机器学习-推荐系统

以推荐电影为例

symbol

基于内容的推荐算法

根据电影内容找到用户特征θ 本质上利用线性回归

其中 Σi:r(i,j) = 1是指 将所有电影 i 的用户评分累加起来

协同过滤（collaborative filtering）及算法

不再根据电影内容，而是直接根据用户评分得到电影特征

其中 Σj:r(i,j) = 1是指 将用户 j 评分过所有电影的分值累加起来

没有 X_0 ， θ_0

同时学习几乎所有电影的特征和所有用户参数 ，最终预测所有用户对未评价电影的评分

矢量化：低秩矩阵分解

电影相似度

实施细节

均值规范化（防止全未评分用户预测全0）

重新对均值进行协同过滤

编程作业

cofiCostFunc.m

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
J = 0;
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
%

J = sum(sum(((X*Theta' - Y).^2) .* R)) / 2 + lambda/2*(sum(sum(Theta.^2)) + sum(sum(X.^2)));
X_grad = ((X*Theta' - Y).* R) * Theta + lambda * X;
Theta_grad = ((X*Theta' - Y).* R)' * X+ lambda * Theta;

% =============================================================

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

end