Apriori 演算法的示意圖：

Apriori演算法較為簡單：只需要明白兩個概念就好：

  1）支援度：

   每次交易的所有商品為一個集合設位Y={.....}，X為二元集合，計算X的支援度，則需遍歷每個集合Y，查詢Y中是否含有與X相同的子集，如果有，則其支援度計數加1，直到得到其最後的支援度F(Xn)；在所有X集合的基礎上建立集合Z，Z為三元集合，含有3個商品元素，同樣遍歷所有商品記錄，計算Z所對應的支援度、

 2）置信度：我們需要為候選集的選擇建立個條件，即為它的閾值，支援度閾值或置信度的閾值，可由支援度計算得出，計算出某商品會在某個商品子集的概率分佈。

程式碼實現如下：

"""
Description     : Simple Python implementation of the Apriori Algorithm


使用方法；


    $python apriori.py -f DATASET.csv -s minSupport  -c minConfidence
說明：-f 對應的是資料檔案  -s 對應的是最小支援度  -c 對應的是最小置信度
    $python apriori.py -f DATASET.csv -s 0.15 -c 0.6
"""


import sys


from itertools import chain, combinations
from collections import defaultdict
from optparse import OptionParser




def subsets(arr):
    """ Returns non empty subsets of arr"""
    return chain(*[combinations(arr, i + 1) for i, a in enumerate(arr)])




def returnItemsWithMinSupport(itemSet, transactionList, minSupport, freqSet):
        """calculates the support for items in the itemSet and returns a subset
       of the itemSet each of whose elements satisfies the minimum support"""
        _itemSet = set()
        localSet = defaultdict(int)


        for item in itemSet:
                for transaction in transactionList:
                        if item.issubset(transaction):
                                freqSet[item] += 1
                                localSet[item] += 1


        for item, count in localSet.items():
                support = float(count)/len(transactionList)


                if support >= minSupport:
                        _itemSet.add(item)


        return _itemSet




def joinSet(itemSet, length):
        """Join a set with itself and returns the n-element itemsets"""
        return set([i.union(j) for i in itemSet for j in itemSet if len(i.union(j)) == length])




def getItemSetTransactionList(data_iterator):
    transactionList = list()
    itemSet = set()
    for record in data_iterator:
        transaction = frozenset(record)
        transactionList.append(transaction)
        for item in transaction:
            itemSet.add(frozenset([item]))              # Generate 1-itemSets
    return itemSet, transactionList




def runApriori(data_iter, minSupport, minConfidence):
    """
    run the apriori algorithm. data_iter is a record iterator
    Return both:
     - items (tuple, support)
     - rules ((pretuple, posttuple), confidence)
    """
    itemSet, transactionList = getItemSetTransactionList(data_iter)


    freqSet = defaultdict(int)
    largeSet = dict()
    # Global dictionary which stores (key=n-itemSets,value=support)
    # which satisfy minSupport


    assocRules = dict()
    # Dictionary which stores Association Rules


    oneCSet = returnItemsWithMinSupport(itemSet,
                                        transactionList,
                                        minSupport,
                                        freqSet)


    currentLSet = oneCSet
    k = 2
    while(currentLSet != set([])):
        largeSet[k-1] = currentLSet
        currentLSet = joinSet(currentLSet, k)
        currentCSet = returnItemsWithMinSupport(currentLSet,
                                                transactionList,
                                                minSupport,
                                                freqSet)
        currentLSet = currentCSet
        k = k + 1


    def getSupport(item):
            """local function which Returns the support of an item"""
            return float(freqSet[item])/len(transactionList)


    toRetItems = []
    for key, value in largeSet.items():
        toRetItems.extend([(tuple(item), getSupport(item))
                           for item in value])


    toRetRules = []
    for key, value in largeSet.items()[1:]:
        for item in value:
            _subsets = map(frozenset, [x for x in subsets(item)])
            for element in _subsets:
                remain = item.difference(element)
                if len(remain) > 0:
                    confidence = getSupport(item)/getSupport(element)
                    if confidence >= minConfidence:
                        toRetRules.append(((tuple(element), tuple(remain)),
                                           confidence))
    return toRetItems, toRetRules




def printResults(items, rules):
    """prints the generated itemsets sorted by support and the confidence rules sorted by confidence"""
    for item, support in sorted(items, key=lambda (item, support): support):
        print "item: %s , %.3f" % (str(item), support)
    print "\n------------------------ RULES:"
    for rule, confidence in sorted(rules, key=lambda (rule, confidence): confidence):
        pre, post = rule
        print "Rule: %s ==> %s , %.3f" % (str(pre), str(post), confidence)




def dataFromFile(fname):
        """Function which reads from the file and yields a generator"""
        file_iter = open(fname, 'rU')
        for line in file_iter:
                line = line.strip().rstrip(',')                         # Remove trailing comma
                record = frozenset(line.split(','))
                yield record




if __name__ == "__main__":


    optparser = OptionParser()
    optparser.add_option('-f', '--inputFile',
                         dest='input',
                         help='filename containing csv',
                         default=None)
    optparser.add_option('-s', '--minSupport',
                         dest='minS',
                         help='minimum support value',
                         default=0.15,
                         type='float')
    optparser.add_option('-c', '--minConfidence',
                         dest='minC',
                         help='minimum confidence value',
                         default=0.6,
                         type='float')


    (options, args) = optparser.parse_args()


    inFile = None
    if options.input is None:
            inFile = sys.stdin
    elif options.input is not None:
            inFile = dataFromFile(options.input)
    else:
            print 'No dataset filename specified, system with exit\n'
            sys.exit('System will exit')


    minSupport = options.minS
    minConfidence = options.minC


    items, rules = runApriori(inFile, minSupport, minConfidence)

    printResults(items, rules)

參考文章：

https://blog.csdn.net/androidlushangderen/article/details/43059211

https://github.com/asaini/Apriori/edit/master