The Experts below are selected from a list of 1998 Experts worldwide ranked by ideXlab platform
Tomohiro Nakatani - One of the best experts on this subject based on the ideXlab platform.
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a Joint Diagonalization based efficient approach to underdetermined blind audio source separation using the multichannel wiener filter
arXiv: Sound, 2021Co-Authors: Nobutaka Ito, Hiroshi Sawada, Rintaro Ikeshita, Tomohiro NakataniAbstract:This paper presents a computationally efficient approach to blind source separation (BSS) of audio signals, applicable even when there are more sources than microphones (i.e., the underdetermined case). When there are as many sources as microphones (i.e., the determined case), BSS can be performed computationally efficiently by independent component analysis (ICA). Unfortunately, however, ICA is basically inapplicable to the underdetermined case. Another BSS approach using the multichannel Wiener filter (MWF) is applicable even to this case, and encompasses full-rank spatial covariance analysis (FCA) and multichannel non-negative matrix factorization (MNMF). However, these methods require massive numbers of matrix inversions to design the MWF, and are thus computationally inefficient. To overcome this drawback, we exploit the well-known property of diagonal matrices that matrix inversion amounts to mere inversion of the diagonal elements and can thus be performed computationally efficiently. This makes it possible to drastically reduce the computational cost of the above matrix inversions based on a Joint Diagonalization (JD) idea, leading to computationally efficient BSS. Specifically, we restrict the N spatial covariance matrices (SCMs) of all N sources to a class of (exactly) Jointly diagonalizable matrices. Based on this approach, we present FastFCA, a computationally efficient extension of FCA. We also present a unified framework for underdetermined and determined audio BSS, which highlights a theoretical connection between FastFCA and other methods. Moreover, we reveal that FastFCA can be regarded as a regularized version of approximate Joint Diagonalization (AJD).
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a Joint Diagonalization based efficient approach to underdetermined blind audio source separation using the multichannel wiener filter
IEEE Transactions on Audio Speech and Language Processing, 2021Co-Authors: Nobutaka Ito, Hiroshi Sawada, Rintaro Ikeshita, Tomohiro NakataniAbstract:Blind source separation (BSS) of audio signals aims to separate original source signals from their mixtures recorded by microphones. The applications include automatic speech recognition in a noisy/multi-speaker environment, hearing aids, and music analysis. Independent component analysis (ICA) can perform BSS efficiently, but it is basically inapplicable to the underdetermined case—the number of sources $\boldsymbol{>}$ the number of microphones. In contrast, a BSS approach using the multichannel Wiener filter (MWF) is applicable even to the underdetermined case, but conventional methods based on this approach—including full-rank spatial covariance analysis (FCA)—are highly inefficient. This is because these methods require massive numbers of matrix inversions to design the MWF. To obtain the best of both worlds, we take a Joint Diagonalization approach: We restrict spatial covariance matrices of all sources to the class of Jointly diagonalizable matrices. This enables the above matrix inversions to be replaced by mere scalar inversions of the diagonal elements of diagonal matrices. Based on this, we present FastFCA and FastMNMF—efficient methods for underdetermined BSS. In an experiment, FastFCA was several orders of magnitude faster than FCA without sacrificing separation performance. We also present a unified framework for underdetermined and determined BSS, which highlights theoretical connections between various methods including ours. The efficiency of our BSS methods makes them suitable for large data (e.g., data augmentation for machine learning) or limited computational resources encountered in, e.g., hearing aids, distributed microphone arrays, and online BSS.
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fastmnmf Joint Diagonalization based accelerated algorithms for multichannel nonnegative matrix factorization
International Conference on Acoustics Speech and Signal Processing, 2019Co-Authors: Nobutaka Ito, Tomohiro NakataniAbstract:A multichannel extension of nonnegative matrix factorization (NMF) for audio/music data, called multichannel $NMF$ (MNMF), has been proposed by Sawada et $al$ ["Multichannel extensions of non-negative matrix factorization with complex-valued data IEEE Trans. ASLP, vol. 21, no. 5, pp. 971-982, May 2013]. However, conventional MNMF algorithms have a major drawback of a heavy computational load due to numerous matrix operations, such as matrix inversions and matrix multiplications. Here we propose FastMNMF, accelerated algorithms for the MNMF based on Joint Diagonalization of matrices. It is well known that, for diagonal matrices, matrix operations reduce to mere scalar operations on diagonal entries. Because of this property, the Joint Diagonalization results in a significantly reduced computational load compared to conventional MNMF algorithms. This makes the proposed FastMNMF even applicable to a situation with alarge database or restricted computational resources.
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multiplicative updates and Joint Diagonalization based acceleration for under determined bss using a full rank spatial covariance model
IEEE Global Conference on Signal and Information Processing, 2018Co-Authors: Nobutaka Ito, Tomohiro NakataniAbstract:Here we introduce multiplicative update rules for full-rank spatial covariance analysis (FCA), a blind source separation (BSS) method proposed by Duong et al. ["Under-determined reverberant audio source separation using a full-rank spatial covariance model," IEEE Trans. ASLP, vol. 18, no. 7, pp. 1830–1840, Sept. 2010]. In the FCA, source separation is performed by multichannel Wiener filtering with the covariance matrix of each source signal estimated by the expectation-maximization (EM) algorithm. A drawback of this EM algorithm is that it does not necessarily yield good covariance matrix estimates within a feasible number of iterations. In contrast, the proposed multiplicative update rules tend to give covariance matrix estimates that result in better source separation performance than the EM algorithm. Furthermore, we propose Joint Diagonalization based acceleration of the multiplicative update rules, which leads to signifi-cantly reduced computation time per iteration. In a BSS experiment, the proposed multiplicative update rules resulted in higher source separation performance than the conventional EM algorithm overall. Moreover, the Joint Diagonalization based accelerated algorithm was up to 200 times faster than the algorithm without acceleration, which is realized without much degradation in the source separation performance.
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fastfca as Joint Diagonalization based acceleration of full rank spatial covariance analysis for separating any number of sources
International Workshop on Acoustic Signal Enhancement, 2018Co-Authors: Nobutaka Ito, Tomohiro NakataniAbstract:Here we propose FastFCA-AS, an accelerated algorithm for Full-rank spatial Covariance Analysis (FCA), which is a robust audio source separation method proposed by Duong et al. [“Under-determined reverberant audio source separation using a full-rank spatial covariance model,” IEEE Trans. ASLP, vol. 18, no. 7, pp. 1830–1840, Sept. 2010]. In the conventional FCA, matrix inversion and matrix multiplication are required at each time-frequency point in each iteration of an iterative parameter estimation algorithm. This causes a heavy computational load, thereby rendering the FCA infeasible in many applications. To overcome this drawback, we take a Joint Diagonalization approach, whereby matrix inversion and matrix multiplication are reduced to mere inversion and multiplication of diagonal entries. This makes the FastFCA-AS significantly faster than the FCA and even applicable to observed data of long duration or a situation with restricted computational resources. Although we have already proposed another acceleration of the FCA for two sources, the proposed FastFCA-AS is applicable to an arbitrary number of sources. In an experiment with three sources and three microphones, the FastFCA-AS was over 420 times faster than the FCA with a slightly better source separation performance.
Eric Moreau - One of the best experts on this subject based on the ideXlab platform.
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a two step algorithm for Joint eigenvalue decomposition application to canonical polyadic decomposition of fluorescence spectra
Chemometrics and Intelligent Laboratory Systems, 2020Co-Authors: Remi Andre, Xavier Luciani, Laurent Albera, Eric MoreauAbstract:Abstract In this paper, we propose a new Joint EigenValue Decomposition (JEVD) algorithm. JEVD problem belongs to the family of Joint Diagonalization problems. Hence, JEVD algorithms aim at estimating the common basis of eigenvectors of a matrix set. This problem occurs in many signal processing applications. It has notably allowed to develop efficient algorithms for the Canonical Polyadic Decomposition (CPD) of multiway arrays. The proposed JEVD algorithm is based on an original two-step approach. The first step consists in transforming the considered matrix set into a set of positive definite matrices. In this purpose, we introduce an ad hoc Joint symmetrization algorithm. This first step allows us to transform the JEVD problem into a simpler orthogonal Joint Diagonalization problem. The second step is then performed using an efficient orthogonal Joint Diagonalization algorithm of the literature. Eventually, the performance of the proposed approach is deeply investigated in the CPD context of multidimensional fluorescence data. More particularly, we consider difficult scenarios such as the cases of an overestimated rank and highly correlated factors.
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fast jacobi algorithm for non orthogonal Joint Diagonalization of non symmetric third order tensors
European Signal Processing Conference, 2015Co-Authors: Victor Maurandi, Eric MoreauAbstract:We consider the problem of non-orthogonal Joint Diagonalization of a set of non-symmetric real-valued third-order tensors. This appears in many signal processing problems and it is instrumental in source separation. We propose a new Jacobi-like algorithm based on an LU decomposition of the so-called diagonalizing matrices. The parameters estimation is done entirely analytically following a strategy based on a classical inverse criterion and a fully decoupled estimation. One important point is that the Diagonalization is directly done on the set of third-order tensors and not on their unfolded version. Computer simulations illustrate the overall good performances of the proposed algorithm.
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a decoupled jacobi like algorithm for non unitary Joint Diagonalization of complex valued matrices
IEEE Signal Processing Letters, 2014Co-Authors: Victor Maurandi, Eric MoreauAbstract:We consider the problem of non-orthogonal Joint Diagonalization of a set of complex matrices. This appears in many signal processing problems and is instrumental in source separation. We propose a new Jacobi-like algorithm based both on a special parameterization of the diagonalizing matrix and on an adapted local criterion. The optimization scheme is based on an alternate estimation of the useful parameters. Numerical simulations illustrate the overall very good performances of the proposed algorithm in comparison to two other Jacobi-like algorithms and to a global algorithm existing in the literature.
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jacobi like algorithm for non orthogonal Joint Diagonalization of hermitian matrices
International Conference on Acoustics Speech and Signal Processing, 2014Co-Authors: Victor Maurandi, Eric Moreau, Christophe De LuigiAbstract:In this paper, we consider the problem of non-orthogonal Joint Diagonalization of a set of hermitian matrices. This appears in many blind signal processing problems as source separation and independent component analysis. We propose a new Jacobi like algorithm based on a LU decomposition. The main point consists of the analytical derivation of the elementary two by two matrix. In order to determine the diagonalizing matrix parameters, we propose a useful approximation. Numerical simulations illustrate the overall good performances of the proposed algorithm in comparison to two other Jacobi like algorithms existing in the literature.
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variations around gradient like algorithms for Joint Diagonalization of hermitian matrices
European Signal Processing Conference, 2012Co-Authors: Tual Trainini, Eric MoreauAbstract:In this paper, we address the problem of Joint Diagonalization of hermitian complex matrix sets, which arises in many signal processing problems (telecommunications, radioastronomy, biology). We present different gradient based algorithms using an optimal step size multiplicative update. Computer simulations are provided to illustrate the comparative behavior of those algorithms together with an application to source separation.
Nobutaka Ito - One of the best experts on this subject based on the ideXlab platform.
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a Joint Diagonalization based efficient approach to underdetermined blind audio source separation using the multichannel wiener filter
arXiv: Sound, 2021Co-Authors: Nobutaka Ito, Hiroshi Sawada, Rintaro Ikeshita, Tomohiro NakataniAbstract:This paper presents a computationally efficient approach to blind source separation (BSS) of audio signals, applicable even when there are more sources than microphones (i.e., the underdetermined case). When there are as many sources as microphones (i.e., the determined case), BSS can be performed computationally efficiently by independent component analysis (ICA). Unfortunately, however, ICA is basically inapplicable to the underdetermined case. Another BSS approach using the multichannel Wiener filter (MWF) is applicable even to this case, and encompasses full-rank spatial covariance analysis (FCA) and multichannel non-negative matrix factorization (MNMF). However, these methods require massive numbers of matrix inversions to design the MWF, and are thus computationally inefficient. To overcome this drawback, we exploit the well-known property of diagonal matrices that matrix inversion amounts to mere inversion of the diagonal elements and can thus be performed computationally efficiently. This makes it possible to drastically reduce the computational cost of the above matrix inversions based on a Joint Diagonalization (JD) idea, leading to computationally efficient BSS. Specifically, we restrict the N spatial covariance matrices (SCMs) of all N sources to a class of (exactly) Jointly diagonalizable matrices. Based on this approach, we present FastFCA, a computationally efficient extension of FCA. We also present a unified framework for underdetermined and determined audio BSS, which highlights a theoretical connection between FastFCA and other methods. Moreover, we reveal that FastFCA can be regarded as a regularized version of approximate Joint Diagonalization (AJD).
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a Joint Diagonalization based efficient approach to underdetermined blind audio source separation using the multichannel wiener filter
IEEE Transactions on Audio Speech and Language Processing, 2021Co-Authors: Nobutaka Ito, Hiroshi Sawada, Rintaro Ikeshita, Tomohiro NakataniAbstract:Blind source separation (BSS) of audio signals aims to separate original source signals from their mixtures recorded by microphones. The applications include automatic speech recognition in a noisy/multi-speaker environment, hearing aids, and music analysis. Independent component analysis (ICA) can perform BSS efficiently, but it is basically inapplicable to the underdetermined case—the number of sources $\boldsymbol{>}$ the number of microphones. In contrast, a BSS approach using the multichannel Wiener filter (MWF) is applicable even to the underdetermined case, but conventional methods based on this approach—including full-rank spatial covariance analysis (FCA)—are highly inefficient. This is because these methods require massive numbers of matrix inversions to design the MWF. To obtain the best of both worlds, we take a Joint Diagonalization approach: We restrict spatial covariance matrices of all sources to the class of Jointly diagonalizable matrices. This enables the above matrix inversions to be replaced by mere scalar inversions of the diagonal elements of diagonal matrices. Based on this, we present FastFCA and FastMNMF—efficient methods for underdetermined BSS. In an experiment, FastFCA was several orders of magnitude faster than FCA without sacrificing separation performance. We also present a unified framework for underdetermined and determined BSS, which highlights theoretical connections between various methods including ours. The efficiency of our BSS methods makes them suitable for large data (e.g., data augmentation for machine learning) or limited computational resources encountered in, e.g., hearing aids, distributed microphone arrays, and online BSS.
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fastmnmf Joint Diagonalization based accelerated algorithms for multichannel nonnegative matrix factorization
International Conference on Acoustics Speech and Signal Processing, 2019Co-Authors: Nobutaka Ito, Tomohiro NakataniAbstract:A multichannel extension of nonnegative matrix factorization (NMF) for audio/music data, called multichannel $NMF$ (MNMF), has been proposed by Sawada et $al$ ["Multichannel extensions of non-negative matrix factorization with complex-valued data IEEE Trans. ASLP, vol. 21, no. 5, pp. 971-982, May 2013]. However, conventional MNMF algorithms have a major drawback of a heavy computational load due to numerous matrix operations, such as matrix inversions and matrix multiplications. Here we propose FastMNMF, accelerated algorithms for the MNMF based on Joint Diagonalization of matrices. It is well known that, for diagonal matrices, matrix operations reduce to mere scalar operations on diagonal entries. Because of this property, the Joint Diagonalization results in a significantly reduced computational load compared to conventional MNMF algorithms. This makes the proposed FastMNMF even applicable to a situation with alarge database or restricted computational resources.
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multiplicative updates and Joint Diagonalization based acceleration for under determined bss using a full rank spatial covariance model
IEEE Global Conference on Signal and Information Processing, 2018Co-Authors: Nobutaka Ito, Tomohiro NakataniAbstract:Here we introduce multiplicative update rules for full-rank spatial covariance analysis (FCA), a blind source separation (BSS) method proposed by Duong et al. ["Under-determined reverberant audio source separation using a full-rank spatial covariance model," IEEE Trans. ASLP, vol. 18, no. 7, pp. 1830–1840, Sept. 2010]. In the FCA, source separation is performed by multichannel Wiener filtering with the covariance matrix of each source signal estimated by the expectation-maximization (EM) algorithm. A drawback of this EM algorithm is that it does not necessarily yield good covariance matrix estimates within a feasible number of iterations. In contrast, the proposed multiplicative update rules tend to give covariance matrix estimates that result in better source separation performance than the EM algorithm. Furthermore, we propose Joint Diagonalization based acceleration of the multiplicative update rules, which leads to signifi-cantly reduced computation time per iteration. In a BSS experiment, the proposed multiplicative update rules resulted in higher source separation performance than the conventional EM algorithm overall. Moreover, the Joint Diagonalization based accelerated algorithm was up to 200 times faster than the algorithm without acceleration, which is realized without much degradation in the source separation performance.
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fastfca as Joint Diagonalization based acceleration of full rank spatial covariance analysis for separating any number of sources
International Workshop on Acoustic Signal Enhancement, 2018Co-Authors: Nobutaka Ito, Tomohiro NakataniAbstract:Here we propose FastFCA-AS, an accelerated algorithm for Full-rank spatial Covariance Analysis (FCA), which is a robust audio source separation method proposed by Duong et al. [“Under-determined reverberant audio source separation using a full-rank spatial covariance model,” IEEE Trans. ASLP, vol. 18, no. 7, pp. 1830–1840, Sept. 2010]. In the conventional FCA, matrix inversion and matrix multiplication are required at each time-frequency point in each iteration of an iterative parameter estimation algorithm. This causes a heavy computational load, thereby rendering the FCA infeasible in many applications. To overcome this drawback, we take a Joint Diagonalization approach, whereby matrix inversion and matrix multiplication are reduced to mere inversion and multiplication of diagonal entries. This makes the FastFCA-AS significantly faster than the FCA and even applicable to observed data of long duration or a situation with restricted computational resources. Although we have already proposed another acceleration of the FCA for two sources, the proposed FastFCA-AS is applicable to an arbitrary number of sources. In an experiment with three sources and three microphones, the FastFCA-AS was over 420 times faster than the FCA with a slightly better source separation performance.
Arie Yeredor - One of the best experts on this subject based on the ideXlab platform.
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on hybrid exact approximate Joint Diagonalization
IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, 2009Co-Authors: Arie YeredorAbstract:We consider a particular form of the classical approximate Joint Diagonalization problem, often encountered in Maximum Likelihood source separation based on second-order statistics with Gaussian sources. In this form the number of target-matrices equals their dimension, and the Joint diagonality criterion requires that in each transformed (“diagonalized”) target-matrix, all off-diagonal elements on one specific row and column be exactly zeros, but does not care about the other (diagonal or off-diagonal) elements. We show that this problem always has a solution for symmetric, positive-definite target-matrices and present some interesting alternative formulations. We review two existing iterative approaches for obtaining the diagonalizing matrices and propose a third one with faster convergence.
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fast approximate Joint Diagonalization incorporating weight matrices
IEEE Transactions on Signal Processing, 2009Co-Authors: Petr Tichavsky, Arie YeredorAbstract:We propose a new low-complexity approximate Joint Diagonalization (AJD) algorithm, which incorporates nontrivial block-diagonal weight matrices into a weighted least-squares (WLS) AJD criterion. Often in blind source separation (BSS), when the sources are nearly separated, the optimal weight matrix for WLS-based AJD takes a (nearly) block-diagonal form. Based on this observation, we show how the new algorithm can be utilized in an iteratively reweighted separation scheme, thereby giving rise to fast implementation of asymptotically optimal BSS algorithms in various scenarios. In particular, we consider three specific (yet common) scenarios, involving stationary or block-stationary Gaussian sources, for which the optimal weight matrices can be readily estimated from the sample covariance matrices (which are also the target-matrices for the AJD). Comparative simulation results demonstrate the advantages in both speed and accuracy, as well as compliance with the theoretically predicted asymptotic optimality of the resulting BSS algorithms based on the weighted AJD, both on large scale problems with matrices of the size 100times100.
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blind separation of superimposed shifted images using parameterized Joint Diagonalization
IEEE Transactions on Image Processing, 2008Co-Authors: E Beery, Arie YeredorAbstract:We consider the blind separation of source images from linear mixtures thereof, involving different relative spatial shifts of the sources in each mixture. Such mixtures can be caused, e.g., by the presence of a semi-reflective medium (such as a window glass) across a photographed scene, due to slight movements of the medium (or of the sources) between snapshots. Classical separation approaches assume either a static mixture model or a fully convolutive mixture model, which are, respectively, either under-or over-parameterized for this problem. In this paper, we develop a specially parameterized scheme for approximate Joint Diagonalization of estimated spectrum matrices, aimed at estimating the succinct set of mixture parameters: the static (gain) coefficients and the shift values. The estimated parameters are, in turn, used for convenient frequency-domain separation. As we demonstrate using both synthetic mixtures and real-life photographs, the advantage of the ability to incorporate spatial shifts is twofold: Not only does it enable separation when such shifts are present, but it also warrants deliberate introduction of such shifts as a simple source of added diversity whenever the static mixing coefficients form a singular matrix - thereby enabling separation in otherwise inseparable scenes.
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A fast approximate Joint Diagonalization algorithm using a criterion with a block diagonal weight matrix
2008 IEEE International Conference on Acoustics Speech and Signal Processing, 2008Co-Authors: Petr Tichavsky, Arie Yeredor, Jan NielsenAbstract:We propose a new algorithm for approximate Joint Diagonalization (AJD) with two main advantages over existing state-of-the-art algorithms: Improved overall running speed, especially in large-scale (high-dimensional) problems; and an ability to incorporate specially structured weight-matrices into the AJD criterion. The algorithm is based on approximate Gauss iterations for successive reduction of a weighted least squares off-diagonality criterion. The proposed Matlabreg implementation allows AJD of ten 100 times 100 matrices in 3-4 seconds (for the unweighted case) on a common PC (Pentium M, 1.86 GHz, 2 GB RAM), generally 3-5 times faster than the fastest competitor. The ability to incorporate weights allows fast large-scale realization of optimized versions of classical blind source separation algorithms, such as second-order blind identification (SOBI), whose weighted version (WA- SOBI) yields significantly improved separation performance.
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on using exact Joint Diagonalization for noniterative approximate Joint Diagonalization
IEEE Signal Processing Letters, 2005Co-Authors: Arie YeredorAbstract:We propose a novel, noniterative approach for the problem of nonunitary, least-squares (LS) approximate Joint Diagonalization (AJD) of several Hermitian target matrices. Dwelling on the fact that exact Joint Diagonalization (EJD) of two Hermitian matrices can almost always be easily obtained in closed form, we show how two "representative matrices" can be constructed out of the original set of all target matrices, such that their EJD would be useful in the AJD of the original set. Indeed, for the two-by-two case, we show that the EJD of the representative matrices yields the optimal AJD solution. For larger-scale cases, the EJD can provide a suboptimal AJD solution, possibly serving as a good initial guess for a subsequent iterative algorithm. Additionally, we provide an informative lower bound on the attainable LS fit, which is useful in gauging the distance of prospective solutions from optimality.
Laurent Albera - One of the best experts on this subject based on the ideXlab platform.
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a two step algorithm for Joint eigenvalue decomposition application to canonical polyadic decomposition of fluorescence spectra
Chemometrics and Intelligent Laboratory Systems, 2020Co-Authors: Remi Andre, Xavier Luciani, Laurent Albera, Eric MoreauAbstract:Abstract In this paper, we propose a new Joint EigenValue Decomposition (JEVD) algorithm. JEVD problem belongs to the family of Joint Diagonalization problems. Hence, JEVD algorithms aim at estimating the common basis of eigenvectors of a matrix set. This problem occurs in many signal processing applications. It has notably allowed to develop efficient algorithms for the Canonical Polyadic Decomposition (CPD) of multiway arrays. The proposed JEVD algorithm is based on an original two-step approach. The first step consists in transforming the considered matrix set into a set of positive definite matrices. In this purpose, we introduce an ad hoc Joint symmetrization algorithm. This first step allows us to transform the JEVD problem into a simpler orthogonal Joint Diagonalization problem. The second step is then performed using an efficient orthogonal Joint Diagonalization algorithm of the literature. Eventually, the performance of the proposed approach is deeply investigated in the CPD context of multidimensional fluorescence data. More particularly, we consider difficult scenarios such as the cases of an overestimated rank and highly correlated factors.
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an alternating direction method of multipliers for constrained Joint Diagonalization by congruence
IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, 2015Co-Authors: Lu Wang, Laurent Albera, Lotfi Senhadji, Jeanchristophe PesquetAbstract:In this paper, we address the problem of Joint Diagonalization by congruence (i.e. the canonical polyadic decomposition of semi-symmetric 3rd order tensors) subject to arbitrary convex constraints. Sufficient conditions for the existence of a solution are given. An efficient algorithm based on the Alternating Direction Method of Multipliers (ADMM) is then designed. ADMM provides an elegant approach for handling the additional constraint terms, while taking advantage of the structure of the objective function. Numerical tests on simulated matrices show the benefits of the proposed method for low signal to noise ratios. Simulations in the context of nuclear magnetic resonance spectroscopy are also provided.
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a new jacobi like nonnegative Joint Diagonalization by congruence
European Signal Processing Conference, 2013Co-Authors: Lu Wang, Laurent Albera, Hua Zhong Shu, Lotfi SenhadjiAbstract:A new Joint Diagonalization by congruence algorithm is presented, which allows the computation of a nonnegative Joint diagonalizer. The nonnegativity constraint is ensured by means of a square change of variable. Then we propose a Jacobi-like approach using LU matrix factorization, which consists of formulating a high-dimensional optimization problem into several sequential one-dimensional subproblems. Numerical experiments emphasize the advantages of the proposed method, especially in the presence of bottlenecks such as for low SNR values and a small number of available matrices. An illustration of blind source separation shows the interest of the proposed algorithm.
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nonnegative Joint Diagonalization by congruence based on lu matrix factorization
IEEE Signal Processing Letters, 2013Co-Authors: Lu Wang, Laurent Albera, Hua Zhong Shu, Amar Kachenoura, Lotfi SenhadjiAbstract:In this letter, a new algorithm for Joint Diagonalization of a set of matrices by congruence is proposed to compute the nonnegative Joint diagonalizer. The nonnegativity constraint is imposed by means of a square change of variables. Then we formulate the high-dimensional optimization problem into several sequential polynomial subproblems using LU matrix factorization. Numerical experiments on simulated matrices emphasize the advantages of the proposed method, especially in the case of degeneracies such as for low SNR values and a small number of matrices. An illustration of blind separation of nuclear magnetic resonance spectroscopy confirms the validity and improvement of the proposed method.
