Decentralized Nonconvex Low-rank Matrix Recovery

For the low-rank matrix recovery problem, algorithms that directly manipulate the low-rank matrix typically require computing the top singular values/vectors of the matrix and thus are computationally expensive. Matrix factorization is a computationally efficient nonconvex approach for low-rank matr...

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Bibliographic Details
Published in:IEEE transactions on image processing Vol. 34; pp. 4806 - 4813
Main Authors: Gao, Junzhuo, Lian, Heng
Format: Journal Article
Language:English
Published: United States IEEE 01.01.2025
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithms
Approximation algorithms
Approximation error
Convergence
Distributed estimation
Estimation
Factorization
Gradient tracking
Linear convergence
Low-rank estimation
Matrix decomposition
Minimization
Recovery
Signal processing algorithms
Singular value decomposition
Training
Urban areas
ISSN:1057-7149, 1941-0042, 1941-0042
Online Access:Get full text
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Summary:For the low-rank matrix recovery problem, algorithms that directly manipulate the low-rank matrix typically require computing the top singular values/vectors of the matrix and thus are computationally expensive. Matrix factorization is a computationally efficient nonconvex approach for low-rank matrix recovery, utilizing an alternating minimization or a gradient descent algorithm, and its theoretical properties have been investigated in recent years. However, the behavior of the factorization-based matrix recovery problem in the decentralized setting is still unknown when data are distributed on multiple nodes. In this paper, we consider the distributed gradient descent algorithm and establish its (local) linear convergence up to the approximation error. Numerical results are also presented to illustrate the convergence of the algorithm over a general network.
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ISSN:1057-7149
1941-0042
1941-0042
DOI:10.1109/TIP.2025.3588719