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【数据挖掘】联系关系分析之Apriori

热度:109   发布时间:2016-05-05 15:43:55.0
【数据挖掘】关联分析之Apriori

1.Apriori算法


如果一个事务中有X,则该事务中则很有可能有Y,写成关联规则

{X}→{Y}

将这种找出项目之间联系的方法叫做关联分析。关联分析中最有名的问题是购物蓝问题,在超市购物时,有一个奇特的现象——顾客在买完尿布之后通常会买啤酒,即{尿布}→{啤酒}。原来,妻子嘱咐丈夫回家的时候记得给孩子买尿布,丈夫买完尿布后通常会买自己喜欢的啤酒。


考虑到规则的合理性,引入了两个度量:支持度(support)、置信度(confidence),定义如下


支持度保证项集(X, Y)在数据集出现的频繁程度,置信度确定Y在包含X中出现的频繁程度。


对于包含有d个项的数据集,可能的规则数为


如果用brute-force的方法,计算代价太大了。为此,R. Agrawal与R. Srikant提出了Apriori算法。同大部分的关联分析算法一样,Apriori算法分为两步:

  1. 生成频繁项集,即满足最小支持度阈值的所有项集;
  2. 生成关联规则,从上一步中找出的频繁项集中找出搞置信度的规则,即满足最小置信度阈值。

A priori在拉丁语中是“from before”(先验)的意思。Apriori算法也确实是用到了一个简单到不能再简单的先验:一个频繁项集的子集也是频繁的。

生成频繁项集、关联规则用到了剪枝,具体参看[2]。

class associationRule:    def __init__(self,dataSet):        self.sentences=map(set,dataSet)        self.minSupport=0.5        self.minConf=0.98        self.numSents=float(len(self.sentences))        self.supportData={}        self.L=[]        self.ruleList=[]    def createC1(self):        """create candidate itemsets of size 1 C1"""        C1=[]        for sentence in self.sentences:            for word in sentence:                if not [word] in C1:                    C1.append([word])        C1.sort()        return map(frozenset,C1)    def scan(self,Ck):        """generate frequent itemsets Lk from candidate itemsets Ck"""        wscnt={}         retList=[]        #calculate support for every itemset in Ck        for words in Ck:            for sentence in self.sentences:                if words.issubset(sentence):                    if not wscnt.has_key(words): wscnt[words]=1                    else: wscnt[words]+=1        for key in wscnt:            support=wscnt[key]/self.numSents            if support>=self.minSupport:                retList.append(key)            self.supportData[key]=support        self.L.append(retList)    def aprioriGen(self,Lk,k):        """the candidate generation: merge a pair of frequent (k ? 1)-itemsets         only if their first k ? 2 items are identical        """        retList=[]        lenLk=len(Lk)        for i in range(lenLk):            for j in range(i+1,lenLk):                L1=list(Lk[i])[:k-2]; L2=list(Lk[j])[:k-2]                L1.sort(); L2.sort()                if L1==L2:                    retList.append(Lk[i]|Lk[j])        return retList    def apriori(self):        """generate a list of frequent itemsets"""        C1=self.createC1()        self.scan(C1)        k=2        while(k<=3):            Ck=self.aprioriGen(self.L[k-2],k)            self.scan(Ck)            k+=1         def generateRules(self):        """generate a list of rules"""        for i in range(1,len(self.L)):    #get only sets with two or more items            for freqSet in self.L[i]:                H1=[frozenset([word]) for word in freqSet]                if(i>1): self.rulesFromConseq(freqSet,H1)                else: self.calcConf(freqSet,H1)  #set with two items    def calcConf(self,freqSet,H):        """calculate confidence, eliminate some rules by confidence-based pruning"""        prunedH=[]        for conseq in H:            conf=self.supportData[freqSet]/self.supportData[freqSet-conseq]            if conf>=self.minConf:                print "%s --> %s, conf=%.3f"%(map(str,freqSet-conseq), map(str,conseq), conf)                self.ruleList.append((freqSet-conseq,conseq,conf))                prunedH.append(conseq)        return prunedH    def rulesFromConseq(self,freqSet,H):        """generate more association rules from freqSet+H"""        m=len(H[0])        if len(freqSet)>m+1:                #try further merging            Hmp1=self.aprioriGen(H,m+1)     #create new candidate Hm+1            hmp1=self.calcConf(freqSet,Hmp1)            if len(Hmp1)>1:                self.rulesFromConseq(freqSet,Hmp1)

读取mushroom.dat数据集
def read_file(raw_file):    """read file"""    return [sorted(list(set(e.split()))) for e in             open(raw_file).read().strip().split('\n')]def main():    sentences=read_file('test.txt')    assrules=associationRule(sentences)    assrules.apriori()    assrules.generateRules()if __name__=="__main__":    main()

生成的规则

['76'] --> ['34'], conf=1.000
['34'] --> ['85'], conf=1.000
['36'] --> ['85'], conf=1.000
['24'] --> ['85'], conf=1.000
['53'] --> ['90'], conf=1.000
['53'] --> ['34'], conf=1.000
['2'] --> ['85'], conf=1.000
['76'] --> ['85'], conf=1.000
['67'] --> ['86'], conf=1.000
['76'] --> ['86'], conf=1.000
['67'] --> ['34'], conf=1.000
['67'] --> ['85'], conf=1.000
['90'] --> ['85'], conf=1.000
['86'] --> ['85'], conf=1.000
['53'] --> ['85'], conf=1.000
['53'] --> ['86'], conf=1.000
['39'] --> ['85'], conf=1.000
['34'] --> ['86'], conf=0.999
['86'] --> ['34'], conf=0.998
['63'] --> ['85'], conf=1.000
['59'] --> ['85'], conf=1.000
['53'] --> ['86', '85'], conf=1.000
['76'] --> ['34', '85'], conf=1.000
['53'] --> ['90', '34'], conf=1.000
['76'] --> ['86', '85'], conf=1.000
['53'] --> ['34', '85'], conf=1.000
['67'] --> ['34', '85'], conf=1.000
['76'] --> ['86', '34'], conf=1.000
['53'] --> ['86', '34'], conf=1.000
['67'] --> ['86', '34'], conf=1.000
['53'] --> ['90', '85'], conf=1.000
['67'] --> ['86', '85'], conf=1.000
['53'] --> ['90', '86'], conf=1.000
['86'] --> ['85', '34'], conf=0.998
['34'] --> ['86', '85'], conf=0.999


源代码在有些数据集上跑得很慢,还需要做一些优化。这里有一些用作关联分析测试的数据集。


2. Referrence


[1]  Peter Harrington, machine learning in action.

[2] Tan, et al., Introduction to data minging.