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

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

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 gradien...

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Veröffentlicht in:Mathematics (Basel) 2023-03, Vol.11 (5), p.1155
Hauptverfasser: Wang, Ke, Chen, Zhuo, Ying, Shihui, Xu, Xinjian
Format: Artikel
Sprache:eng
Schlagworte:
Algorithms
Decomposition
gradient algorithm
manifold
Manifolds
Manifolds (Mathematics)
Matrices
matrix completion
Optimization
QR factorization
Ranking and selection (Statistics)
Tests, problems and exercises
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Zusammenfassung: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%.
ISSN:2227-7390
2227-7390
DOI:10.3390/math11051155