# -*- coding: utf-8 -*-
"""
Created on Sat Aug 25 10:39:22 2018
@author: aoanng
"""
from math import log
##创建数据集
def createDataSet():
"""
创建数据集
"""
dataSet = [['青年', '否', '否', '一般', '拒绝'],
['青年', '否', '否', '好', '拒绝'],
['青年', '是', '否', '好', '同意'],
['青年', '是', '是', '一般', '同意'],
['青年', '否', '否', '一般', '拒绝'],
['中年', '否', '否', '一般', '拒绝'],
['中年', '否', '否', '好', '拒绝'],
['中年', '是', '是', '好', '同意'],
['中年', '否', '是', '非常好', '同意'],
['中年', '否', '是', '非常好', '同意'],
['老年', '否', '是', '非常好', '同意'],
['老年', '否', '是', '好', '同意'],
['老年', '是', '否', '好', '同意'],
['老年', '是', '否', '非常好', '同意'],
['老年', '否', '否', '一般', '拒绝'],
]
featureName = ['年龄', '有工作', '有房子', '信贷情况']
# 返回数据集和每个维度的名称
return dataSet, featureName
##分割数据集
def splitDataSet(dataSet,axis,value):
"""
按照给定特征划分数据集
:param axis:划分数据集的特征的维度
:param value:特征的值
:return: 符合该特征的所有实例（并且自动移除掉这维特征）
"""
# 循环遍历dataSet中的每一行数据
retDataSet = []
for featVec in dataSet:
if featVec[axis] == value:
reduceFeatVec = featVec[:axis] # 删除这一维特征
reduceFeatVec.extend(featVec[axis+1:])
retDataSet.append(reduceFeatVec)
return retDataSet
##计算信息熵
# 计算的始终是类别标签的不确定度
def calcShannonEnt(dataSet):
"""
计算训练数据集中的Y随机变量的香农熵
:param dataSet:
:return:
"""
numEntries = len(dataSet) # 实例的个数
labelCounts = {}
for featVec in dataSet: # 遍历每个实例，统计标签的频次
currentLabel = featVec[-1] # 表示最后一列
# 当前标签不在labelCounts map中，就让labelCounts加入该标签
if currentLabel not in labelCounts.keys():
labelCounts[currentLabel] =0
labelCounts[currentLabel] +=1
shannonEnt = 0.0
for key in labelCounts:
prob = float(labelCounts[key]) / numEntries
shannonEnt -= prob * log(prob,2) # log base 2
return shannonEnt
## 计算条件熵
def calcConditionalEntropy(dataSet,i,featList,uniqueVals):
"""
计算x_i给定的条件下，Y的条件熵
:param dataSet: 数据集
:param i: 维度i
:param featList: 数据集特征列表
:param unqiueVals: 数据集特征集合
:return: 条件熵
"""
ce = 0.0
for value in uniqueVals:
subDataSet = splitDataSet(dataSet,i,value)
prob = len(subDataSet) / float(len(dataSet)) # 极大似然估计概率
ce += prob * calcShannonEnt(subDataSet) #∑pH(Y|X=xi) 条件熵的计算
return ce
##计算信息增益
def calcInformationGain(dataSet,baseEntropy,i):
"""
计算信息增益
:param dataSet: 数据集
:param baseEntropy: 数据集中Y的信息熵
:param i: 特征维度i
:return: 特征i对数据集的信息增益g(dataSet | X_i)
"""
featList = [example[i] for example in dataSet] # 第i维特征列表
uniqueVals = set(featList) # 换成集合 - 集合中的每个元素不重复
newEntropy = calcConditionalEntropy(dataSet,i,featList,uniqueVals)#计算条件熵，
infoGain = baseEntropy - newEntropy # 信息增益 = 信息熵 - 条件熵
return infoGain
## 算法框架
def chooseBestFeatureToSplitByID3(dataSet):
"""
选择最好的数据集划分
:param dataSet:
:return:
"""
numFeatures = len(dataSet[0]) -1 # 最后一列是分类
baseEntropy = calcShannonEnt(dataSet) #返回整个数据集的信息熵
bestInfoGain = 0.0
bestFeature = -1
for i in range(numFeatures): # 遍历所有维度特征
infoGain = calcInformationGain(dataSet,baseEntropy,i) #返回具体特征的信息增益
if(infoGain > bestInfoGain):
bestInfoGain = infoGain
bestFeature = i
return bestFeature # 返回最佳特征对应的维度
def createTree(dataSet,featureName,chooseBestFeatureToSplitFunc = chooseBestFeatureToSplitByID3):
"""
创建决策树
:param dataSet: 数据集
:param featureName: 数据集每一维的名称
:return: 决策树
"""
classList = [example[-1] for example in dataSet] # 类别列表
if classList.count(classList[0]) == len(classList): # 统计属于列别classList[0]的个数
return classList[0] # 当类别完全相同则停止继续划分
if len(dataSet[0]) ==1: # 当只有一个特征的时候，遍历所有实例返回出现次数最多的类别
return majorityCnt(classList) # 返回类别标签
bestFeat = chooseBestFeatureToSplitFunc(dataSet)#最佳特征对应的索引
bestFeatLabel = featureName[bestFeat] #最佳特征
myTree ={bestFeatLabel:{}} # map 结构，且key为featureLabel
del (featureName[bestFeat])
# 找到需要分类的特征子集
featValues = [example[bestFeat] for example in dataSet]
uniqueVals = set(featValues)
for value in uniqueVals:
subLabels = featureName[:] # 复制操作
myTree[bestFeatLabel][value] = createTree(splitDataSet(dataSet,bestFeat,value),subLabels)
return myTree
# 测试决策树的构建
dataSet,featureName = createDataSet()
myTree = createTree(dataSet,featureName)
print(myTree)
可视化treePlotter.py文件：
# -*- coding: utf-8 -*-
"""
Created on Sat Aug 25 11:04:40 2018
@author: aoanng
"""
import matplotlib.pyplot as plt
# 定义文本框和箭头格式
decisionNode = dict(boxstyle="round4", color='#3366FF') #定义判断结点形态
leafNode = dict(boxstyle="circle", color='#FF6633') #定义叶结点形态
arrow_args = dict(arrowstyle="<-", color='g') #定义箭头
#绘制带箭头的注释
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)
#计算叶结点数
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
#计算树的层数
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
#在父子结点间填充文本信息
def plotMidText(cntrPt, parentPt, txtString):
xMid = (parentPt[0] - cntrPt[0]) / 2.0 + cntrPt[0]
yMid = (parentPt[1] - cntrPt[1]) / 2.0 + cntrPt[1]
createPlot.ax1.text(xMid, yMid, txtString, va="center", ha="center", rotation=30)
def plotTree(myTree, parentPt, nodeTxt):
numLeafs = getNumLeafs(myTree)
depth = getTreeDepth(myTree)
firstStr = list(myTree.keys())[0]
cntrPt = (plotTree.xOff + (1.0 + float(numLeafs)) / 2.0 / plotTree.totalW, plotTree.yOff)
plotMidText(cntrPt, parentPt, nodeTxt) #在父子结点间填充文本信息
plotNode(firstStr, cntrPt, parentPt, decisionNode) #绘制带箭头的注释
secondDict = myTree[firstStr]
plotTree.yOff = plotTree.yOff - 1.0 / plotTree.totalD
for key in secondDict.keys():
if type(secondDict[key]).__name__ == 'dict':
plotTree(secondDict[key], cntrPt, str(key))
else:
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
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.xOff = -0.5 / plotTree.totalW;
plotTree.yOff = 1.0;
plotTree(inTree, (0.5, 1.0), '')
plt.show()
完整调用main.py:
# -*- coding: utf-8 -*-
"""
Created on Sat Aug 25 10:00:16 2018
@author: aoanng
"""
from pylab import *
import treePlotter
from ID3Tree import *
mpl.rcParams['font.sans-serif'] = ['SimHei'] # 指定默认字体
mpl.rcParams['axes.unicode_minus'] = False # 解决保存图像时负号'-'显示为方块的问题
##################################
# 测试决策树的构建
myDat, labels = createDataSet()
myTree = createTree(myDat, labels)
# 绘制决策树
treePlotter.createPlot(myTree)
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