最近学习了关联分析和用于寻找频繁项集的Apriori算法，做了一些笔记，并且来自己实现一下。
一、Apriori原理
首先需要了解几个基本概念：
项(item)： 每个item成为一个项，例如购物记录里的apple, banana, orange每一件不同的物品就是一个项。
项集： 一个或多个项的集合组成项集。
频繁项集： 出现次数大于某个阈值的项集，称为频繁项集。
事务(transaction)： 每一条记录称为一次事务，本质是一个项集，例如某一次购买的商品集合。
频繁项集的评估标准
-
支持度(support)是A，B同时出现的次数占总事务数的百分比。
-
置信度(confidence)是已知A出现条件下B出现的概率。
Apriori基本思想与原理
前提假设：频繁项集的所有非空子集也一定是频繁的。
步骤：
- 找出频繁项集：
- 对每条记录进行排序，使得item按照字典序排列，防止出现（a,b）和（b,a）同一个项集出现两次的情况。
- 产生频繁一项集，即数据列表中的每个item
- 由频繁项集产生强关联规则
二、评价
- 缺点：
- 频繁一项集会很大
- 未考虑出现次数
- 应用于商业领域可能需要考虑能产生更高效益的频繁项集
- 单纯频繁项集搜索及其改进算法比较成熟，但与推荐系统相结合仍然是值得探索的领域。
三、python实现Apriori算法
可惜的是，scikit-learn中并没有频繁集挖掘相关的算法类库，所以我自己编写python代码实现了一下这个算法。（借鉴了《数据挖掘》上提供的代码）
# 加载数据集，输出二维列表形式的数据
def load_data_set():
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_set
# 生成频繁一项集
def create_C1(data_set):
C1 = set()
for t in data_set:
for item in t:
item_set = frozenset([item])
C1.add(item_set)
return C1
# 判断是否满足apriori基本性质
def 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 frequent
candidate 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 False
return True
def create_Ck(Lksub1, k):
"""
Create Ck, a set which contains all all frequent candidate k-itemsets
by 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]
# pruning
if is_apriori(Ck_item, Lksub1):
Ck.add(Ck_item)
return Ck
def 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] = 1
else:
item_count[item] += 1
t_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_num
return Lk
def 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_data
def 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 represented
as 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_list
if __name__ == "__main__":
# Get the dataset in list format.
data_set = load_data_set()
# Do the iteration for n
L, support_data = generate_L(data_set, k=3, min_support=0.2)
# Get the frequent itemsets by given minimal confidence.
big_rules_list = generate_big_rules(L, support_data, min_conf=0.7)
# print the results
for Lk in L:
print("="*50)
print("frequent " + str(len(list(Lk)[0])) + "-itemsets\t\tsupport")
print("="*50)
for freq_set in Lk:
print(freq_set, support_data[freq_set])
print()
print()
print("Big Rules:")
for item in big_rules_list:
print(item[0], "=>", item[1], "confidence: ", item[2])
以上是以列表形式对数据进行处理，但对于大量样本数据，效率比较低下，而且机器学习模型标注数据集的格式是行表示记录，列表示特征，所以我想如果将列表数据转换成矩阵，然后通过对矩阵处理重新实现Apriori算法或许对于计算效率会有较大的提升。
参考文章
- Apriori算法介绍（Python实现）
文章出处登录后可见！
已经登录？立即刷新
