Non-iterative solution for PARAFAC with a Toeplitz matrix factor

Alain Kibangou (1, 2) , Gérard Favier (3)

1 NECS - Networked Controlled Systems
2 GIPSA-lab - Grenoble Images Parole Signal Automatique
3 Laboratoire d'Informatique, Signaux, et Systèmes de Sophia-Antipolis (I3S) / Equipe SIGNAL

Recently, tensor signal processing has received an increased attention, particularly in the context of wireless communication applications. The so-called PARAllel FACtor (PARAFAC) decomposition is certainly the most used tensor tool. In general, the parameter estimation of a PARAFAC decomposition is carried out by means of the iterative ALS algorithm, which exhibits the following main drawbacks: convergence towards local minima, a high number of iterations for convergence, and difficulty to take, optimally, special matrix structures into account. In this paper, we propose a non-iterative parameter estimation method for a PARAFAC decomposition when one matrix factor has a Toeplitz structure, a situation that is commonly encountered in signal processing applications. We illustrate the proposed method by means of simulation results.

Mots clés: Tensor; Toeplitz matrices; PARAFAC

Domaines: Traitement du signal et de l'image [eess.SP]; Traitement du signal et de l'image [eess.SP]

Alain Kibangou, Gérard Favier. Non-iterative solution for PARAFAC with a Toeplitz matrix factor. EUSIPCO 2009 - 17th European Signal Processing Conference, Aug 2009, Glasgow, United Kingdom. pp.691-695. ⟨hal-00397808⟩