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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：
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)
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()
[‘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。
[1] Peter Harrington, machine learning in action.
[2] Tan, et al., Introduction to data minging.
【数据挖掘】关联分析之Apriori,布布扣,bubuko.com
标签：style blog class code tar ext
原文地址：http://blog.csdn.net/keyboardlabourer/article/details/25184825
