一个很重要的思想：
如果某元素不是频繁的，那么包含该元素的超集也是不频繁的。
发现dataSet的频繁集：
import numpy as np
import pandas as pd
def loadDataSet():
return [[1, 3, 4], [2, 3, 5], [1, 2, 3, 5], [2, 5]]
#提取数据集中所有的单独数据，参数是数据集
def createC1(dataSet):
C1 = []
for transaction in dataSet:
for item in transaction:
if not [item] in C1:
C1.append([item])
C1.sort()
return map(frozenset, C1)#use frozen set so we
#can use it as a key in a dict
#找出ck字典中所有的序列在D数据集中出现的次数以及由此 计算出的频繁度
def scanD(D, Ck, minSupport):
ssCnt = {}
#找出ck字典中所有的序列在D数据集中出现的次数
for tid in D:
for can in Ck:
if can.issubset(tid):
if not ssCnt.has_key(can): ssCnt[can]=1
else: ssCnt[can] += 1
numItems = float(len(D))
retList = []
supportData = {}
#计算每个序列的频繁度
for key in ssCnt:
support = ssCnt[key]/numItems
if support >= minSupport:
retList.insert(0,key)
supportData[key] = support
#返回合格的序列和对于的支持度
return retList, supportData
#Lk是k-1层的频繁度序列，这里是拼接处k层序列，在用上面的scanD函数计算出合格的序列
def aprioriGen(Lk, k): #creates Ck
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: #if first k-2 elements are equal
retList.append(Lk[i] | Lk[j]) #set union
return retList
# Apriori算法的主函数，用到以上的所有函数
def apriori(dataSet, minSupport = 0.5):
C1 = createC1(dataSet)
D = map(set, dataSet)
L1, supportData = 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)
supportData.update(supK)
L.append(Lk)
k += 1
#L是所有的合格的频繁度序列，supportData是一个字典，键是序列，值是支持度
return L, supportData从找出的频繁集中找关联规则：
def generateRules(L, supportData, minConf=0.7): #supportData is a dict coming from scanD bigRuleList = [] for i in range(1, len(L)):#only get the sets with two or more items 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 def calcConf(freqSet, H, supportData, brl, minConf=0.7): prunedH = [] #create new list to return for conseq in H: conf = supportData[freqSet]/supportData[freqSet-conseq] #calc confidence 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)): #try further merging Hmp1 = aprioriGen(H, m+1)#create Hm+1 new candidates Hmp1 = calcConf(freqSet, Hmp1, supportData, brl, minConf) if (len(Hmp1) > 1): #need at least two sets to merge rulesFromConseq(freqSet, Hmp1, supportData, brl, minConf)
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