Paper ID sheet UCL-INMA-2021.05


A Riemannian rank-adaptive method for low-rank matrix completion

Bin Gao, P.-A. Absil
The low-rank matrix completion problem can be solved by Riemannian optimization on a fixed-rank manifold. However, a drawback of the known approaches is that the rank parameter has to be fixed a priori. In this paper, we consider the optimization problem on the set of bounded-rank matrices. We propose a Riemannian rank-adaptive method, which consists of fixed-rank optimization, rank increase step and rank reduction step. We explore its performance applied to the low-rank matrix completion problem. Numerical experiments on synthetic and real-world datasets illustrate that the proposed rank-adaptive method compares favorably with state-of-the-art algorithms. In addition, it shows that one can incorporate each aspect of this rank-adaptive framework separately into existing algorithms for the purpose of improving performance.
Key words
rank-adaptive; fixed-rank manifold; bounded-rank matrices; Riemannian optimization; low-rank; matrix completion
Comput Optim Appl (2022)