基于MATLAB实现协同过滤电影推荐系统

基于MATLAB实现协同过滤电影推荐系统，包含用户-用户和物品-物品两种协同过滤方法，并整合了数据预处理、模型训练和推荐生成全流程：

一、核心代码实现

matlab 复制代码

%% 数据加载与预处理
function [Y, R, num_users, num_movies] = load_data()
    load('ex8_movies.mat'); % 加载MovieLens 100k数据集
    Y = double(Y);        % 评分矩阵 (943用户×1682电影)
    R = double(R);        % 评分指示矩阵 (1表示已评分)
    num_users = size(Y,2);
    num_movies = size(Y,1);
    
    % 数据归一化（均值归一化）
    [Ynorm, Ymean] = normalizeRatings(Y, R);
end

function [Ynorm, Ymean] = normalizeRatings(Y, R)
    [m, n] = size(Y);
    Ymean = zeros(m,1);
    Ynorm = zeros(size(Y));
    for i = 1:m
        idx = R(i,:) == 1;
        Ymean(i) = mean(Y(i,idx));
        Ynorm(i,idx) = Y(i,idx) - Ymean(i);
    end
end

二、相似度计算模块

1. 用户-用户相似度（余弦相似度）

matlab 复制代码

function W = user_similarity(Y, num_users)
    W = zeros(num_users,num_users);
    for i = 1:num_users
        for j = i+1:num_users
            % 计算共同评分的电影数量
            common = sum(R(i,:) & R(j,:));
            if common > 0
                % 余弦相似度计算
                W(i,j) = sum(Y(i,R(i,:) & R(j,:)) .* Y(j,R(i,:) & R(j,:))) / ...
                        (sqrt(sum(Y(i,R(i,:) & R(j,:)).^2)) * ...
                        sqrt(sum(Y(j,R(i,:) & R(j,:)).^2)));
                W(j,i) = W(i,j);
            end
        end
    end
end

2. 物品-物品相似度（皮尔逊相关系数）

matlab 复制代码

function sim = item_similarity(Y, R)
    [m,n] = size(Y);
    sim = zeros(m,n);
    for i = 1:m
        for j = i+1:m
            % 找到同时评分的用户
            idx = R(:,i) & R(:,j);
            if sum(idx) > 10
                % 计算皮尔逊相关系数
                sim(i,j) = corr(Y(idx,i), Y(idx,j));
                sim(j,i) = sim(i,j);
            else
                sim(i,j) = 0;
            end
        end
    end
end

三、预测与推荐生成

1. 用户-用户协同过滤

matlab 复制代码

function predictions = user_based_cf(Y, W, user_idx, K)
    % 找到K个最近邻
    [~, idx] = sort(W(user_idx,:), 'descend');
    neighbors = idx(2:K+1); % 排除自身
    
    % 预测未评分电影
    pred_ratings = zeros(size(Y,1),1);
    for i = 1:size(Y,1)
        if R(i,user_idx) == 0
            % 加权平均评分
            pred_ratings(i) = sum(W(user_idx,neighbors) .* Y(neighbors,i)) / ...
                            sum(W(user_idx,neighbors));
        end
    end
    predictions = pred_ratings;
end

2. 物品-物品协同过滤

matlab 复制代码

function predictions = item_based_cf(Y, sim, user_idx, K)
    % 找到用户评分过的电影
    rated_movies = find(R(user_idx,:));
    
    % 预测所有电影评分
    pred_ratings = Y(user_idx,:) * sim;
    
    % 仅保留未评分电影的预测值
    predictions = zeros(size(Y,1),1);
    for i = 1:size(Y,1)
        if R(user_idx,i) == 0
            % 取相似度最高的K个电影加权平均
            [~, top_idx] = maxk(sim(i,:), K);
            predictions(i) = mean(Y(rated_movies,top_idx));
        end
    end
end

四、模型训练与评估

1. 正则化代价函数（带梯度计算）

matlab 复制代码

function [J, grad] = cofiCostFunc(params, Y, R, num_users, num_movies, num_features, lambda)
    X = reshape(params(1:num_movies*num_features), num_movies, num_features);
    Theta = reshape(params(num_movies*num_features+1:end), num_users, num_features);
    
    % 计算预测误差
    E = (X * Theta' - Y) .* R;
    J = 0.5 * sum(sum(E.^2)) / size(Y,1) + ...
        (lambda/2) * sum(sum(Theta.^2)) + ...
        (lambda/2) * sum(sum(X.^2));
    
    % 计算梯度
    X_grad = (E' * Theta) / size(Y,1) + lambda * X;
    Theta_grad = (E * X') / size(Y,1) + lambda * Theta;
    
    grad = [X_grad(:); Theta_grad(:)];
end

2. 模型训练（使用fmincg优化器）

matlab 复制代码

function [X, Theta] = train_model(Ynorm, R, num_features, lambda)
    [num_movies, num_users] = size(Ynorm);
    
    % 初始化参数
    X = randn(num_movies, num_features);
    Theta = randn(num_users, num_features);
    initial_params = [X(:); Theta(:)];
    
    % 设置优化选项
    options = optimset('GradObj', 'on', 'MaxIter', 100);
    
    % 执行优化
    [params, ~] = fmincg(@(t)(cofiCostFunc(t, Ynorm, R, num_users, num_movies, ...
        num_features, lambda)), initial_params, options);
    
    % 恢复参数矩阵
    X = reshape(params(1:num_movies*num_features), num_movies, num_features);
    Theta = reshape(params(num_movies*num_features+1:end), num_users, num_features);
end

五、完整推荐流程

matlab 复制代码

%% 主程序流程
[Y, R, num_users, num_movies] = load_data();
Ynorm = normalizeRatings(Y, R);

% 用户-用户协同过滤
W = user_similarity(Y, num_users);
user_idx = 1; % 假设推荐用户ID为1
K = 20;       % 最近邻数量
user_preds = user_based_cf(Y, W, user_idx, K);

% 物品-物品协同过滤
sim = item_similarity(Y, R);
item_preds = item_based_cf(Y, sim, user_idx, K);

% 模型训练（带特征学习）
lambda = 10;
num_features = 10;
[X, Theta] = train_model(Ynorm, R, num_features, lambda);
learned_ratings = X * Theta' + Ymean;

% 生成推荐列表
[~, sorted_idx] = sort(learned_ratings(user_idx,:), 'descend');
top_movies = sorted_idx(1:10);

% 显示推荐结果
movieList = loadMovieList();
disp('Top 10 Recommendations:');
for i = 1:10
    fprintf('%d. %s (Predicted Rating: %.1f)\n', i, movieList{top_movies(i)}, ...
        learned_ratings(user_idx,top_movies(i)));
end

参考代码电影推荐系统，运用协同过滤算法 www.youwenfan.com/contentcso/96071.html

六、性能评估

matlab 复制代码

%% 交叉验证评估
function rmse = evaluate_model(Y, R, num_users, num_movies, num_features, lambda)
    cv = cvpartition(size(Y,2),'KFold',5);
    rmse = 0;
    for i = 1:cv.NumTestSets
        % 划分训练集和测试集
        test_idx = cv.test(i);
        train_idx = ~test_idx;
        
        % 训练模型
        [X, Theta] = train_model(Y(:,train_idx), R(:,train_idx), ...
            num_features, lambda);
        
        % 预测
        pred = X * Theta';
        pred(test_idx) = 0; % 排除测试集
        
        % 计算RMSE
        rmse = rmse + sqrt(mean((pred(R(:,test_idx)==1) - Y(R(:,test_idx)==1)).^2));
    end
    rmse = rmse / cv.NumTestSets;
end

七、可视化分析

matlab 复制代码

%% 评分热力图
figure;
imagesc(Y);
colormap(jet);
colorbar;
title('用户-电影评分矩阵');
xlabel('电影ID');
ylabel('用户ID');

%% 预测误差分布
figure;
hist(residuals, 30);
title('预测误差分布');
xlabel('误差值');
ylabel('频数');

八、扩展应用场景

实时推荐 结合Redis缓存最近邻计算结果，响应时间<50ms
多模态融合 添加电影类型标签数据，使用SVD++算法增强特征表达
增量学习 设计在线更新机制，处理新用户/新电影的持续流入