Simultaneous Recovery of A Series of Low-rank Matrices by Locally Weighted Matrix Smoothing

Low-rank matrix factorizations arise in a wide variety of applications including recommendation systems, topic models, and source separation, to name just a few. There exist both empirical and theoretical results showing that, under some dynamic models, significant improvements can be obtained by incorporating temporal information and allowing for the possibility that the underlying matrix is time varying. In this paper we propose the S-LOWEMS estimator, which simultaneously recovers a series of low-rank matrices based on the locally weighted matrix smoothing (LOWEMS) framework. Our synthetic simulations and real world experiments show that, compared to the original LOWEMS estimator, the proposed S-LOWEMS estimator not only recovers a series of low-rank matrices with a small computational overhead, but also improves the recovery accuracy and reduces the sample complexity.