掉axis特征
			reducedFeatVec.extend(featVec[axis+1:]) 	#将符合条件的添加到返回的数据集
			retDataSet.append(reducedFeatVec)
	return retDataSet		  							#返回划分后的数据集

"""
函数说明:选择最优特征

Parameters:
	dataSet - 数据集
Returns:
	bestFeature - 信息增益最大的(最优)特征的索引值
Author:
	Jack Cui
Blog:
	http://blog.csdn.net/c406495762
Modify:
	2017-07-20
"""
def chooseBestFeatureToSplit(dataSet):
	numFeatures = len(dataSet[0]) - 1					#特征数量
	baseEntropy = calcShannonEnt(dataSet) 				#计算数据集的香农熵
	bestInfoGain = 0.0  								#信息增益
	bestFeature = -1									#最优特征的索引值
	for i in range(numFeatures): 						#遍历所有特征
		#获取dataSet的第i个所有特征
		featList = [example[i] for example in dataSet]
		uniqueVals = set(featList)     					#创建set集合{},元素不可重复
		newEntropy = 0.0  								#经验条件熵
		for value in uniqueVals: 						#计算信息增益
			subDataSet = splitDataSet(dataSet, i, value) 		#subDataSet划分后的子集
			prob = len(subDataSet) / float(len(dataSet))   		#计算子集的概率
			newEntropy += prob * calcShannonEnt(subDataSet) 	#根据公式计算经验条件熵
		infoGain = baseEntropy - newEntropy 					#信息增益
		# print("第%d个特征的增益为%.3f" % (i, infoGain))			#打印每个特征的信息增益
		if (infoGain > bestInfoGain): 							#计算信息增益
			bestInfoGain = infoGain 							#更新信息增益，找到最大的信息增益
			bestFeature = i 									#记录信息增益最大的特征的索引值
	return bestFeature 											#返回信息增益最大的特征的索引值


"""
函数说明:统计classList中出现此处最多的元素(类标签)

Parameters:
	classList - 类标签列表
Returns:
	sortedClassCount[0][0] - 出现此处最多的元素(类标签)
Author:
	Jack Cui
Blog:
	http://blog.csdn.net/c406495762
Modify:
	2017-07-24
"""
def majorityCnt(classList):
	classCount = {}
	for vote in classList:										#统计classList中每个元素出现的次数
		if vote not in classCount.keys():classCount[vote] = 0	
		classCount[vote] += 1
	sortedClassCount = sorted(classCount.items(), key = operator.itemgetter(1), reverse = True)		#根据字典的值降序排序
	return sortedClassCount[0][0]								#返回classList中出现次数最多的元素

"""
函数说明:创建决策树

Parameters:
	dataSet - 训练数据集
	labels - 分类属性标签
	featLabels - 存储选择的最优特征标签
Returns:
	myTree - 决策树
Author:
	Jack Cui
Blog:
	http://blog.csdn.net/c406495762
Modify:
	2017-07-25
"""
def createTree(dataSet, labels, featLabels):
	classList = [example[-1] for example in dataSet]			#取分类标签(是否放贷:yes or no)
	if classList.count(classList[0]) == len(classList):			#如果类别完全相同则停止继续划分
		return classList[0]
	if len(dataSet[0]) == 1 or len(labels) == 0:									#遍历完所有特征时返回出现次数最多的类标签
		return majorityCnt(classList)
	bestFeat = chooseBestFeatureToSplit(dataSet)				#选择最优特征
	bestFeatLabel = labels[bestFeat]							#最优特征的标签
	featLabels.append(bestFeatLabel)
	myTree = {bestFeatLabel:{}}									#根据最优特征的标签生成树
	del(labels[bestFeat])										#删除已经使用特征标签
	featValues = [example[bestFeat] for example in dataSet]		#得到训练集中所有最优特征的属性值
	uniqueVals = set(featValues)								#去掉重复的属性值
	for value in uniqueVals:									#遍历特征，创建决策树。
		subLabels = labels[:]
		myTree[bestFeatLabel][value] = createTree(splitDataSet(dataSet, bestFeat, value), subLabels, featLabels)
        
	return myTree

"""
函数说明:获取决策树叶子结点的数目

Parameters:
	myTree - 决策树
Returns:
	numLeafs - 决策树的叶子结点的数目
Author:
	Jack Cui
Blog:
	http://blog.csdn.net/c406495762
Modify:
	2017-07-24
"""
def getNumLeafs(myTree):
    numLeafs = 0												#初始化叶子
    firstStr = next(iter(myTree))								#python3中myTree.keys()返回的是dict_keys,不在是list,所以不能使用myTree.keys()[0]的方法获取结点属性，可以使用list(myTree.keys())[0]
    secondDict = myTree[firstStr]								#获取下一组字典
    for key in secondDict.keys():
        if type(secondDict[key]).__name__=='dict':				#测试该结点是否为字典，如果不是字典，代表此结点为叶子结点
            numLeafs += getNumLeafs(secondDict[key])
        else:   numLeafs +=1
    return numLeafs

"""
函数说明:获取决策树的层数

Parameters:
	myTree - 决策树
Returns:
	maxDepth - 决策树的层数
Author:
	Jack Cui
Blog:
	http://blog.csdn.net/c406495762
Modify:
	2017-07-24
"""
def getTreeDepth(myTree):
    maxDepth = 0												#初始化决策树深度
    firstStr = next(iter(myTree))								#python3中myTree.keys()返回的是dict_keys,不在是list,所以不能使用myTree.keys()[0]的方法获取结点属性，可以使用list(myTree.keys())[0]
    secondDict = myTree[firstStr]								#获取下一个字典
    for key in secondDict.keys():
        if type(secondDict[key]).__name__=='dict':				#测试该结点是否为字典，如果不是字典，代表此结点为叶子结点
            thisDepth = 1 + getTreeDepth(secondDict[key])
        else:   thisDepth = 1
        if thisDepth > maxDepth: maxDepth = thisDepth			#更新层数
    return maxDepth

"""
函数说明:绘制结点

Parameters:
	nodeTxt - 结点名
	centerPt - 文本位置
	parentPt - 标注的箭头位置
	nodeType - 结点格式
Returns:
	无
Author:
	Jack Cui
Blog:
	http://blog.csdn.net/c406495762
Modify:
	2017-07-24
"""
def plotNode(nodeTxt, centerPt, parentPt, nodeType):
	arrow_args = dict(arrowstyle="<-")											#定义箭头格式
	font = FontProperties(fname=r"c:\windows\fonts\simsunb.ttf", size=14)		#设置中文字体
	createPlot.ax1.annotate(nodeTxt, xy=parentPt,  xycoords='axes fraction',	#绘制结点
		xytext=centerPt, textcoords='axes fraction',
		va="center", ha="center", bbox=nodeType, arrowprops=arrow_args, FontProperties=font)

"""
函数说明:标注有向边属性值

Parameters:
	cntrPt、parentPt - 用于计算标注位置
	txtString - 标注的内容
Returns:
	无
Author:
	Jack Cui
Blog:
	http://blog.csdn.net/c406495762
Modify:
	2017-07-24
""" 
def plotMidText(cntrPt, parentPt, txtString):
	xMid = (parentPt[0]-cntrPt[0])/2.0 + cntrPt[0]											#计算标注位置					
	yMid = (parentPt[1]-cntrPt[1])/2.0 + cntrPt[1]
	createPlot.ax1.text(xMid, yMid, txtString, va="center", ha="center", rotation=30)

"""
函数说明:绘制决策树

Parameters:
	myTree - 决策树(字典)
	parentPt - 标注的内容
	nodeTxt - 结点名
Returns:
	无
Author:
	Jack Cui
Blog:
	http://blog.csdn.net/c406495762
Modify:
	2017-07-24
""" 
def plotTree(myTree, parentPt, nodeTxt):
	decisionNode = dict(boxstyle="sawtooth", fc="0.8")										#设置结点格式
	leafNode = dict(boxstyle="round4", fc="0.8")											#设置叶结点格式
	numLeafs = getNumLeafs(myTree)  														#获取决策树叶结点数目，决定了树的宽度
	depth = getTreeDepth(myTree)															#获取决策树层数
	firstStr = next(iter(myTree))															#下个字典     											
	cntrPt = (plotTree.xOff + (1.0 + float(numLeafs))/2.0/plotTree.totalW, plotTree.yOff)	#中心位置
	plotMidText(cntrPt, parentPt, nodeTxt)													#标注有向边属性值
	plotNode(firstStr, cntrPt, parentPt, decisionNode)										#绘制结点
	secondDict = myTree[firstStr]															#下一个字典，也就是继续绘制子结点
	plotTree.yOff = plotTree.yOff - 1.0/plotTree.totalD										#y偏移
	for key in secondDict.keys():								
		if type(secondDict[key]).__name__=='dict':											#测试该结点是否为字典，如果不是字典，代表此结点为叶子结点
			plotTree(secondDict[key],cntrPt,str(key))        								#不是叶结点，递归调用继续绘制
		else:																				#如果是叶结点，绘制叶结点，并标注有向边属性值 											
			plotTree.xOff = plotTree.xOff + 1.0/plotTree.totalW
			plotNode(secondDict[key], (plotTree.xOff, plotTree.yOff), cntrPt, leafNode)
			plotMidText((plotTree.xOff, plotTree.yOff), cntrPt, str(key))
	plotTree.yOff = plotTree.yOff + 1.0/plotTree.totalD

"""
函数说明:创建绘制面板

Parameters:
	inTree - 决策树(字典)
Returns:
	无
Author:
	Jack Cui
Blog:
	http://blog.csdn.net/c406495762
Modify:
	2017-07-24
""" 
def createPlot(inTree):
    fig = plt.figure(1, facecolor='white')													#创建fig
    fig.clf()																				#清空fig
    axprops = dict(xticks=[], yticks=[])
    createPlot.ax1 = plt.subplot(111, frameon=False, **axprops)    							#去掉x、y轴
    plotTree.totalW = float(getNumLeafs(inTree))											#获取决策树叶结点数目
    plotTree.totalD = float(getTreeDepth(inTree))											#获取决策树层数
    plotTree.xOff = -0.5/plotTree.totalW; plotTree.yOff = 1.0;								#x偏移
    plotTree(inTree, (0.5,1.0), '')															#绘制决策树
    plt.show()																				#显示绘制结果

"""
函数说明:使用决策树分类

Parameters:
	inputTree - 已经生成的决策树
	featLabels - 存储选择的最优特征标签
	testVec - 测试数据列表，顺序对应最优特征标签
Returns:
	classLabel - 分类结果
Author:
	Jack Cui
Blog:
	http://blog.csdn.net/c406495762
Modify:
	2017-07-25
""" 
def classify(inputTree, featLabels, testVec):
	firstStr = next(iter(inputTree))														#获取决策树结点
	secondDict = inputTree[firstStr]														#下一个字典
	featIndex = featLabels.index(firstStr)												
	for key in secondDict.keys():
		if testVec[featIndex] == key:
			if type(secondDict[key]).__name__ == 'dict':
				classLabel = classify(secondDict[key], featLabels, testVec)
			else: classLabel = secondDict[key]
	return classLabel

"""
函数说明:存储决策树

Parameters:
	inputTree - 已经生成的决策树
	filename - 决策树的存储文件名
Returns:
	无
Author:
	Jack Cui
Blog:
	http://blog.csdn.net/c406495762
Modify:
	2017-07-25
""" 
def storeTree(inputTree, filename):
	with open(filename, 'wb') as fw:
		pickle.dump(inputTree, fw)

"""
函数说明:读取决策树

Parameters:
	filename - 决策树的存储文件名
Returns:
	pickle.load(fr) - 决策树字典
Author:
	Jack Cui
Blog:
	http://blog.csdn.net/c406495762
Modify:
	2017-07-25
""" 
def grabTree(filename):
	fr = open(filename, 'rb')
	return pickle.load(fr)


if __name__ == '__main__':
	dataSet, labels = createDataSet()
	featLabels = []
	myTree = createTree(dataSet, labels, featLabels)
	createPlot(myTree)
	testVec = [0,1]										#测试数据
	result = classify(myTree, featLabels, testVec)
	if result == 'yes':
		print('放贷')
	if result == 'no':
		print('不放贷')