LorSLIM: Low Rank Sparse Linear Methods for Top-N Recommendations

In this paper, we notice that sparse and low-rank structures arise in the context of many collaborative filtering applications where the underlying graphs have block-diagonal adjacency matrices. Therefore, we propose a novel Sparse and Low-Rank Linear Method (Lor SLIM) to capture such structures and apply this model to improve the accuracy of the Top-N recommendation. Precisely, a sparse and low-rank aggregation coefficient matrix W is learned from Lor SLIM by solving an l1-norm and nuclear norm regularized optimization problem. We also develop an efficient alternating augmented Lagrangian method (ADMM) to solve the optimization problem. A comprehensive set of experiments is conducted to evaluate the performance of Lor SLIM. The experimental results demonstrate the superior recommendation quality of the proposed algorithm in comparison with current state-of-the-art methods.