Matrix Decomposition for Recommendation System

Matrix decomposition, when the rating matrix has missing values, is recognized as an outstanding technique for recommendation system. In order to approximate user-item rating matrix, we construct loss function and append regularization constraint to prevent overfitting. Thus, the solution of matrix decomposition becomes an optimization problem. Alternating least squares (ALS) and stochastic gradient descent (SGD) are two popular approaches to solve optimize problems. Alternating least squares with weighted regularization (ALS-WR) is a good parallel algorithm, which can perform independently on userfactor matrix or item-factor matrix. Based on the idea of ALS-WR algorithm, we propose a modified SGD algorithm. With experiments on testing dataset, our algorithm outperforms ALS-WR. In addition, matrix decompositions based on our optimization method have lower RMSE values than some classic collaborate filtering algorithms.