Joint Matrices Decompositions and Blind Source Separation: A survey of methods, identification, and applications

Chabriel, Gilles; Kleinsteuber, Martin; Moreau, Éric; Shen, Hao; Tichavský, Petr; Yeredor, Arie

doi:10.1109/msp.2014.2298045

Cited by 111 publications

(48 citation statements)

References 47 publications

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“…To use this criterion, the matrix A (or Z) should be properly constrained in order to avoid the trivial zero solution and/or degenerate solutions [34].…”

Section: Jdc Cost Functionsmentioning

confidence: 99%

“…During the past two decades, many successful JDC methods have been proposed, such as Yeredor's alternating columns and diagonal center (ACDC) algorithm [23], the joint approximate diagonalization (JAD) algorithm proposed by Cardoso and Souloumiac [24], the fast Frobenius diagonalization (FFDIAG) algorithm proposed by Ziehe et al [25], Afsari's LUJ1D algorithm [26], and many others [27][28][29][30][31][32][33]. A recent survey of JDC can be found in [34]. The second special form of CP model is defined when all the factors in the CP decomposition are constrained to be nonnegative, commonly known as nonnegative tensor factorization (NTF).…”

Section: Introductionmentioning

confidence: 99%

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Canonical polyadic decomposition of third-order semi-nonnegative semi-symmetric tensors using LU and QR matrix factorizations

Wang

Albera

Kachenoura

et al. 2014

EURASIP J. Adv. Signal Process.

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Semi-symmetric three-way arrays are essential tools in blind source separation (BSS) particularly in independent component analysis (ICA). These arrays can be built by resorting to higher order statistics of the data. The canonical polyadic (CP) decomposition of such semi-symmetric three-way arrays allows us to identify the so-called mixing matrix, which contains the information about the intensities of some latent source signals present in the observation channels. In addition, in many applications, such as the magnetic resonance spectroscopy (MRS), the columns of the mixing matrix are viewed as relative concentrations of the spectra of the chemical components. Therefore, the two loading matrices of the three-way array, which are equal to the mixing matrix, are nonnegative. Most existing CP algorithms handle the symmetry and the nonnegativity separately. Up to now, very few of them consider both the semi-nonnegativity and the semi-symmetry structure of the three-way array. Nevertheless, like all the methods based on line search, trust region strategies, and alternating optimization, they appear to be dependent on initialization, requiring in practice a multi-initialization procedure. In order to overcome this drawback, we propose two new methods, called JD + LU and JD + QR , to solve the problem of CP decomposition of semi-nonnegative semi-symmetric three-way arrays. Firstly, we rewrite the constrained optimization problem as an unconstrained one. In fact, the nonnegativity constraint of the two symmetric modes is ensured by means of a square change of variable. Secondly, a Jacobi-like optimization procedure is adopted because of its good convergence property. More precisely, the two new methods use LU and QR matrix factorizations, respectively, which consist in formulating high-dimensional optimization problems into several sequential polynomial and rational subproblems. By using both LU and QR matrix factorizations, we aim at studying the influence of the used matrix factorization. Numerical experiments on simulated arrays emphasize the advantages of the proposed methods especially the one based on LU factorization, in the presence of high-variance model error and of degeneracies such as bottlenecks. A BSS application on MRS data confirms the validity and improvement of the proposed methods.

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“…To use this criterion, the matrix A (or Z) should be properly constrained in order to avoid the trivial zero solution and/or degenerate solutions [34].…”

Section: Jdc Cost Functionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Canonical polyadic decomposition of third-order semi-nonnegative semi-symmetric tensors using LU and QR matrix factorizations

Wang

Albera

Kachenoura

et al. 2014

EURASIP J. Adv. Signal Process.

View full text Add to dashboard Cite

show abstract

“…The following works have addressed either the problem of the JD of tensors (Comon 1994;Moreau 2001) or the problem of the JD of matrix sets, discarding the unitary constraint (Chabriel and Barrère 2012;Maurandi et al 2013;Souloumiac 2009;Yeredor 2002). A fairly exhaustive overview of all the suggested approaches is available in Chabriel et al 2014. This first particular type of matrix decomposition proves useful to solve two kinds of problems i) those of sources localization and direction finding and ii) those of blind separation of instantaneous mixtures of sources.…”

Section: Introductionmentioning

confidence: 99%

Preconditioned optimization algorithms solving the problem of the non unitary joint block diagonalization: application to blind separation of convolutive mixtures

Cherrak

Ghennioui

Thirion-Moreau

et al. 2017

Multidim Syst Sign Process

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This article addresses the problem of the Non Unitary Joint Block Diagonalization (NU − JBD) of a given set of complex matrices for the blind separation of convolutive mixtures of sources. We propose new different iterative optimization schemes based on Conjugate Gradient, Preconditioned Conjugate Gradient, Levenberg-Marquardt and Quasi-Newton methods. We perform also a study to determine which of these algorithms offer the best compromise between efficiency and convergence speed in the studied context. To be able to derive all these algorithms, a preconditioner has to be computed which requires either the calculation of the complex Hessian matrices or the use of an approximation to these Hessian matrices. Furthermore, the optimal stepsize is also computed algebraically to speed up the convergence of these algorithms. Computer simulations are provided in order to illustrate the behavior of the different algorithms in various contexts: when exactly block-diagonal matrices are considered but also when these matrices are progressively perturbed by an additive Gaussian noise. Finally, it is shown that these algorithms enable solving the blind separation of the convolutive mixtures of sources problem. Keywords

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“…The STFD matrices allow extraction of high energy points in the time-frequency (t-f) domain so that the estimate of the signal covariance matrix is improved. This results in a more robust DOA estimation against noisy disturbances (Amin and Zhang 2000;Boashash et al 2015;Chabriel et al 2014;Belouchrani and Amin 1999). The selection of proper t-f signatures belonging to a specific set of sources allows an improved DOA estimation in an under-determined case (sensors are less than the number of sources).…”

Section: Introductionmentioning

confidence: 99%

Direction of arrival estimation using adaptive directional time-frequency distributions

Khan

Ali

Jansson

2016

Multidim Syst Sign Process

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Time-frequency distributions (TFDs) allow direction of arrival (DOA) estimation algorithms to be used in scenarios when the total number of sources are more than the number of sensors. The performance of such time-frequency (t-f) based DOA estimation algorithms depends on the resolution of the underlying TFD as a higher resolution TFD leads to better separation of sources in the t-f domain. This paper presents a novel DOA estimation algorithm that uses the adaptive directional t-f distribution (ADTFD) for the analysis of close signal components. The ADTFD optimizes the direction of kernel at each point in the t-f domain to obtain a clear t-f representation, which is then exploited for DOA estimation. Moreover, the proposed methodology can also be applied for DOA estimation of sparse signals. Experimental results indicate that the proposed DOA algorithm based on the ADTFD outperforms other fixed and adaptive kernel based DOA algorithms.

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Joint Matrices Decompositions and Blind Source Separation: A survey of methods, identification, and applications

Cited by 111 publications

References 47 publications

Canonical polyadic decomposition of third-order semi-nonnegative semi-symmetric tensors using LU and QR matrix factorizations

Canonical polyadic decomposition of third-order semi-nonnegative semi-symmetric tensors using LU and QR matrix factorizations

Preconditioned optimization algorithms solving the problem of the non unitary joint block diagonalization: application to blind separation of convolutive mixtures

Direction of arrival estimation using adaptive directional time-frequency distributions

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