Tensor CP Decomposition with Structured Factor Matrices: Algorithms and Performance

Abstract : The canonical polyadic decomposition (CPD) of high-order tensors, also known as Candecomp/Parafac, is very useful for representing and analyzing multidimensional data. This paper considers a CPD model having structured matrix factors, as e.g. Toeplitz, Hankel or circulant matrices, and studies its associated estimation problem. This model arises in signal processing applications such as Wiener-Hammerstein system identification and cumulant-based wireless communication channel estimation. After introducing a general formulation of the considered struc-tured CPD (SCPD), we derive closed-form expressions for the Cramér-Rao bound (CRB) of its parameters under the presence of additive white Gaussian noise. Formulas for special cases of interest, as when the CPD contains identical factors, are also provided. Aiming at a more relevant statistical evaluation from a practical standpoint, we discuss the application of our formulas in a Bayesian context, where prior distributions are assigned to the model parameters. Three existing algorithms for computing SCPDs are then described: a constrained alternating least squares (CALS) algorithm, a subspace-based solution and an algebraic solution for SCPDs with circulant factors. Subsequently, we present three numerical simulation scenarios, in which several specialized estimators based on these algorithms are proposed for concrete examples of SCPD involving circulant factors. In particular, the third scenario concerns the identification of a Wiener-Hammerstein system via the SCPD of an associated Volterra kernel. The statistical performance of the proposed estimators is assessed via Monte Carlo simulations, by comparing their Bayesian mean-square error with the expected CRB.
Type de document :
Article dans une revue
IEEE Journal of Selected Topics in Signal Processing, IEEE, 2016, 10 (4), pp.757-769
Liste complète des métadonnées


https://hal-supelec.archives-ouvertes.fr/hal-01246855
Contributeur : Remy Boyer <>
Soumis le : dimanche 20 décembre 2015 - 04:49:17
Dernière modification le : samedi 18 février 2017 - 01:20:41
Document(s) archivé(s) le : lundi 21 mars 2016 - 10:11:10

Fichier

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

Licence


Distributed under a Creative Commons Paternité - Pas d'utilisation commerciale - Partage selon les Conditions Initiales 4.0 International License

Identifiants

  • HAL Id : hal-01246855, version 1

Citation

José Henrique De Morais Goulart, Maxime Boizard, Rémy Boyer, Gérard Favier, Pierre Comon. Tensor CP Decomposition with Structured Factor Matrices: Algorithms and Performance. IEEE Journal of Selected Topics in Signal Processing, IEEE, 2016, 10 (4), pp.757-769. <hal-01246855>

Partager

Métriques

Consultations de
la notice

640

Téléchargements du document

261