C4.5演算法使用資訊增益率來代替ID3的資訊增益進行特徵的選擇，克服了資訊增益選擇特徵時偏向於特徵值個數較多的不足。資訊增益率的定義如下：

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


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


class C45DTree(object):
    def __init__(self):  # 構造方法
        self.tree = {}  # 生成樹
        self.dataSet = []  # 資料集
        self.labels = []  # 標籤集
 



    # 資料匯入函式
    def loadDataSet(self, path, labels):
        recordList = []
        fp = open(path, "rb")  # 讀取檔案內容
        content = fp.read()
        fp.close()
        rowList = content.splitlines()  # 按行轉換為一維表
        recordList = [row.split("\t") for row in rowList if row.strip()]  # strip()函式刪除空格、Tab等
 

        self.dataSet = recordList
        self.labels = labels


    # 執行決策樹函式
    def train(self):
        labels = copy.deepcopy(self.labels)
        self.tree = self.buildTree(self.dataSet, labels)


    # 構件決策樹：穿件決策樹主程式
    def buildTree(self, dataSet, lables):
        cateList = [data[-1] for data in
 
 dataSet]  # 抽取源資料集中的決策標籤列
        # 程式終止條件1：如果classList只有一種決策標籤，停止劃分，返回這個決策標籤
        if cateList.count(cateList[0]) == len(cateList):
            return cateList[0]
        # 程式終止條件2：如果資料集的第一個決策標籤只有一個，返回這個標籤
        if len(dataSet[0]) == 1:
            return self.maxCate(cateList)
        # 核心部分
        bestFeat, featValueList= self.getBestFeat(dataSet)  # 返回資料集的最優特徵軸
        bestFeatLabel = lables[bestFeat]
        tree = {bestFeatLabel: {}}
        del (lables[bestFeat])
        for value in featValueList:  # 決策樹遞迴生長
            subLables = lables[:]  # 將刪除後的特徵類別集建立子類別集
            # 按最優特徵列和值分隔資料集
            splitDataset = self.splitDataSet(dataSet, bestFeat, value)
            subTree = self.buildTree(splitDataset, subLables)  # 構建子樹
            tree[bestFeatLabel][value] = subTree
        return tree


    # 計算出現次數最多的類別標籤
    def maxCate(self, cateList):
        items = dict([(cateList.count(i), i) for i in cateList])
        return items[max(items.keys())]


    # 計算最優特徵
    def getBestFeat(self, dataSet):
        Num_Feats = len(dataSet[0][:-1])
        totality = len(dataSet)
        BaseEntropy = self.computeEntropy(dataSet)
        ConditionEntropy = []     # 初始化條件熵
        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)    # 總條件熵
        infoGainArray = BaseEntropy*ones(Num_Feats)-array(ConditionEntropy)
        infoGainRatio = infoGainArray/array(slpitInfo)  # C4.5資訊增益的計算
        bestFeatureIndex = argsort(-infoGainRatio)[0]
        return bestFeatureIndex, allFeatVList[bestFeatureIndex]

    # 計算劃分資訊
    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


 # 計算資訊熵
    # @staticmethod
    def computeEntropy(self, dataSet):
        dataLen = float(len(dataSet))
        cateList = [data[-1] for data in dataSet]  # 從資料集中得到類別標籤
        # 得到類別為key、 出現次數value的字典
        items = dict([(i, cateList.count(i)) for i in cateList])
        infoEntropy = 0.0
        for key in items:  # 夏農熵： = -p*log2(p) --infoEntropy = -prob * log(prob, 2)
            prob = float(items[key]) / dataLen
            infoEntropy -= prob * math.log(prob, 2)
        return infoEntropy


    # 劃分資料集： 分割資料集； 刪除特徵軸所在的資料列，返回剩餘的資料集
    # dataSet : 資料集； axis: 特徵軸； value: 特徵軸的取值
    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:])   # 將特徵軸之後的元素加回
                rtnList.append(rFeatVec)
        return rtnList

    # 存取樹到檔案
    def storetree(self, inputTree, filename):
        fw = open(filename,'w')
        pickle.dump(inputTree, fw)
        fw.close()

    # 從檔案抓取樹
    def grabTree(self, filename):
        fr = open(filename)
        return pickle.load(fr)

呼叫程式碼

# -*- 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