Usevich, Konstantin, Gillard, Jonathan  ORCID: https://orcid.org/0000-0001-9166-298X, Dreesen, Philippe and Markovsky, Ivan
2025.
Structured nuclear norm matrix completion: Guaranteeing exact recovery via block-column scaling.
Numerical Linear Algebra with Applications
32
(4)
, e70031.
10.1002/nla.70031
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Abstract
The goal of low-rank matrix completion is to minimize the rank of a matrix while adhering to the constraint that known (non-missing) elements are fixed in the approximation. Minimizing rank is a difficult, non-convex, NP-hard problem, often addressed by substituting rank with the nuclear norm to achieve a convex relaxation. We focus on structured matrices for completion, where, in addition to the constraints described earlier, matrices also adhere to a predefined structure. We propose a technique that ensures the exact recovery of missing entries by minimizing the nuclear norm of a matrix where the non-missing entries are first subject to block-column scaling. We provide the proofs for exact recovery and propose a way for choosing the scaling parameter to ensure exact recovery. The method is demonstrated in several numerical examples, showing the usefulness of the proposed technique.
| Item Type: | Article |
|---|---|
| Date Type: | Publication |
| Status: | Published |
| Schools: | Schools > Mathematics |
| Publisher: | Wiley |
| ISSN: | 1070-5325 |
| Funders: | Catalan Institution for Research and Advanced Studies, Fond for Scientific Research Vlaanderen, Spanish Ministry of Science State Research Agency |
| Date of First Compliant Deposit: | 27 June 2025 |
| Date of Acceptance: | 9 June 2025 |
| Last Modified: | 22 Jul 2025 11:08 |
| URI: | https://orca.cardiff.ac.uk/id/eprint/179366 |
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