python實(shí)現(xiàn)C4.5決策樹(shù)算法
C4.5算法使用信息增益率來(lái)代替ID3的信息增益進(jìn)行特征的選擇,克服了信息增益選擇特征時(shí)偏向于特征值個(gè)數(shù)較多的不足。信息增益率的定義如下:

# -*- coding: utf-8 -*-
from numpy import *
import math
import copy
import cPickle as pickle
class C45DTree(object):
def __init__(self): # 構(gòu)造方法
self.tree = {} # 生成樹(shù)
self.dataSet = [] # 數(shù)據(jù)集
self.labels = [] # 標(biāo)簽集
# 數(shù)據(jù)導(dǎo)入函數(shù)
def loadDataSet(self, path, labels):
recordList = []
fp = open(path, "rb") # 讀取文件內(nèi)容
content = fp.read()
fp.close()
rowList = content.splitlines() # 按行轉(zhuǎn)換為一維表
recordList = [row.split("\t") for row in rowList if row.strip()] # strip()函數(shù)刪除空格、Tab等
self.dataSet = recordList
self.labels = labels
# 執(zhí)行決策樹(shù)函數(shù)
def train(self):
labels = copy.deepcopy(self.labels)
self.tree = self.buildTree(self.dataSet, labels)
# 構(gòu)件決策樹(shù):穿件決策樹(shù)主程序
def buildTree(self, dataSet, lables):
cateList = [data[-1] for data in dataSet] # 抽取源數(shù)據(jù)集中的決策標(biāo)簽列
# 程序終止條件1:如果classList只有一種決策標(biāo)簽,停止劃分,返回這個(gè)決策標(biāo)簽
if cateList.count(cateList[0]) == len(cateList):
return cateList[0]
# 程序終止條件2:如果數(shù)據(jù)集的第一個(gè)決策標(biāo)簽只有一個(gè),返回這個(gè)標(biāo)簽
if len(dataSet[0]) == 1:
return self.maxCate(cateList)
# 核心部分
bestFeat, featValueList= self.getBestFeat(dataSet) # 返回?cái)?shù)據(jù)集的最優(yōu)特征軸
bestFeatLabel = lables[bestFeat]
tree = {bestFeatLabel: {}}
del (lables[bestFeat])
for value in featValueList: # 決策樹(shù)遞歸生長(zhǎng)
subLables = lables[:] # 將刪除后的特征類別集建立子類別集
# 按最優(yōu)特征列和值分隔數(shù)據(jù)集
splitDataset = self.splitDataSet(dataSet, bestFeat, value)
subTree = self.buildTree(splitDataset, subLables) # 構(gòu)建子樹(shù)
tree[bestFeatLabel][value] = subTree
return tree
# 計(jì)算出現(xiàn)次數(shù)最多的類別標(biāo)簽
def maxCate(self, cateList):
items = dict([(cateList.count(i), i) for i in cateList])
return items[max(items.keys())]
# 計(jì)算最優(yōu)特征
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信息增益的計(jì)算
bestFeatureIndex = argsort(-infoGainRatio)[0]
return bestFeatureIndex, allFeatVList[bestFeatureIndex]
# 計(jì)算劃分信息
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
# 計(jì)算信息熵
# @staticmethod
def computeEntropy(self, dataSet):
dataLen = float(len(dataSet))
cateList = [data[-1] for data in dataSet] # 從數(shù)據(jù)集中得到類別標(biāo)簽
# 得到類別為key、 出現(xiàn)次數(shù)value的字典
items = dict([(i, cateList.count(i)) for i in cateList])
infoEntropy = 0.0
for key in items: # 香農(nóng)熵: = -p*log2(p) --infoEntropy = -prob * log(prob, 2)
prob = float(items[key]) / dataLen
infoEntropy -= prob * math.log(prob, 2)
return infoEntropy
# 劃分?jǐn)?shù)據(jù)集: 分割數(shù)據(jù)集; 刪除特征軸所在的數(shù)據(jù)列,返回剩余的數(shù)據(jù)集
# dataSet : 數(shù)據(jù)集; axis: 特征軸; value: 特征軸的取值
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:]) # 將特征軸之后的元素加回
rtnList.append(rFeatVec)
return rtnList
# 存取樹(shù)到文件
def storetree(self, inputTree, filename):
fw = open(filename,'w')
pickle.dump(inputTree, fw)
fw.close()
# 從文件抓取樹(shù)
def grabTree(self, filename):
fr = open(filename)
return pickle.load(fr)
調(diào)用代碼
# -*- 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
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