A fuzzy matrix factor recommendation method with forgetting function and user features

Abstract In recent years, a variety of recommendation algorithms have been proposed. However, there are still some issues such as cold start, sparsity and timeliness. On the basis of traditional collaborative filtering, matrix decomposition technologies can greatly reduce the computational complexity and address the issues of cold start and sparsity. Based on forgetting functions and users’ multi-attribute features, in this paper, a fuzzy matrix decomposition and trace norm minimization method is proposed. Firstly, a forgetting function is incorporated into the historical scores, which makes existing scoring information more efficient. Then the user features are applied to find trusted users, which will give some valuable suggestions and possible scores to target items. The user features are also applied to list the relationships among users. In this paper, the relations between users and items are represented by the scores between them. Secondly, both time and feature information is integrated into the proposed optimization model. Then a fuzzy matrix decomposition and trace norm minimization model is established and further solved by our proposed algorithm to give better recommendations. Moreover, the convergence of the proposed algorithm is also proved in theoretically. Finally, we investigate the empirical recoverability properties of our model and analyze its advantages over classical norm minimization models. Extensive experimental results on synthetic and real-world data sets verify the efficiency and effectiveness of our method compared with the state-of-the-art algorithms.