apriori算法实验

### APRIORI算法实验与实现

#### 1. 理解APRIORI算法的核心概念
APRIORI算法是一种经典的关联规则挖掘技术，旨在从大型数据集中找出频繁项集并生成强关联规则。为了有效执行此操作，该算法依赖于两个主要参数：最小支持度(minimum support)和最小置信度(minimum confidence)[^1]。

#### 2. 实验设计思路
在准备进行APRIORI算法的实验之前，需先定义好目标数据库以及预期要解决的具体问题。通常情况下，会选取具有代表性的交易记录作为输入数据源，并设置合理的最小支持度阈值以筛选出有意义的频繁项集。之后再利用这些频繁项集构建满足条件的关联规则[^1]。

#### 3. Python代码示例
下面是一个简单的Python版本APRIORI算法实现：

from collections import defaultdict, Counter
import itertools


def apriori(transactions, min_support=0.5):
    # 记录所有候选集合的支持计数
    item_counts = defaultdict(int)

    # 初始化单个商品的支持度统计
    for transaction in transactions:
        for item in transaction:
            item_counts[frozenset([item])] += 1
    
    num_transactions = float(len(transactions))
    
    # 过滤掉低于最低支持度的商品组合
    frequent_items = set()
    current_frequent_k_itemsets = []
    for key, value in item_counts.items():
        if (value / num_transactions) >= min_support:
            frequent_items.add(key)
            current_frequent_k_itemsets.append(key)
            
    k = 2
    while True:
        new_candidates = generate_new_candidate_sets(current_frequent_k_itemsets, k=k)
        
        candidate_counts = Counter()
        for transaction in transactions:
            for candidate_set in new_candidates:
                if all(item in transaction for item in candidate_set):
                    candidate_counts[candidate_set] += 1
                    
        next_level_frequent_itemsets = [
            frozenset(candidate_set) 
            for candidate_set, count in candidate_counts.items() 
            if ((count/num_transactions)>=min_support)]
                    
        if not next_level_frequent_itemsets:
            break
            
        frequent_items.update(next_level_frequent_itemsets)
        current_frequent_k_itemsets = next_level_frequent_itemsets
        
        k+=1
                
    return frequent_items
    

def generate_new_candidate_sets(frequent_itemset_list, k=None):
    """Generate the immediate supersets of length `k` from a list."""
    candidates = []

    n = len(frequent_itemset_list)
    for i in range(n):
        for j in range(i+1,n):

            l1=list(frequent_itemset_list[i])
            l2=list(frequent_itemset_list[j])

            if sorted(l1[:-1]) == sorted(l2[:-1]):
                
                unioned=frozenset(set.union(*map(set,[l1,l2])))
                if len(unioned)==k and check_subset_frequency(unioned,frequent_itemset_list,k-1):
                    candidates.append(tuple(sorted(list(unioned))))
                        
    return candidates


def check_subset_frequency(candiate_set, prev_freq_itemsets, subset_size):
    subsets = map(lambda s: tuple(s),itertools.combinations(candiate_set,subset_size))

    for ss in subsets:
        if frozenset(ss) not in prev_freq_itemsets:
            return False
    return True


if __name__=='__main__':
    sample_data=[
      ['bread', 'milk'],
      ['bread', 'diaper','beer','egg'],
      ['milk', 'diaper','beer','cola'],
      ['bread', 'milk', 'diaper','beer'],
      ['bread', 'milk', 'diaper','cola']
     ]
     
    result = apriori(sample_data,min_support=0.6)
    print('Frequent Item Sets:',result)

这段程序实现了基本的功能框架，可以根据实际需求调整参数或优化性能[^2]。