Improved Bounded Matrix Completion for Large-Scale Recommender Systems

Matrix completion is a widely used technique for personalized recommender systems. In this paper, we focus on the idea of Bounded Matrix Completion (BMC) which imposes bounded constraints into the standard matrix completion problem. It has been shown that BMC works well for several real world datasets, and an efficient coordinate descent solver called BMA has been proposed in [R. Kannan and Park., 2012]. However, we observe that BMA can sometimes converge to nonstationary points, resulting in a relatively poor accuracy in those cases. To overcome this issue, we propose our new approach for solving BMC under the ADMM framework. The proposed algorithm is guaranteed to converge to stationary points. Experimental results on real world datasets show that our algorithm can reach a lower objective function value, obtain a higher prediction accuracy and have better scalability compared with existing bounded matrix completion approaches. Moreover, our method outperforms the state-of-art standard matrix factorization in terms of prediction error in many real datasets.