一、程序及函数

1.引导脚本ex8_cofi.m

%% Machine Learning Online Class
%  Exercise 8 | Anomaly Detection and Collaborative Filtering

%  Instructions
%  ---------------------------------------------------------------
%  This file contains code that helps you get started on the
%  exercise. You will need to complete the following functions:
%
%     estimateGaussian.m
%     selectThreshold.m
%     cofiCostFunc.m
%
%  For this exercise, you will not need to change any code in this file,
%  or any other files other than those mentioned above.

%% =============== Part 1: Loading movie ratings dataset ================
%  You will start by loading the movie ratings dataset to understand the
%  structure of the data.
%  
fprintf('Loading movie ratings dataset.\n\n');

%  Load data
load ('ex8_movies.mat');

%  Y is a 1682x943 matrix, containing ratings (1-5) of 1682 movies on 
%  943 users
%
%  R is a 1682x943 matrix, where R(i,j) = 1 if and only if user j gave a
%  rating to movie i

%  From the matrix, we can compute statistics like average rating.
fprintf('Average rating for movie 1 (Toy Story): %f / 5\n\n', ...
        mean(Y(1, R(1, :))));

%  We can "visualize" the ratings matrix by plotting it with imagesc
imagesc(Y);
ylabel('Movies');
xlabel('Users');

fprintf('\nProgram paused. Press enter to continue.\n');
pause;

%% ============ Part 2: Collaborative Filtering Cost Function ===========
%  You will now implement the cost function for collaborative filtering.
%  To help you debug your cost function, we have included set of weights
%  that we trained on that. Specifically, you should complete the code in 
%  cofiCostFunc.m to return J.

%  Load pre-trained weights (X, Theta, num_users, num_movies, num_features)
load ('ex8_movieParams.mat');

%  Reduce the data set size so that this runs faster
num_users = 4;
num_movies = 5;
num_features = 3;
X = X(1:num_movies, 1:num_features);
Theta = Theta(1:num_users, 1:num_features);
Y = Y(1:num_movies, 1:num_users);
R = R(1:num_movies, 1:num_users);

%  Evaluate cost function
J = cofiCostFunc([X(:) ; Theta(:)], Y, R, num_users, num_movies, num_features, 0);

fprintf(['Cost at loaded parameters: %f '...
         '\n(this value should be about 22.22)\n'], J);

fprintf('\nProgram paused. Press enter to continue.\n');
pause;

%% ============== Part 3: Collaborative Filtering Gradient ==============
%  Once your cost function matches up with ours, you should now implement 
%  the collaborative filtering gradient function. Specifically, you should 
%  complete the code in cofiCostFunc.m to return the grad argument.

fprintf('\nChecking Gradients (without regularization) ... \n');

%  Check gradients by running checkNNGradients
checkCostFunction;

fprintf('\nProgram paused. Press enter to continue.\n');
pause;

%% ========= Part 4: Collaborative Filtering Cost Regularization ========
%  Now, you should implement regularization for the cost function for 
%  collaborative filtering. You can implement it by adding the cost of
%  regularization to the original cost computation.

%  Evaluate cost function
J = cofiCostFunc([X(:) ; Theta(:)], Y, R, num_users, num_movies, ...
               num_features, 1.5);
           
fprintf(['Cost at loaded parameters (lambda = 1.5): %f '...
         '\n(this value should be about 31.34)\n'], J);

fprintf('\nProgram paused. Press enter to continue.\n');
pause;

%% ======= Part 5: Collaborative Filtering Gradient Regularization ======
%  Once your cost matches up with ours, you should proceed to implement 
%  regularization for the gradient. 

fprintf('\nChecking Gradients (with regularization) ... \n');

%  Check gradients by running checkNNGradients
checkCostFunction(1.5);

fprintf('\nProgram paused. Press enter to continue.\n');
pause;

%% ============== Part 6: Entering ratings for a new user ===============
%  Before we will train the collaborative filtering model, we will first
%  add ratings that correspond to a new user that we just observed. This
%  part of the code will also allow you to put in your own ratings for the
%  movies in our dataset!

movieList = loadMovieList();

%  Initialize my ratings
my_ratings = zeros(1682, 1);

% Check the file movie_idx.txt for id of each movie in our dataset
% For example, Toy Story (1995) has ID 1, so to rate it "4", you can set
my_ratings(3) = 4;

% Or suppose did not enjoy Silence of the Lambs (1991), you can set
my_ratings(98) = 2;

% We have selected a few movies we liked / did not like and the ratings we
% gave are as follows:
my_ratings(41) = 3;
my_ratings(67)= 5;
my_ratings(85) = 4;
my_ratings(127)= 5;
my_ratings(173)= 3;
my_ratings(214) = 5;
my_ratings(498) = 1;
my_ratings(696) = 3;
my_ratings(1028)= 2;
my_ratings(1147)= 5;
my_ratings(1246)= 4;
my_ratings(1498)= 5;
my_ratings(1572)= 5;

fprintf('\n\nNew user ratings:\n');
for i = 1:length(my_ratings)
    if my_ratings(i) > 0 
        fprintf('Rated %d for %s\n', my_ratings(i), ...
                 movieList{i});
    end
end

fprintf('\nProgram paused. Press enter to continue.\n');
pause;

%% ================== Part 7: Learning Movie Ratings ====================
%  Now, you will train the collaborative filtering model on a movie rating 
%  dataset of 1682 movies and 943 users

fprintf('\nTraining collaborative filtering...\n');

%  Load data
load('ex8_movies.mat');

%  Y is a 1682x943 matrix, containing ratings (1-5) of 1682 movies by 943 users

%  R is a 1682x943 matrix, where R(i,j) = 1 if and only if user j gave a rating to movie i

%  Add our own ratings to the data matrix
Y = [my_ratings Y];
R = [(my_ratings ~= 0) R];

%  Normalize Ratings
[Ynorm, Ymean] = normalizeRatings(Y, R);

%  Useful Values
num_users = size(Y, 2);
num_movies = size(Y, 1);
num_features = 10;

% Set Initial Parameters (Theta, X)
X = randn(num_movies, num_features);
Theta = randn(num_users, num_features);

initial_parameters = [X(:); Theta(:)];

% Set options for fmincg
options = optimset('GradObj', 'on', 'MaxIter', 100);

% Set Regularization
lambda = 10;
theta = fmincg (@(t)(cofiCostFunc(t, Ynorm, R, num_users, num_movies, ...
                                num_features, lambda)), ...
                initial_parameters, options);

% Unfold the returned theta back into U and W
X = reshape(theta(1:num_movies*num_features), num_movies, num_features);
Theta = reshape(theta(num_movies*num_features+1:end), ...
                num_users, num_features);

fprintf('Recommender system learning completed.\n');

fprintf('\nProgram paused. Press enter to continue.\n');
pause;

%% ================== Part 8: Recommendation for you ====================
%  After training the model, you can now make recommendations by computing
%  the predictions matrix.

p = X * Theta';
my_predictions = p(:,1) + Ymean;

movieList = loadMovieList();

[r, ix] = sort(my_predictions, 'descend');
fprintf('\nTop recommendations for you:\n');
for i=1:10
    j = ix(i);
    fprintf('Predicting rating %.1f for movie %s\n', my_predictions(j), movieList{j});
end

fprintf('\n\nOriginal ratings provided:\n');
for i = 1:length(my_ratings)
    if my_ratings(i) > 0 
        fprintf('Rated %d for %s\n', my_ratings(i), ...
                 movieList{i});
    end
end

2.cofiCostFunc.m
核心函数：计算协同过滤推荐算法的损失函数J值以及J对X，Theta的偏导值。里面的计算推荐用向量化的方式写，可以提高运行性能。一开始可以写成for循环验证结果是否正确，正确之后再慢慢想怎么改成向量化的表达方式。

function [J, grad] = cofiCostFunc(params, Y, R, num_users, num_movies, num_features, lambda)
%COFICOSTFUNC Collaborative filtering cost function
%   [J, grad] = COFICOSTFUNC(params, Y, R, num_users, num_movies, ...
%   num_features, lambda) returns the cost and gradient for the
%   collaborative filtering problem.
% Unfold the U and W matrices from params
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);
       
% You need to return the following values correctly
X_grad = zeros(size(X));
Theta_grad = zeros(size(Theta));

% ====================== YOUR CODE HERE ======================
% Instructions: Compute the cost function and gradient for collaborative
%               filtering. Concretely, you should first implement the cost
%               function (without regularization) and make sure it is
%               matches our costs. After that, you should implement the 
%               gradient and use the checkCostFunction routine to check
%               that the gradient is correct. Finally, you should implement
%               regularization.
%
% Notes: X - num_movies  x num_features matrix of movie features
%        Theta - num_users  x num_features matrix of user features
%        Y - num_movies x num_users matrix of user ratings of movies
%        R - num_movies x num_users matrix, where R(i, j) = 1 if the 
%            i-th movie was rated by the j-th user
%
% You should set the following variables correctly:
%
%        X_grad - num_movies x num_features matrix, containing the 
%                 partial derivatives w.r.t. to each element of X
%        Theta_grad - num_users x num_features matrix, containing the 
%                     partial derivatives w.r.t. to each element of Theta
% 循环法
% [m,n] = size(R);
% sum = 0;
% for i = 1 : m
%     for j = 1 : n
%         if R(i,j) == 1
%             sum = sum + (Theta(j,:) * X(i,:)' - Y(i,j)).^2;
%         end
%     end
% end
% 计算J值
% J = 1 / 2 * sum;

% 矩阵化法
predY = (X*Theta') .* R;
J = 1/2 * sum(sum((predY-Y).^2)) + lambda/2 * sum(sum(Theta.^2)) + lambda/2 * sum(sum(X.^2));

% 计算X_grad
for i = 1 : num_movies
    % <!---这里的sum一定要在内层循环开始前清零---！>
    sum1 = zeros(1,num_features);
    for j = 1 : num_users
        if R(i,j) == 1
            sum1 = sum1 + (Theta(j,:) * X(i,:)' - Y(i,j)) .* Theta(j,:);
        end
    end
    X_grad(i,:) = sum1 + lambda * X(i,:);
end

% 计算Theta_grad
for j = 1 : num_users
    % <!---这里的sum一定要在内层循环开始前清零---！>
    sum2 = zeros(1,num_features);
    for i = 1 : num_movies
        if R(i,j) == 1
            sum2 = sum2 + (Theta(j,:) * X(i,:)' - Y(i,j)) .* X(i,:);
        end
    end
    Theta_grad(j,:) = sum2 + lambda * Theta(j,:);
end

grad = [X_grad(:); Theta_grad(:)];

end

二、运行结果

1.将每个用户对每个电影的评分用Matlab自带的imagesc函数可视化一下：

2.一些计算值的正确性验证：


3.进行100次迭代训练CF算法的参数：

4.在我们自己对一些电影评分后，利用CF算法对我们可能喜欢的电影进行预测（推荐），并返回top50我们可能会喜欢的电影（预测我们对这1682部电影的评分，然后将评分降序排列，取top50来展示）：