【大数据分析与挖掘算法】matlab实现——改进的Apriori关联规则算法

实验二 ：改进的Apriori关联规则算法

一、实验目的

改进Apriori关联规则算法，实现对大型数据库系统扫描时关联规则的快速提取，提高产生效率，降低时间复杂度。

二、实验任务

根据某超市的五条客户购物清单记录，使用改进的Apriori关联规则算法进行计算，实例如下：

三、实验过程

四、实验结果

实现平台：++Matlab 2022A++

实验代码：

function apriori_improved(goods, min_sup, min_conf)
    % 初始化和参数设定
    clear; clc; close all;
    
    if nargin < 1
        goods = {'C,J,B,O,S'; 'J,S'; 'C,M,S'; 'C,W,S'; 'C,B,M'};
        min_sup = 0.4;
        min_conf = 0.6;
    end
    
    % 计算事务数量
    num_transactions = numel(goods);
    
    % 获取所有唯一项
    all_items = [];
    for i = 1:num_transactions
        items = strsplit(goods{i}, ',');
        all_items = [all_items, items];
    end
    all_items = unique(all_items);

    % 初始化支持度数据结构
    support_data = struct();
    
    % 计算1-项集支持度并生成强1-项集L1
    L1 = [];
    for i = 1:numel(all_items)
        item = all_items{i};
        support = calculate_support(item, goods);
        if support >= min_sup
            support_data.(item) = support;
            L1 = [L1; {item, support}];
        end
    end
    
    % 将不满足最小支持度的属性逻辑标记
    candidate_items = fieldnames(support_data);
    
    % 初始化频繁项集列表
    frequent_itemsets = L1;
    
    % 初始化候选集
    Ck = L1(:, 1);
    k = 1;
    
    while true
        % 生成k+1项候选集
        Ck_plus_1 = generate_candidates(Ck, k);
        
        % 计算k+1项集的支持度
        Ck_plus_1_support = [];
        for i = 1:numel(Ck_plus_1)
            itemset = Ck_plus_1{i};
            support = calculate_support(itemset, goods);
            if support >= min_sup
                Ck_plus_1_support = [Ck_plus_1_support; {itemset, support}];
            end
        end
        
        % 更新频繁项集列表
        if isempty(Ck_plus_1_support)
            break;
        end
        
        frequent_itemsets = [frequent_itemsets; Ck_plus_1_support];
        Ck = Ck_plus_1_support(:, 1);
        k = k + 1;
    end
    
    % 计算关联规则的置信度和提升度
    all_rules = generate_rules(frequent_itemsets, min_conf, goods);
    
    % 输出最终频繁项集和关联规则
    disp('Frequent Itemsets:');
    disp(frequent_itemsets);
    disp('Association Rules:');
    disp(all_rules);
end

function support = calculate_support(itemset, transactions)
    count = 0;
    for j = 1:numel(transactions)
        str_chars = strsplit(transactions{j}, ',');
        substr_chars = strsplit(itemset, ',');
        if all(ismember(substr_chars, str_chars))
            count = count + 1;
        end
    end
    support = count / numel(transactions);
end

function Ck_plus_1 = generate_candidates(Ck, k)
    Ck_plus_1 = {};
    for i = 1:numel(Ck)
        for j = i+1:numel(Ck)
            itemset1 = strsplit(Ck{i}, ',');
            itemset2 = strsplit(Ck{j}, ',');
            if all(strcmp(itemset1(1:k-1), itemset2(1:k-1)))
                new_itemset = unique([itemset1, itemset2]);
                new_itemset = strjoin(sort(new_itemset), ',');
                if ~ismember(new_itemset, Ck_plus_1)
                    Ck_plus_1{end+1} = new_itemset;
                end
            end
        end
    end
end

function all_rules = generate_rules(frequent_itemsets, min_conf, transactions)
    all_rules = {};
    for i = 1:size(frequent_itemsets, 1)
        itemset = frequent_itemsets{i, 1};
        subsets = generate_subsets(itemset);
        for j = 1:size(subsets, 1)
            antecedent = subsets{j};
            consequent = setdiff(strsplit(itemset, ','), strsplit(antecedent, ','));
            if ~isempty(consequent)
                confidence = calculate_support(itemset, transactions) / calculate_support(antecedent, transactions);
                if confidence >= min_conf
                    all_rules{end+1, 1} = [antecedent, ' => ', strjoin(consequent, ',')];
                    all_rules{end, 2} = confidence;
                end
            end
        end
    end
end

function subsets = generate_subsets(itemset)
    items = strsplit(itemset, ',');
    n = numel(items);
    subsets = {};
    for i = 1:2^n-2
        subset = items(logical(bitget(i, n:-1:1)));
        subsets{end+1} = strjoin(subset, ',');
    end
end

实验结果：

五、总结

1.对改进的Apriori关联规则算法的理解

算法改进的方式有很多，书上给出的这个示例主要是考虑到空间的充分利用，将直接扫描k项集改成k项集通过k-1项集来合成，从而方便快速地产生强项集，在产生过程中也要注意逻辑标记以跳过某些属性减少扫描次数，从而降低整体的时间复杂性。