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

Bin Gao () and P.-A. Absil ()
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Bin Gao: ICTEAM Institute, UCLouvain
P.-A. Absil: ICTEAM Institute, UCLouvain

Computational Optimization and Applications, 2022, vol. 81, issue 1, No 3, 67-90

Abstract: Abstract 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.

Keywords: Rank-adaptive; Fixed-rank manifold; Bounded-rank matrices; Riemannian optimization; Low-rank; Matrix completion (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10589-021-00328-w

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