Python实现决策树C4.5算法的示例

为什么要改进成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。

#coding=utf-8
import operator
from math import log
import time
import os, sys
import string

def createDataSet(trainDataFile):
 print trainDataFile
 dataSet = []
 try:
 fin = open(trainDataFile)
 for line in fin:
  line = line.strip()
  cols = line.split('\t')
  row = [cols[1], cols[2], cols[3], cols[4], cols[5], cols[6], cols[7], cols[8], cols[9], cols[10], cols[0]]
  dataSet.append(row)
  #print row
 except:
 print 'Usage xxx.py trainDataFilePath'
 sys.exit()
 labels = ['cip1', 'cip2', 'cip3', 'cip4', 'sip1', 'sip2', 'sip3', 'sip4', 'sport', 'domain']
 print 'dataSetlen', len(dataSet)
 return dataSet, labels

#calc shannon entropy of label or feature
def calcShannonEntOfFeature(dataSet, feat):
 numEntries = len(dataSet)
 labelCounts = {}
 for feaVec in dataSet:
 currentLabel = feaVec[feat]
 if currentLabel not in labelCounts:
  labelCounts[currentLabel] = 0
 labelCounts[currentLabel] += 1
 shannonEnt = 0.0
 for key in labelCounts:
 prob = float(labelCounts[key])/numEntries
 shannonEnt -= prob * log(prob, 2)
 return shannonEnt

def splitDataSet(dataSet, axis, value):
 retDataSet = []
 for featVec in dataSet:
 if featVec[axis] == value:
  reducedFeatVec = featVec[:axis]
  reducedFeatVec.extend(featVec[axis+1:])
  retDataSet.append(reducedFeatVec)
 return retDataSet

def chooseBestFeatureToSplit(dataSet):
 numFeatures = len(dataSet[0]) - 1 #last col is label
 baseEntropy = calcShannonEntOfFeature(dataSet, -1)
 bestInfoGainRate = 0.0
 bestFeature = -1
 for i in range(numFeatures):
 featList = [example[i] for example in dataSet]
 uniqueVals = set(featList)
 newEntropy = 0.0
 for value in uniqueVals:
  subDataSet = splitDataSet(dataSet, i, value)
  prob = len(subDataSet) / float(len(dataSet))
  newEntropy += prob *calcShannonEntOfFeature(subDataSet, -1) #calc conditional entropy
 infoGain = baseEntropy - newEntropy
 　　 iv = calcShannonEntOfFeature(dataSet, i)
 if(iv == 0): #value of the feature is all same,infoGain and iv all equal 0, skip the feature
 continue
 　　 infoGainRate = infoGain / iv
 if infoGainRate > bestInfoGainRate:
  bestInfoGainRate = infoGainRate
  bestFeature = i
 return bestFeature

#feature is exhaustive, reture what you want label
def majorityCnt(classList):
 classCount = {}
 for vote in classList:
 if vote not in classCount.keys():
  classCount[vote] = 0
 classCount[vote] += 1
 return max(classCount)  

def createTree(dataSet, labels):
 classList = [example[-1] for example in dataSet]
 if classList.count(classList[0]) ==len(classList): #all data is the same label
 return classList[0]
 if len(dataSet[0]) == 1: #all feature is exhaustive
 return majorityCnt(classList)
 bestFeat = chooseBestFeatureToSplit(dataSet)
 bestFeatLabel = labels[bestFeat]
 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
 return classList[0]
 myTree = {bestFeatLabel:{}}
 del(labels[bestFeat])
 featValues = [example[bestFeat] for example in dataSet]
 uniqueVals = set(featValues)
 for value in uniqueVals:
 subLabels = labels[:]
 myTree[bestFeatLabel][value] = createTree(splitDataSet(dataSet, bestFeat, value),subLabels)
 return myTree

def main():
 if(len(sys.argv) < 3):
 print 'Usage xxx.py trainSet outputTreeFile'
 sys.exit()
 data,label = createDataSet(sys.argv[1])
 t1 = time.clock()
 myTree = createTree(data,label)
 t2 = time.clock()
 fout = open(sys.argv[2], 'w')
 fout.write(str(myTree))
 fout.close()
 print 'execute for ',t2-t1
if __name__=='__main__':
 main()

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