关联分析-Apriori法python代码注解

自己的一点点领悟,可能会有点小错误,欢迎交流^_^

获得频繁项集

主要思想

python代码

def loadDataSet():
    return [[1,3,4],[2,3,5],[1,2,3,5],[2,5]]

createC1(dataSet)获得所有第一层的所有项集

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)

#scanD是根据训练数据D,来判断Ck里面一堆的项集是否是频繁的。

def scanD(D,Ck,minSupport):
    ssCnt = {}
    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 = {}
    for key in ssCnt:
        support = ssCnt[key] / numItems
        if support >= minSupport:
            retList.insert(0,key)
        supportData[key] = support
    return retList,supportData

#根据前一层的项集的合并得到下一层的。比如
#值得注意的是这样得到的下一层不一定就是频繁项集,还得进行k-2次的判断
{1,2} {3,4} {1,3} 就可以得到{1,2,3}
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

#主函数,给出数据返回频繁项集
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
    return L,supportData

根据频繁项集获得关联规则

主要思想

只看规则的右边发现就是之前获得频繁项集的方法哦
然后对于一个频繁项集定义的规则必须包含所有的元素,那么只要一个规则的右边确定了的话,规则的左边=频繁项集-右边的。下面就是用H规则右边的可能情况表示。

pythoh代码

//主函数. 初始状态 使得规则右边也就是H只有一个元素。
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

//计算规则的支持度是否符合要求。最后返回所有可能的 规则右边的集合prunedH. brl存放了所有满足要求的规则。
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

//就像频繁项集一样，试图对规则的右边也就是H进行合并.然后产生新的规则
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)

注意点

apriori

转自Henry
At each level kk, you have kk-item sets which are frequent (have sufficent support).

At the next level, the kk+11-item sets you need to consider must have the property that each of their subsets must be frequent (have sufficent support). This is the apriori property: any subset of frequent itemset must be frequent.

So if you know at level 2 that the sets {1,2}{1,2}, {1,3}{1,3}, {1,5}{1,5} and {3,5}{3,5} are the only sets with sufficient support, then at level 3 you join these with each other to produce {1,2,3}{1,2,3}, {1,2,5}{1,2,5}, {1,3,5}{1,3,5} and {2,3,5}{2,3,5} but you need only consider {1,3,5}{1,3,5} further: the others each have subsets with insufficent support (such as {2,3}{2,3} or {2,5}{2,5} ).

极大频繁集

包含他的都不是频繁集

闭频繁集

包含他的支持度计数都小于他

习题

1

2

(a) s({e}) = 0.8 s({b,d}) = 0.2 s({b,d,e}) = 0.2

3

(a) $C(\phi \rightarrow A) = S(A)$
(b) c1>c2,c2<c3 -> c1>=c2,c2 <= c3
(c) 规则具有相同的置信度->支持度也就是left->right {left,rigth}的支持度一样

6

(a) $3^6-2^6*2+1 = 602$
(b) 4
(c) 5+C(4,3)+1+C(4,3) -> C(6,3)
(d) 黄油,面包

7

(b) {1,2,3,4},{1,2,3,5},{1,2,4,5},{1,3,4,5},{2,3,4,5}
(c) {1,2,3,4},{1,2,3,5}, //无{1,4,5},无{2,4,5}

8

1. 在画图的时候要注意,不仅仅是I的时候要向下画N，在是N的时候也也要向下画N。
2. F/total
3. I/total