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

Ke Wang, Zhuo Chen, Shihui Ying and Xinjian Xu ()
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Ke Wang: Department of Mathematics, Shanghai University, Shanghai 200444, China
Zhuo Chen: Department of Mathematics, Shanghai University, Shanghai 200444, China
Shihui Ying: Department of Mathematics, Shanghai University, Shanghai 200444, China
Xinjian Xu: Qianweichang College, Shanghai University, Shanghai 200444, China

Mathematics, 2023, vol. 11, issue 5, 1-17

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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