Diagonality measures of Hermitian positive-definite matrices with application to the approximate joint diagonalization problem

Abstract : In this paper, we introduce properly-invariant diagonality measures of Hermitian positive-definite matrices. These diagonality measures are defined as distances or divergences between a given positive-definite matrix and its diagonal part. We then give closed-form expressions of these diagonality measures and discuss their invariance properties. The diagonality measure based on the log-determinant α-divergence is general enough as it includes a diagonality criterion used by the signal processing community as a special case. These diagonality measures are then used to formulate minimization problems for finding the approximate joint diagonalizer of a given set of Hermitian positive-definite matrices. Numerical computations based on a modified Newton method are presented and commented.
Type de document :
Article dans une revue
Linear Algebra and its Applications, Elsevier, 2017, 528, pp.290 - 320. 〈10.1016/j.laa.2016.08.031〉
Liste complète des métadonnées

Littérature citée [35 références]  Voir  Masquer  Télécharger

https://hal.archives-ouvertes.fr/hal-01578462
Contributeur : Marco Congedo <>
Soumis le : mardi 29 août 2017 - 11:37:03
Dernière modification le : lundi 9 avril 2018 - 12:22:44

Fichier

1608.06613.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

Collections

Citation

Khaled Alyani, Marco Congedo, Maher Moakher. Diagonality measures of Hermitian positive-definite matrices with application to the approximate joint diagonalization problem. Linear Algebra and its Applications, Elsevier, 2017, 528, pp.290 - 320. 〈10.1016/j.laa.2016.08.031〉. 〈hal-01578462〉

Partager

Métriques

Consultations de la notice

148

Téléchargements de fichiers

76