Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/287208 
Year of Publication: 
2021
Citation: 
[Journal:] Computational Optimization and Applications [ISSN:] 1573-2894 [Volume:] 81 [Issue:] 1 [Publisher:] Springer US [Place:] New York, NY [Year:] 2021 [Pages:] 67-90
Publisher: 
Springer US, New York, NY
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.
Subjects: 
Rank-adaptive
Fixed-rank manifold
Bounded-rank matrices
Riemannian optimization
Low-rank
Matrix completion
Persistent Identifier of the first edition: 
Creative Commons License: 
cc-by Logo
Document Type: 
Article
Document Version: 
Published Version

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