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Plug-and-play low-rank tensor completion and reconstruction algorithms with improved applicability of tensor decompositions

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Titel: Plug-and-play low-rank tensor completion and reconstruction algorithms with improved applicability of tensor decompositions
Autoren: Manabu Mukai, Hidekata Hontani, Tatsuya Yokota
Quelle: Frontiers in Applied Mathematics and Statistics. 11
Verlagsinformationen: Frontiers Media SA, 2025.
Publikationsjahr: 2025
Beschreibung: In this paper, we propose a new unified optimization algorithm for general tensor completion and reconstruction problems, which is formulated as an inverse problem for low-rank tensors in general linear observation models. The proposed algorithm supports at least three basic loss functions (ℓ2 loss, ℓ1 loss, and generalized KL divergence) and various TD models (CP, Tucker, TT, TR decompositions, non-negative matrix/tensor factorizations, and other constrained TD models). We derive the optimization algorithm based on a hierarchical combination of the alternating direction method of multipliers (ADMM) and majorization-minimization (MM). We show that the proposed algorithm can solve a wide range of applications and can be easily extended to any established TD model in a plug-and-play manner.
Publikationsart: Article
ISSN: 2297-4687
DOI: 10.3389/fams.2025.1594873
Rights: CC BY
Dokumentencode: edsair.doi...........d9b8ec68f3d893efc0f8f383c6166a7a
Datenbank: OpenAIRE
Beschreibung
Abstract:In this paper, we propose a new unified optimization algorithm for general tensor completion and reconstruction problems, which is formulated as an inverse problem for low-rank tensors in general linear observation models. The proposed algorithm supports at least three basic loss functions (ℓ2 loss, ℓ1 loss, and generalized KL divergence) and various TD models (CP, Tucker, TT, TR decompositions, non-negative matrix/tensor factorizations, and other constrained TD models). We derive the optimization algorithm based on a hierarchical combination of the alternating direction method of multipliers (ADMM) and majorization-minimization (MM). We show that the proposed algorithm can solve a wide range of applications and can be easily extended to any established TD model in a plug-and-play manner.
ISSN:22974687
DOI:10.3389/fams.2025.1594873