Matlab梯度下降解决评分矩阵分解

for iter = 1:num_iters

%梯度下降 用户向量
for i = 1:m
%返回有0有1 是逻辑值
ratedIndex1 = R_training(i,:)~=0 ;
%U(i,:) * V'  第i个用户分别对每个电影的评分

%sumVec1  第i个用户分别对每个电影的评分 减去真实值
sumVec1 = ratedIndex1 .* (U(i,:) * V' - R_training(i,:));
product1 = sumVec1 * V;
derivative1 = product1 + lambda_u * U(i,:);
old_U(i,:) = U(i,:) - theta * derivative1;
end

%梯度下降 电影向量
for j = 1:n
ratedIndex2 = R_training(:,j)~=0;
sumVec2 = ratedIndex2 .* (U * V(j,:)' - R_training(:,j));
product2 = sumVec2' * U;
derivative2 = product2 + lambda_v * V(j,:);
old_V(j,:) = V(j,:) - theta * derivative2;
end

U = old_U;
V = old_V;
RMSE(i,1) = CompRMSE(train_vec,U,V);
RMSE(i,2) = CompRMSE(probe_vec,U,V);

end

function [ recItems ] = mf_gd( trainMatrix, featureNumber, maxEpoch, learnRate, lambdaU, lambdaV, k)

%get the size the train matrix
[userNumber,itemNumber] = size(trainMatrix);

%init user factors and item factors
Ut = 0.01 * randn(userNumber, featureNumber);
Vt = 0.01 * randn(itemNumber, featureNumber);
%逻辑1和0
logitMatrix = trainMatrix > 0;

%calculate the gradient of user factors and item factors
%and user sgd to optimize the risk function
%alternative update user factors and item factors alternative
for round = 1:maxEpoch,
dU = -(logitMatrix  .* trainMatrix)  * Vt + (Ut * Vt' .* logitMatrix ) * Vt + lambdaU * Ut;
dV = -(logitMatrix' .* trainMatrix') * Ut + (Vt * Ut' .* logitMatrix') * Ut + lambdaV * Vt;
Ut = Ut - learnRate * dU * 2;
Vt = Vt - learnRate * dV * 2;
end

%predict the rating of each item given by each user
predictMatrix = Ut * Vt';

%sort the score of items for each user
[sortedMatrix, sortedItems] = sort(predictMatrix, 2, 'descend');

%get the top-k items for each suer
recItems = sortedItems(:, 1:k);
end