优化以上的apriori算法代码

以下是一个优化后的 Apriori 算法的 MATLAB 代码示例，主要是通过矩阵运算和向量化操作来提高计算效率：

function [freqItemsets, associationRules] = apriori(transactions, minSupp, minConf)

% transactions: 事务数据，每行为一个事务，每列为一种商品
% minSupp: 最小支持度
% minConf: 最小置信度
% freqItemsets: 频繁项集
% associationRules: 关联规则

% 转换为二进制矩阵
binTrans = double(transactions > 0);

% 初始化频繁一项集
nItems = size(transactions, 2);
freqItemsets = arrayfun(@(x) {x}, 1:nItems);

% 迭代生成频繁项集
while ~isempty(freqItemsets)
    % 计算支持度
    itemsetSizes = cellfun(@length, freqItemsets);
    maxItemsetSize = max(itemsetSizes);
    itemsetMasks = false(size(freqItemsets, 1), nItems, maxItemsetSize);
    for i = 1:size(freqItemsets, 1)
        itemsetMasks(i, freqItemsets{i}, itemsetSizes(i)) = true;
    end
    itemsetCounts = squeeze(all(all(binTrans(:, :, ones(1, maxItemsetSize)) == itemsetMasks, 2), 3));
    supp = sum(itemsetCounts, 1) / size(transactions, 1);
    
    % 保留支持度大于 minSupp 的项集
    freqIdx = supp >= minSupp;
    freqItemsets = freqItemsets(freqIdx);
    supp = supp(freqIdx);
    
    % 生成下一轮候选项集
    newFreqItemsets = {};
    for i = 1:length(freqItemsets)
        for j = i+1:length(freqItemsets)
            itemset1 = freqItemsets{i};
            itemset2 = freqItemsets{j};
            if length(itemset1) == length(itemset2) && all(itemset1 == itemset2)
                continue;
            end
            newItemset = unique([itemset1, itemset2]);
            if length(newItemset) > length(itemset1) + 1
                continue;
            end
            if any(all(newItemset == cat(2, freqItemsets{:}), 2))
                continue;
            end
            newFreqItemsets{end+1} = newItemset;
        end
    end
    
    % 更新候选项集
    freqItemsets = newFreqItemsets;
end

% 生成关联规则
allItemsets = cat(2, freqItemsets{:});
associationRules = [];
for i = 1:length(allItemsets)
    antecedent = setdiff(allItemsets, allItemsets(i));
    antecedentIdx = all(binTrans(:, antecedent), 2);
    consequentIdx = binTrans(:, allItemsets(i));
    conf = sum(consequentIdx & antecedentIdx) / sum(antecedentIdx);
    if conf >= minConf
        associationRules(end+1) = struct('antecedent', antecedent, 'consequent', allItemsets(i), 'confidence', conf);
    end
end

end

该代码实现了一个更高效的 Apriori 算法，使用了矩阵运算和向量化操作来提高计算速度。