c4.5决策树算法python_决策树之python实现C4.5算法
原理
C4.5算法是在ID3算法上的一种改进,它与ID3算法最大的区别就是特征选择上有所不同,一个是基于信息增益比,一个是基于信息增益。
之所以这样做是因为信息增益倾向于选择取值比较多的特征(特征越多,条件熵(特征划分后的类别变量的熵)越小,信息增益就越大);因此在信息增益下面加一个分母,该分母是当前所选特征的熵,注意:这里而不是类别变量的熵了。
这样就构成了新的特征选择准则,叫做信息增益比。为什么加了这样一个分母就会消除ID3算法倾向于选择取值较多的特征呢?
因为特征取值越多,该特征的熵就越大,分母也就越大,所以信息增益比就会减小,而不是像信息增益那样增大了,一定程度消除了算法对特征取值范围的影响。
实现
在算法实现上,C4.5算法只是修改了信息增益计算的函数calcShannonEntOfFeature和最优特征选择函数chooseBestFeatureToSplit。
calcShannonEntOfFeature在ID3的calcShannonEnt函数上加了个参数feat,ID3中该函数只用计算类别变量的熵,而calcShannonEntOfFeature可以计算指定特征或者类别变量的熵。
chooseBestFeatureToSplit函数在计算好信息增益后,同时计算了当前特征的熵IV,然后相除得到信息增益比,以最大信息增益比作为最优特征。
在划分数据的时候,有可能出现特征取同一个值,那么该特征的熵为0,同时信息增益也为0(类别变量划分前后一样,因为特征只有一个取值),0/0没有意义,可以跳过该特征。
代码
1 #coding=utf-8
2 import operator
3 frommath import log4 import time5 import os, sys6 import string
7
8 def createDataSet(trainDataFile):9 print trainDataFile10 dataSet =[]11 try:12 fin =open(trainDataFile)13 for line infin:14 line =line.strip()15 cols = line.split('\t')16 row = [cols[1], cols[2], cols[3], cols[4], cols[5], cols[6], cols[7], cols[8], cols[9], cols[10], cols[0]]17 dataSet.append(row)18 #print row19 except:20 print 'Usage xxx.py trainDataFilePath'
21 sys.exit()22 labels = ['cip1', 'cip2', 'cip3', 'cip4', 'sip1', 'sip2', 'sip3', 'sip4', 'sport', 'domain']23 print 'dataSetlen', len(dataSet)24 returndataSet, labels25
26 #calc shannon entropy of label or feature27 def calcShannonEntOfFeature(dataSet, feat):28 numEntries =len(dataSet)29 labelCounts ={}30 for feaVec indataSet:31 currentLabel =feaVec[feat]32 if currentLabel not inlabelCounts:33 labelCounts[currentLabel] = 0
34 labelCounts[currentLabel] += 1
35 shannonEnt = 0.0
36 for key inlabelCounts:37 prob = float(labelCounts[key])/numEntries38 shannonEnt -= prob * log(prob, 2)39 returnshannonEnt40
41 def splitDataSet(dataSet, axis, value):42 retDataSet =[]43 for featVec indataSet:44 if featVec[axis] ==value:45 reducedFeatVec =featVec[:axis]46 reducedFeatVec.extend(featVec[axis+1:])47 retDataSet.append(reducedFeatVec)48 returnretDataSet49
50 def chooseBestFeatureToSplit(dataSet):51 numFeatures = len(dataSet[0]) - 1 #last col islabel52 baseEntropy = calcShannonEntOfFeature(dataSet, -1)53 bestInfoGainRate = 0.0
54 bestFeature = -1
55 for i inrange(numFeatures):56 featList = [example[i] for example indataSet]57 uniqueVals = set(featList)58 newEntropy = 0.0
59 for value inuniqueVals:60 subDataSet =splitDataSet(dataSet, i, value)61 prob = len(subDataSet) / float(len(dataSet))62 newEntropy += prob *calcShannonEntOfFeature(subDataSet, -1) #calc conditional entropy63 infoGain = baseEntropy -newEntropy64 iv =calcShannonEntOfFeature(dataSet, i)65 if(iv == 0): #value of the feature is all same,infoGain and iv all equal 0, skip the feature66 continue
67 infoGainRate = infoGain /iv68 if infoGainRate >bestInfoGainRate:69 bestInfoGainRate =infoGainRate70 bestFeature =i71 returnbestFeature72
73 #feature isexhaustive, reture what you want label74 def majorityCnt(classList):75 classCount ={}76 for vote inclassList:77 if vote not inclassCount.keys():78 classCount[vote] = 0
79 classCount[vote] += 1
80 returnmax(classCount)81
82 def createTree(dataSet, labels):83 classList = [example[-1] for example indataSet]84 if classList.count(classList[0]) ==len(classList): #all data isthe same label85 return classList[0]86 if len(dataSet[0]) == 1: #all feature isexhaustive87 returnmajorityCnt(classList)88 bestFeat =chooseBestFeatureToSplit(dataSet)89 bestFeatLabel =labels[bestFeat]90 if(bestFeat == -1): #特征一样,但类别不一样,即类别与特征不相关,随机选第一个类别做分类结果91 return classList[0]92 myTree ={bestFeatLabel:{}}93 del(labels[bestFeat])94 featValues = [example[bestFeat] for example indataSet]95 uniqueVals = set(featValues)96 for value inuniqueVals:97 subLabels =labels[:]98 myTree[bestFeatLabel][value] =createTree(splitDataSet(dataSet, bestFeat, value),subLabels)99 returnmyTree100
101 def main():102 if(len(sys.argv) < 3):103 print 'Usage xxx.py trainSet outputTreeFile'
104 sys.exit()105 data,label = createDataSet(sys.argv[1])106 t1 =time.clock()107 myTree =createTree(data,label)108 t2 =time.clock()109 fout = open(sys.argv[2], 'w')110 fout.write(str(myTree))111 fout.close()112 print 'execute for',t2-t1113 if __name__=='__main__':114 main()
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