TRUNCATED LSQR FOR MATRIX LEAST SQUARES PROBLEMS AND APPLICATION TO DICTIONARY LEARNING * - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2024

TRUNCATED LSQR FOR MATRIX LEAST SQUARES PROBLEMS AND APPLICATION TO DICTIONARY LEARNING *

Résumé

We are interested in the numerical solution of the matrix least squares problem min X∈R^{m×m} ∥AXB + CXD-F ∥_F , with A and C full column rank, B, D full row rank, F an n×n matrix of low rank, and ∥•∥_F the Frobenius norm. We derive a matrix-oriented implementation of LSQR, and devise an implementation of the truncation step that exploits the properties of the method. Experimental comparisons with the Conjugate Gradient method applied to the normal matrix equation and with a (new) sketched implementation of matrix LSQR illustrate the competitiveness of the proposed algorithm. We also explore the applicability of our method in the context of Kronecker-based Dictionary Learning, and devise a representation of the data that seems to be promising for classification purposes.
Fichier principal
Vignette du fichier
TruncLSQR1.pdf (888.73 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Licence : Domaine public

Dates et versions

hal-04437719 , version 1 (04-02-2024)

Identifiants

  • HAL Id : hal-04437719 , version 1

Citer

Valeria Simoncini, Lorenzo Piccinini. TRUNCATED LSQR FOR MATRIX LEAST SQUARES PROBLEMS AND APPLICATION TO DICTIONARY LEARNING *. 2024. ⟨hal-04437719⟩
67 Consultations
51 Téléchargements

Partager

Gmail Facebook X LinkedIn More