python实现C4.5决策树算法

C4.5算法使用信息增益率来代替ID3的信息增益进行特征的选择，克服了信息增益选择特征时偏向于特征值个数较多的不足。信息增益率的定义如下：

# -*- 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("\t") 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)

调用代码

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

from numpy import *
from C45DTree import *

dtree = C45DTree()
dtree.loadDataSet("dataset.dat",["age", "revenue", "student", "credit"])
dtree.train()

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

来源：https://blog.csdn.net/yjIvan/article/details/71272968