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Volume 11
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Article

Low-Rank Matrix Completion via QR-Based Retraction on Manifolds

by
Ke Wang
1,
Zhuo Chen
1,
Shihui Ying
1 and
Xinjian Xu
2,*
1
Department of Mathematics, Shanghai University, Shanghai 200444, China
2
Qianweichang College, Shanghai University, Shanghai 200444, China
*
Author to whom correspondence should be addressed.
Mathematics 2023, 11(5), 1155; https://doi.org/10.3390/math11051155
Submission received: 17 January 2023 / Revised: 23 February 2023 / Accepted: 23 February 2023 / Published: 26 February 2023
(This article belongs to the Special Issue Advanced Optimization Methods and Applications)
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Abstract

Low-rank matrix completion aims to recover an unknown matrix from a subset of observed entries. In this paper, we solve the problem via optimization of the matrix manifold. Specially, we apply QR factorization to retraction during optimization. We devise two fast algorithms based on steepest gradient descent and conjugate gradient descent, and demonstrate their superiority over the promising baseline with the ratio of at least 24%.
Keywords: matrix completion; QR factorization; gradient algorithm; manifold matrix completion; QR factorization; gradient algorithm; manifold

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MDPI and ACS Style

Wang, K.; Chen, Z.; Ying, S.; Xu, X. Low-Rank Matrix Completion via QR-Based Retraction on Manifolds. Mathematics 2023, 11, 1155. https://doi.org/10.3390/math11051155

AMA Style

Wang K, Chen Z, Ying S, Xu X. Low-Rank Matrix Completion via QR-Based Retraction on Manifolds. Mathematics. 2023; 11(5):1155. https://doi.org/10.3390/math11051155

Chicago/Turabian Style

Wang, Ke, Zhuo Chen, Shihui Ying, and Xinjian Xu. 2023. "Low-Rank Matrix Completion via QR-Based Retraction on Manifolds" Mathematics 11, no. 5: 1155. https://doi.org/10.3390/math11051155

APA Style

Wang, K., Chen, Z., Ying, S., & Xu, X. (2023). Low-Rank Matrix Completion via QR-Based Retraction on Manifolds. Mathematics, 11(5), 1155. https://doi.org/10.3390/math11051155

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