Top-N Recommender System via Matrix Completion

Top-N recommender systems have been investigated widely both in industry and academia. However, the recommendation quality is far from satisfactory. In this paper, we propose a simple yet promising algorithm. We fill the user-item matrix based on a low-rank assumption and simultaneously keep the original information. To do that, a nonconvex rank relaxation rather than the nuclear norm is adopted to provide a better rank approximation and an efficient optimization strategy is designed. A comprehensive set of experiments on real datasets demonstrates that our method pushes the accuracy of Top-N recommendation to a new level.Comment: AAAI 201

A Nonconvex Relaxation Approach for Rank Minimization Problems

Recently, solving rank minimization problems by leveraging nonconvex relaxations has received significant attention. Some theoretical analyses demonstrate that it can provide a better approximation of original problems than convex relaxations. However, designing an effective algorithm to solve nonconvex optimization problems remains a big challenge. In this paper, we propose an Iterative Shrinkage-Thresholding and Reweighted Algorithm (ISTRA) to solve rank minimization problems using the nonconvex weighted nuclear norm as a low rank regularizer. We prove theoretically that under certain assumptions our method achieves a high-quality local optimal solution efficiently. Experimental results on synthetic and real data show that the proposed ISTRA algorithm outperforms state-of-the-art methods in both accuracy and efficiency