Parafac-based Blind Identification of Convolutive MIMO Linear Systems

Fernandes, Carlos Estêvão Rolim; Favier, Gérard; Mota, J.C.M.

doi:10.3182/20090706-3-fr-2004.00283

Cited by 8 publications

(10 citation statements)

References 20 publications

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“…5). Convolutive extensions of this type of ICA wherein a block-Hankel structure arises in the factor matrices corresponding to the first three modes of the cumulant and first mode of the covariance matrix have also been proposed [14]. A different approach to ICA identifies the mixing matrix by computing several time-lagged covariance matrices and fusing them with a joint factorization [15], [16].…”

mentioning

confidence: 99%

Structured Data Fusion

Sorber

Barel

Lathauwer

2015

IEEE J. Sel. Top. Signal Process.

178

192

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We present structured data fusion (SDF) as a framework for the rapid prototyping of knowledge discovery in one or more possibly incomplete data sets. In SDF, each data set-stored as a dense, sparse, or incomplete tensor-is factorized with a matrix or tensor decomposition. Factorizations can be coupled, or fused, with each other by indicating which factors should be shared between data sets. At the same time, factors may be imposed to have any type of structure that can be constructed as an explicit function of some underlying variables. With the right choice of decomposition type and factor structure, even well-known matrix factorizations such as the eigenvalue decomposition, singular value decomposition and QR factorization can be computed with SDF. A domain specific language (DSL) for SDF is implemented as part of the software package Tensorlab, with which we offer a library of tensor decompositions and factor structures to choose from. The versatility of the SDF framework is demonstrated by means of four diverse applications, which are all solved entirely within Tensorlab's DSL.Index Terms-Big data, tensor, data fusion, structured matrices, canonical polyadic decomposition, block term decomposition, structured factors, domain specific language.

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mentioning

confidence: 99%

Structured Data Fusion

Sorber

Barel

Lathauwer

2015

IEEE J. Sel. Top. Signal Process.

178

192

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“…-La séparation aveugle de sources, appelée aussi identification aveugle de mélanges instantanés ou convolutifs, sous-déterminés ou sur-déterminés, sujet qui depuis les travaux de pionnier de (Cardoso, 1990), (Cardoso, 1991) a donné lieu au développement de très nombreuses méthodes basées sur l'utilisation de tenseurs de statistiques (cumulants ou multispectres) d'ordre quatre (Ferréol et al, 2005), (Acar et al, 2006), (de Lathauwer et al, 2007), (Fernandes et al, 2008), (Fernandes et al, 2009b) ou d'ordre plus élevé (Albera et al, 2004), (Karfoul et al, 2008), (Yu et al, 2008).…”

Section: Resultsunclassified

Identification de modèles de Volterra basée sur la décomposition PARAFAC de leurs noyaux et le filtre de Kalman étendu

Favier¹,

Bouilloc²

2010

Traitement du signal

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Les modèles de Volterra sont très utilisés dans de nombreux domaines d'application du fait qu'ils permettent de représenter, avec une précision arbitraire, tout système non linéaire de mémoire finie. Ils possèdent de plus la propriété d'être linéaires vis-à-vis de leurs paramètres, les coefficients des noyaux. Le principal inconvénient de ces modèles est leur complexité paramétrique qui nécessite d'estimer un très grand nombre de paramètres. Cet article présente une nouvelle méthode permettant de réduire cette complexité paramétrique en considérant les noyaux de Volterra d'ordre supérieur à un comme des tenseurs symétriques et en les décomposant à l'aide de la décomposition PARAFAC. Les modèles de Volterra-Parafac ainsi obtenus peuvent être vus comme une série de modèles de Wiener mis en parallèle. En exploitant cette nouvelle formulation des modèles de Volterra, nous proposons un algorithme d'identification récursif basé sur le filtre de Kalman étendu. Des résultats de simulation illustrent le comportement de la méthode d'identification proposée, dans le cas de systèmes de Volterra cubiques. ABSTRACT. Volterra models are widely used in various application areas. Their usefulness is mainly due to their ability to approximate with an arbitrary precision any fading memory nonlinear system, and their property of linearity with respect to parameters, the kernels coefficients. The main drawback of these models is their parametric complexity needing to estimate a huge number of parameters. Considering Volterra kernels as symmetric tensors, we use their PARAFAC decomposition to derive the Volterra-Parafac models inducing a substantial parametric complexity reduction. We show that these models can be viewed as a set of Wiener models in parallel. Then, we apply the extended Kalman filter for recursively identifying such Volterra-Parafac models. Some simulation results illustrate the effectiveness of the proposed identification method, in the case of cubic Volterra systems.

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“…In this paper, we focus on high-order CPD models [5]. Such models have a great interest in signal processing for blind equalization [7], [4], blind source separation [16], radar [10], wireless communications [12], [3], among many other fields of application. Most methods of factor estimation are ALS-based techniques [2].…”

Section: Introductionmentioning

confidence: 99%

High-Order CPD Estimation with Dimensionality Reduction Using a Tensor Train Model

Zniyed

Boyer

Almeida

et al. 2018

2018 26th European Signal Processing Conference (EUSIPCO)

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The canonical polyadic decomposition (CPD) is one of the most popular tensor-based analysis tools due to its usefulness in numerous fields of application. The Q-order CPD is parametrized by Q matrices also called factors which have to be recovered. The factors estimation is usually carried out by means of the alternating least squares (ALS) algorithm. In the context of multi-modal big data analysis, i.e., large order (Q) and dimensions, the ALS algorithm has two main drawbacks. Firstly, its convergence is generally slow and may fail, in particular for large values of Q, and secondly it is highly time consuming. In this paper, it is proved that a Q-order CPD of rank-R is equivalent to a train of Q 3order CPD(s) of rank-R. In other words, each tensor train (TT)-core admits a 3-order CPD of rank-R. Based on the structure of the TT-cores, a new dimensionality reduction and factor retrieval scheme is derived. The proposed method has a better robustness to noise with a smaller computational cost than the ALS algorithm.

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Parafac-based Blind Identification of Convolutive MIMO Linear Systems

Cited by 8 publications

References 20 publications

Structured Data Fusion

Structured Data Fusion

Identification de modèles de Volterra basée sur la décomposition PARAFAC de leurs noyaux et le filtre de Kalman étendu

High-Order CPD Estimation with Dimensionality Reduction Using a Tensor Train Model

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