Low-Rank and Sparse Matrix Completion for Recommendation

Recently, recommendation algorithms have been widely used to improve the benefit of businesses and the satisfaction of users in many online platforms. However, most of the existing algorithms generate intermediate output when predicting ratings and the error of intermediate output will be propagated to the final results. Besides, since most algorithms predict all the unrated items, some predicted ratings may be unreliable and useless which will lower the efficiency and effectiveness of recommendation. To this end, we propose a Low-rank and Sparse Matrix Completion (LSMC) method which recovers rating matrix directly to improve the quality of rating prediction. Following the common methodology, we assume the structure of the predicted rating matrix is low-rank since rating is just connected with some factors of user and item. However, different from the existing methods, we assume the matrix is sparse so some unreliable predictions will be removed and important results will be retained. Besides, a slack variable will be used to prevent overfitting and weaken the influence of noisy data. Extensive experiments on four real-world datasets have been conducted to verify that the proposed method outperforms the state-of-the-art recommendation algorithms.