• 连接步骤：频繁(k-1)项集Lk-1的自身连接产生候选k项集Ck

"""
# Python 2.7
# Filename: apriori.py
# Author: llhthinker
# Email: hangliu56[AT]gmail[DOT]com
# Blog: http://www.cnblogs.com/llhthinker/p/6719779.html
# Date: 2017-04-16
"""def load_data_set():"""Load a sample data set (From Data Mining: Concepts and Techniques, 3th Edition)Returns: A data set: A list of transactions. Each transaction contains several items."""data_set = [['l1', 'l2', 'l5'], ['l2', 'l4'], ['l2', 'l3'],['l1', 'l2', 'l4'], ['l1', 'l3'], ['l2', 'l3'],['l1', 'l3'], ['l1', 'l2', 'l3', 'l5'], ['l1', 'l2', 'l3']]return data_setdef create_C1(data_set):"""Create frequent candidate 1-itemset C1 by scaning data set.Args:data_set: A list of transactions. Each transaction contains several items.Returns:C1: A set which contains all frequent candidate 1-itemsets"""C1 = set()for t in data_set:for item in t:item_set = frozenset([item])C1.add(item_set)return C1def is_apriori(Ck_item, Lksub1):"""Judge whether a frequent candidate k-itemset satisfy Apriori property.Args:Ck_item: a frequent candidate k-itemset in Ck which contains all frequentcandidate k-itemsets.Lksub1: Lk-1, a set which contains all frequent candidate (k-1)-itemsets.Returns:True: satisfying Apriori property.False: Not satisfying Apriori property."""for item in Ck_item:sub_Ck = Ck_item - frozenset([item])if sub_Ck not in Lksub1:return Falsereturn Truedef create_Ck(Lksub1, k):"""Create Ck, a set which contains all all frequent candidate k-itemsetsby Lk-1's own connection operation.Args:Lksub1: Lk-1, a set which contains all frequent candidate (k-1)-itemsets.k: the item number of a frequent itemset.Return:Ck: a set which contains all all frequent candidate k-itemsets."""Ck = set()len_Lksub1 = len(Lksub1)list_Lksub1 = list(Lksub1)for i in range(len_Lksub1):for j in range(1, len_Lksub1):l1 = list(list_Lksub1[i])l2 = list(list_Lksub1[j])l1.sort()l2.sort()if l1[0:k-2] == l2[0:k-2]:Ck_item = list_Lksub1[i] | list_Lksub1[j]# pruningif is_apriori(Ck_item, Lksub1):Ck.add(Ck_item)return Ckdef generate_Lk_by_Ck(data_set, Ck, min_support, support_data):"""Generate Lk by executing a delete policy from Ck.Args:data_set: A list of transactions. Each transaction contains several items.Ck: A set which contains all all frequent candidate k-itemsets.min_support: The minimum support.support_data: A dictionary. The key is frequent itemset and the value is support.Returns:Lk: A set which contains all all frequent k-itemsets."""Lk = set()item_count = {}for t in data_set:for item in Ck:if item.issubset(t):if item not in item_count:item_count[item] = 1else:item_count[item] += 1t_num = float(len(data_set))for item in item_count:if (item_count[item] / t_num) >= min_support:Lk.add(item)support_data[item] = item_count[item] / t_numreturn Lkdef generate_L(data_set, k, min_support):"""Generate all frequent itemsets.Args:data_set: A list of transactions. Each transaction contains several items.k: Maximum number of items for all frequent itemsets.min_support: The minimum support.Returns:L: The list of Lk.support_data: A dictionary. The key is frequent itemset and the value is support."""support_data = {}C1 = create_C1(data_set)L1 = generate_Lk_by_Ck(data_set, C1, min_support, support_data)Lksub1 = L1.copy()L = []L.append(Lksub1)for i in range(2, k+1):Ci = create_Ck(Lksub1, i)Li = generate_Lk_by_Ck(data_set, Ci, min_support, support_data)Lksub1 = Li.copy()L.append(Lksub1)return L, support_datadef generate_big_rules(L, support_data, min_conf):"""Generate big rules from frequent itemsets.Args:L: The list of Lk.support_data: A dictionary. The key is frequent itemset and the value is support.min_conf: Minimal confidence.Returns:big_rule_list: A list which contains all big rules. Each big rule is representedas a 3-tuple."""big_rule_list = []sub_set_list = []for i in range(0, len(L)):for freq_set in L[i]:for sub_set in sub_set_list:if sub_set.issubset(freq_set):conf = support_data[freq_set] / support_data[freq_set - sub_set]big_rule = (freq_set - sub_set, sub_set, conf)if conf >= min_conf and big_rule not in big_rule_list:# print freq_set-sub_set, " => ", sub_set, "conf: ", conf
                        big_rule_list.append(big_rule)sub_set_list.append(freq_set)return big_rule_listif __name__ == "__main__":"""Test"""data_set = load_data_set()L, support_data = generate_L(data_set, k=3, min_support=0.2)big_rules_list = generate_big_rules(L, support_data, min_conf=0.7)for Lk in L:print "="*50print "frequent " + str(len(list(Lk)[0])) + "-itemsets\t\tsupport"print "="*50for freq_set in Lk:print freq_set, support_data[freq_set]printprint "Big Rules"for item in big_rules_list:print item[0], "=>", item[1], "conf: ", item[2]