关联是机器学习中研究的一种问题，研究事物的关系，其中啤酒与尿布的故事是这个问题的典型。这里要引入几个概念：
1.支持度（Support）
支持度表示项集{X,Y}在总项集里出现的概率。公式为：
Support(X→Y) = P(X,Y) / P(I) = P(X∪Y) / P(I) = num(XUY) / num(I)
其中，I表示总事务集。num()表示求事务集里特定项集出现的次数。
比如，num(I)表示总事务集的个数
num(X∪Y)表示含有{X,Y}的事务集的个数（个数也叫次数）。
2.置信度 （Confidence）
置信度表示在先决条件X发生的情况下，由关联规则”X→Y“推出Y的概率。即在含有X的项集中，含有Y的可能性，公式为：
Confidence(X→Y) = P(Y|X) = P(X,Y) / P(X) = P(XUY) / P(X)
3.提升度（Lift）
提升度表示含有X的条件下，同时含有Y的概率，与Y总体发生的概率之比。
Lift(X→Y) = P(Y|X) / P(Y)
一、Apriori算法
Apriori 算法是一种最有影响力的挖掘布尔关联规则的频繁项集的 算法，它是由Rakesh Agrawal 和RamakrishnanSkrikant 提出的。
def createC1(dataSet):
C1 = []
for transaction in dataSet:
for item in transaction:
if [item] not in C1:
C1.append([item])
C1.sort()
return map(frozenset, C1)
def scanD(D, Ck, minSupport):
ssCnt = {}
for tid in D:
for can in Ck:
if can.issubset(tid):
ssCnt[can] = ssCnt.get(can, 0) + 1
numItems = float(len(D))
retList = []
supportData = {}
for key in ssCnt:
support = ssCnt[key] / numItems
if support >= minSupport:
retList.insert(0, key)
supportData[key] = support
return retList, supportData
def aprioriGen(Lk, k):
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(dataSet, minSupport=0.5):
C1 = createC1(dataSet)
D = map(set, dataSet)
L1, suppData = scanD(D, C1, minSupport)
L = [L1]
k = 2
while (len(L[k - 2]) > 0):
Ck = aprioriGen(L[k - 2], k)
Lk, supK = scanD(D, Ck, minSupport)
suppData.update(supK)
L.append(Lk)
k += 1
return L, suppData
def calcConf(freqSet, H, supportData, brl, minConf=0.7):
prunedH = []
for conseq in H:
conf = supportData[freqSet] / supportData[freqSet - conseq]
if conf >= minConf:
print freqSet - conseq, '-->', conseq, 'conf:', conf
brl.append((freqSet - conseq, conseq, conf))
prunedH.append(conseq)
return prunedH
def rulesFromConseq(freqSet, H, supportData, brl, minConf=0.7):
m = len(H[0])
if len(freqSet) > m + 1:
Hmp1 = aprioriGen(H, m + 1)
Hmp1 = calcConf(freqSet, Hmp1, supportData, brl, minConf)
if len(Hmp1) > 1:
rulesFromConseq(freqSet, Hmp1, supportData, brl, minConf)
def generateRules(L, supportData, minConf=0.7):
bigRuleList = []
for i in range(1, len(L)):
for freqSet in L[i]:
H1 = [frozenset([item]) for item in freqSet]
if i > 1:
rulesFromConseq(freqSet, H1, supportData, bigRuleList, minConf)
else:
calcConf(freqSet, H1, supportData, bigRuleList, minConf)
return bigRuleList
if __name__ == '__main__':
myDat = [ [ 1, 3, 4 ], [ 2, 3, 5 ], [ 1, 2, 3, 5 ], [ 2, 5 ] ]
L, suppData = apriori(myDat, 0.5)
rules = generateRules(L, suppData, minConf=0.7)
print 'rules:\n', rules
2.FP-growth算法
FP-growth算法是在Apriori改造而来的加快了速度
要使用这个算法需要下载库
sudo pip install pyfpgrowth
#-*- coding:utf-8 -*-
import pyfpgrowth
transactions = [[1, 2, 5],
[2, 4],
[2, 3],
[1, 2, 4],
[1, 3],
[2, 3],
[1, 3],
[1, 2, 3, 5],
[1, 2, 3]]
patterns = pyfpgrowth.find_frequent_patterns(transactions, 2)#2 这个位置的参数代表支持度
rules = pyfpgrowth.generate_association_rules(patterns, 0.7)#0.7 这个位置的参数代表置信度
print rules