【Python学习系列十一】Python实现决策树实现C4.5(信息增益率)

C4.5是基于ID3改进的分类决策树算法，特点是C4.用信息增益率来选择属性，而ID3使用的是熵（entropy， 熵是一种不纯度度量准则），且对非离散数据也能处理，能够对不完整数据进行处理。

1、信息熵：





2、条件熵：





3、信息增益：

g(D,A)​=H(D)-H(D/A)

4、信息增益率：

gr(D,A)=g(D,A)/H(A)​

参考代码如下：

1）C45DTree.py

# -*- coding: utf-8 -*-

from numpy import *
import math
import copy
import cPickle as pickle

class C45DTree(object):
def __init__(self): # 构造方法
self.tree = {} # 生成树
self.dataSet = [] # 数据集
self.labels = [] # 标签集

# 数据导入函数
def loadDataSet(self, path, labels):
recordList = []
fp = open(path, "rb") # 读取文件内容
content = fp.read()
fp.close()
rowList = content.splitlines() # 按行转换为一维表
recordList = [row.split(",") for row in rowList if row.strip()] # strip()函数删除空格、Tab等
self.dataSet = recordList
self.labels = labels

# 执行决策树函数
def train(self):
labels = copy.deepcopy(self.labels)
self.tree = self.buildTree(self.dataSet, labels)

# 构件决策树：穿件决策树主程序
def buildTree(self, dataSet, lables):
cateList = [data[-1] for data in dataSet] # 抽取源数据集中的决策标签列
# 程序终止条件1：如果classList只有一种决策标签，停止划分，返回这个决策标签
if cateList.count(cateList[0]) == len(cateList):
return cateList[0]
# 程序终止条件2：如果数据集的第一个决策标签只有一个，返回这个标签
if len(dataSet[0]) == 1:
return self.maxCate(cateList)
# 核心部分
bestFeat, featValueList= self.getBestFeat(dataSet) # 返回数据集的最优特征轴
bestFeatLabel = lables[bestFeat]
tree = {bestFeatLabel: {}}
del (lables[bestFeat])
for value in featValueList: # 决策树递归生长
subLables = lables[:] # 将删除后的特征类别集建立子类别集
# 按最优特征列和值分隔数据集
splitDataset = self.splitDataSet(dataSet, bestFeat, value)
subTree = self.buildTree(splitDataset, subLables) # 构建子树
tree[bestFeatLabel][value] = subTree
return tree

# 计算出现次数最多的类别标签
def maxCate(self, cateList):
items = dict([(cateList.count(i), i) for i in cateList])
return items[max(items.keys())]

# 计算最优特征
def getBestFeat(self, dataSet):
Num_Feats = len(dataSet[0][:-1])
totality = len(dataSet)
BaseEntropy = self.computeEntropy(dataSet)
ConditionEntropy = [] # 初始化条件熵
slpitInfo = [] # for C4.5,caculate gain ratio
allFeatVList = []
for f in xrange(Num_Feats):
featList = [example[f] for example in dataSet]
[splitI, featureValueList] = self.computeSplitInfo(featList)
allFeatVList.append(featureValueList)
slpitInfo.append(splitI)
resultGain = 0.0
for value in featureValueList:
subSet = self.splitDataSet(dataSet, f, value)
appearNum = float(len(subSet))
subEntropy = self.computeEntropy(subSet)
resultGain += (appearNum/totality)*subEntropy
ConditionEntropy.append(resultGain) # 总条件熵
infoGainArray = BaseEntropy*ones(Num_Feats)-array(ConditionEntropy)
infoGainRatio = infoGainArray/array(slpitInfo) # C4.5信息增益的计算
bestFeatureIndex = argsort(-infoGainRatio)[0]
return bestFeatureIndex, allFeatVList[bestFeatureIndex]

# 计算划分信息
def computeSplitInfo(self, featureVList):
numEntries = len(featureVList)
featureVauleSetList = list(set(featureVList))
valueCounts = [featureVList.count(featVec) for featVec in featureVauleSetList]
pList = [float(item)/numEntries for item in valueCounts]
lList = [item*math.log(item, 2) for item in pList]
splitInfo = -sum(lList)
return splitInfo, featureVauleSetList

# 计算信息熵
# @staticmethod
def computeEntropy(self, dataSet):
dataLen = float(len(dataSet))
cateList = [data[-1] for data in dataSet] # 从数据集中得到类别标签
# 得到类别为key、 出现次数value的字典
items = dict([(i, cateList.count(i)) for i in cateList])
infoEntropy = 0.0
for key in items: # 香农熵： = -p*log2(p) --infoEntropy = -prob * log(prob, 2)
prob = float(items[key]) / dataLen
infoEntropy -= prob * math.log(prob, 2)
return infoEntropy

# 划分数据集： 分割数据集； 删除特征轴所在的数据列，返回剩余的数据集
# dataSet : 数据集； axis: 特征轴； value: 特征轴的取值
def splitDataSet(self, dataSet, axis, value):
rtnList = []
for featVec in dataSet:
if featVec[axis] == value:
rFeatVec = featVec[:axis] # list操作：提取0~（axis-1）的元素
rFeatVec.extend(featVec[axis + 1:]) # 将特征轴之后的元素加回
rtnList.append(rFeatVec)
return rtnList

# 存取树到文件
def storetree(self, inputTree, filename):
fw = open(filename,'w')
pickle.dump(inputTree, fw)
fw.close()

# 从文件抓取树
def grabTree(self, filename):
fr = open(filename)
return pickle.load(fr)


2）C45DTreeDemo.py
# -*- coding: utf-8 -*-

from numpy import *
from C45DTree import *

dtree = C45DTree()
dtree.loadDataSet("D:\dataset.dat",["outlook", "temperature", "humidity", "windy"])
dtree.train()

dtree.storetree(dtree.tree, "data.tree")
mytree = dtree.grabTree("data.tree")

print mytree

3）测试数据和执行结果：
0, 0, 0, 0, N
0, 0, 0, 1, N
1, 0, 0, 0, Y
2, 1, 0, 0, Y
2, 2, 1, 0, Y
2, 2, 1, 1, N
1, 2, 1, 1, Y

{'windy': {' 0': {'outlook': {'1': ' Y ', '0': ' N ', '2': ' Y '}}, ' 1': {'outlook': {'1': ' Y', '0': ' N ', '2': ' N '}}}}