The Experts below are selected from a list of 9219 Experts worldwide ranked by ideXlab platform
Xavier Luciani - One of the best experts on this subject based on the ideXlab platform.
-
Joint Eigenvalue Decomposition Algorithms Based on First-Order Taylor Expansion
IEEE Transactions on Signal Processing, 2020Co-Authors: Rémi André, Xavier Luciani, Eric MoreauAbstract:In this paper, we propose a new approach to compute the Joint Eigenvalue Decomposition (JEVD) of real or complex matrix sets. JEVD aims to find a common basis of eigenvectors to a set of matrices. JEVD problem is encountered in many signal processing applications. In particular, recent and efficient algorithms for the Canonical Polyadic Decomposition (CPD) of multiway arrays resort to a JEVD step. The suggested method is based on multiplicative updates. It is distinguishable by the use of a first-order Taylor Expansion to compute the inverse of the updating matrix. We call this approach Joint Eigenvalue Decomposition based on Taylor Expansion (JDTE). This approach is derived in two versions based on simultaneous and sequential optimization schemes respectively. Here, simultaneous optimization means that all entries of the updating matrix are simultaneously optimized at each iteration. To the best of our knowledge, such an optimization scheme had never been proposed to solve the JEVD problem in a multiplicative update procedure. Our numerical simulations show that, in many situations involving complex matrices, the proposed approach improves the eigenvectors estimation while keeping a limited computational cost. Finally, these features are highlighted in a practical context of source separation through the CPD of telecommunication signals.
-
A COUPLED JOINT Eigenvalue Decomposition ALGORITHM FOR CANONICAL POLYADIC Decomposition OF TENSORS
2016Co-Authors: Rémi André, Xavier Luciani, Eric MoreauAbstract:In this paper we propose a novel algorithm to compute the joint Eigenvalue Decomposition of a set of squares matrices. This problem is at the heart of recent direct canonical polyadic Decomposition algorithms. Contrary to the existing approaches the proposed algorithm can deal equally with real or complex-valued matrices without any modifications. The algorithm is based on the algebraic polar Decomposition which allows to make the optimization step directly with complex parameters. Furthermore, both factorization matrices are estimated jointly. This " coupled " approach allows us to limit the numerical complexity of the algorithm. We then show with the help of numerical simulations that this approach is suitable for tensors canonical polyadic Decomposition.
-
a fast algorithm for joint Eigenvalue Decomposition of real matrices
European Signal Processing Conference, 2015Co-Authors: Rémi André, Xavier Luciani, Tual Trainini, Eric MoreauAbstract:We introduce an original algorithm to perform the joint eigen value Decomposition of a set of real matrices. The proposed algorithm is iterative but does not resort to any sweeping procedure such as classical Jacobi approaches. Instead we use a first order approximation of the inverse of the matrix of eigen vectors and at each iteration the whole matrix of eigenvectors is updated. This algorithm is called Joint Eigenvalue Decomposition using Taylor Expansion and has been designed in order to decrease the overall numerical complexity of the procedure (which is a trade off between the number of iterations and the cost of each iteration) while keeping the same level of performances. Numerical comparisons with reference algorithms show that this goal is achieved.
-
EUSIPCO - A fast algorithm for joint Eigenvalue Decomposition of real matrices
2015 23rd European Signal Processing Conference (EUSIPCO), 2015Co-Authors: Rémi André, Xavier Luciani, Tual Trainini, Eric MoreauAbstract:We introduce an original algorithm to perform the joint eigen value Decomposition of a set of real matrices. The proposed algorithm is iterative but does not resort to any sweeping procedure such as classical Jacobi approaches. Instead we use a first order approximation of the inverse of the matrix of eigen vectors and at each iteration the whole matrix of eigenvectors is updated. This algorithm is called Joint Eigenvalue Decomposition using Taylor Expansion and has been designed in order to decrease the overall numerical complexity of the procedure (which is a trade off between the number of iterations and the cost of each iteration) while keeping the same level of performances. Numerical comparisons with reference algorithms show that this goal is achieved.
-
Canonical Polyadic Decomposition based on joint Eigenvalue Decomposition
Chemometrics and Intelligent Laboratory Systems, 2014Co-Authors: Xavier Luciani, Laurent AlberaAbstract:A direct algorithm based on Joint Eigenvalue Decomposition (JEVD) has been proposed to compute the Canonical Polyadic Decomposition (CPD) of multi-way arrays (tensors). The iterative part of our method is thus limited to the JEVD computation. At this occasion we also propose an original JEVD technique. Most of the iterative CPD algorithms such as ALS have been shown by means of practical studies to suffer from convergence problems (local minima, slow convergence or high computational cost per iteration). On the other hand, direct methods seem in practice to confine these disadvantages but impose some restrictive necessary conditions. In this context, our proposed algorithm involves less restrictive necessary conditions than other recent direct approaches and a limited computational complexity. It has been compared to reference (direct and non-direct) algorithms on synthetic arrays and real spectroscopic data. These numerical examples highlight the main advantages of the proposed methods to solve both the JEVD and CPD problems
Stephan Weiss - One of the best experts on this subject based on the ideXlab platform.
-
Eigenvalue Decomposition of a Parahermitian Matrix: Extraction of Analytic Eigenvalues
IEEE Transactions on Signal Processing, 2021Co-Authors: Stephan Weiss, Ian K. Proudler, Fraser K. CouttsAbstract:An analytic parahermitian matrix admits an Eigenvalue Decomposition (EVD) with analytic Eigenvalues and eigenvectors except in the case of multiplexed data. In this paper, we propose an iterative algorithm for the estimation of the analytic Eigenvalues. Since these are generally transcendental, we find a polynomial approximation with a defined error. Our approach operates in the discrete Fourier transform (DFT) domain and for every DFT length generates a maximally smooth association through EVDs evaluated in DFT bins; an outer loop iteratively grows the DFT order and is shown, in general, to converge to the analytic Eigenvalues. In simulations, we compare our results to existing approaches.
-
Corrections to “On the Existence and Uniqueness of the Eigenvalue Decomposition of a Parahermitian Matrix”
IEEE Transactions on Signal Processing, 2018Co-Authors: Stephan Weiss, Ian K. Proudler, Jennifer Pestana, Fraser K. CouttsAbstract:Presents corrections to the paper, “On the existence and uniqueness of the Eigenvalue Decomposition of a paraher mitian matrix,” (Weiss, S. et al), IEEE Trans. Signal Process., vol. 66, no. 10, pp. 2659–2672, May 2018.
-
ACSSC - An Iterative DFT-based Approach to the Polynomial Matrix Eigenvalue Decomposition
2018 52nd Asilomar Conference on Signals Systems and Computers, 2018Co-Authors: Fraser K. Coutts, Keith Thompson, Ian K. Proudler, Stephan WeissAbstract:As an extension of the ordinary EVD to polynomial matrices, the polynomial matrix Eigenvalue Decomposition (PEVD) will generate paraunitary matrices that diagonalise a parahermitian matrix. Frequency-based PEVD algorithms have shown promise for the Decomposition of problems of finite order, but require a priori knowledge of the length of the Decomposition. This paper presents a novel iterative frequency-based PEVD algorithm which can compute an accurate Decomposition without requiring this information. We demonstrate through the use of simulations that the algorithm can achieve superior performance over existing iterative PEVD methods.
-
ACSSC - Multichannel spectral factorization algorithm using polynomial matrix Eigenvalue Decomposition
2015 49th Asilomar Conference on Signals Systems and Computers, 2015Co-Authors: Zeliang Wang, John G. Mcwhirter, Stephan WeissAbstract:In this paper, we present a new multichannel spectral factorization algorithm which can be utilized to calculate the approximate spectral factor of any para-Hermitian polynomial matrix. The proposed algorithm is based on an iterative method for polynomial matrix Eigenvalue Decomposition (PEVD). By using the PEVD algorithm, the multichannel spectral factorization problem is simply broken down to a set of single channel problems which can be solved by means of existing one-dimensional spectral factorization algorithms. In effect, it transforms the multichannel spectral factorization problem into one which is much easier to solve.
-
Multichannel spectral factorization algorithm using polynomial matrix Eigenvalue Decomposition
2015 49th Asilomar Conference on Signals Systems and Computers, 2015Co-Authors: Zeliang Wang, John G. Mcwhirter, Stephan WeissAbstract:In this paper, we present a new multichannel spectral factorization algorithm which can be utilized to calculate the approximate spectral factor of any para-Hermitian polynomial matrix. The proposed algorithm is based on an iterative method for polynomial matrix Eigenvalue Decomposition (PEVD). By using the PEVD algorithm, the multichannel spectral factorization problem is simply broken down to a set of single channel problems which can be solved by means of existing one-dimensional spectral factorization algorithms. In effect, it transforms the multichannel spectral factorization problem into one which is much easier to solve.
Laurent Albera - One of the best experts on this subject based on the ideXlab platform.
-
Canonical Polyadic Decomposition based on joint Eigenvalue Decomposition
Chemometrics and Intelligent Laboratory Systems, 2014Co-Authors: Xavier Luciani, Laurent AlberaAbstract:A direct algorithm based on Joint Eigenvalue Decomposition (JEVD) has been proposed to compute the Canonical Polyadic Decomposition (CPD) of multi-way arrays (tensors). The iterative part of our method is thus limited to the JEVD computation. At this occasion we also propose an original JEVD technique. Most of the iterative CPD algorithms such as ALS have been shown by means of practical studies to suffer from convergence problems (local minima, slow convergence or high computational cost per iteration). On the other hand, direct methods seem in practice to confine these disadvantages but impose some restrictive necessary conditions. In this context, our proposed algorithm involves less restrictive necessary conditions than other recent direct approaches and a limited computational complexity. It has been compared to reference (direct and non-direct) algorithms on synthetic arrays and real spectroscopic data. These numerical examples highlight the main advantages of the proposed methods to solve both the JEVD and CPD problems
-
Semi-algebraic canonical Decomposition of multi-way arrays and joint Eigenvalue Decomposition
2011Co-Authors: Xavier Luciani, Laurent AlberaAbstract:A semi-algebraic algorithm based on Joint Eigenvalue Decomposition (JEVD) is proposed to compute the CP Decomposition of multi-way arrays. The iterative part of the method is thus limited to the JEVD computation. In addition it involves less restrictive hypothesis than other recent semi-algebraic approaches. We also propose an original JEVD technique based on the LU factorization. Numerical examples highlight the main advantages of the proposed methods to solve both the JEVD and CP problems.
-
ICASSP - Semi-algebraic canonical Decomposition of multi-way arrays and Joint Eigenvalue Decomposition
2011 IEEE International Conference on Acoustics Speech and Signal Processing (ICASSP), 2011Co-Authors: Xavier Luciani, Laurent AlberaAbstract:A semi-algebraic algorithm based on Joint Eigenvalue Decomposition (JEVD) is proposed to compute the CP Decomposition of multi-way arrays. The iterative part of the method is thus limited to the JEVD computation. In addition it involves less restrictive hypothesis than other recent semi-algebraic approaches. We also propose an original JEVD technique based on the LU factorization. Numerical examples highlight the main advantages of the proposed methods to solve both the JEVD and CP problems.
-
Joint Eigenvalue Decomposition Using Polar Matrix Factorization.
2010Co-Authors: Xavier Luciani, Laurent AlberaAbstract:In this paper we propose a new algorithm for the joint Eigenvalue Decomposition of a set of real non-defective matrices. Our approach resorts to a Jacobi-like procedure based on polar matrix Decomposition. We introduce a new criterion in this context for the optimization of the hyperbolic matrices, giving birth to an original algorithm called JDTM. This algorithm is described in detail and a comparison study with reference algorithms is performed. Comparison results show that our approach provides quicker and more accurate results in all the considered situations.
-
LVA/ICA - Joint Eigenvalue Decomposition using polar matrix factorization
Latent Variable Analysis and Signal Separation, 2010Co-Authors: Xavier Luciani, Laurent AlberaAbstract:In this paper we propose a new algorithm for the joint Eigenvalue Decomposition of a set of real non-defective matrices. Our approach resorts to a Jacobi-like procedure based on polar matrix Decomposition. We introduce a new criterion in this context for the optimization of the hyperbolic matrices, giving birth to an original algorithm called JDTM. This algorithm is described in detail and a comparison study with reference algorithms is performed. Comparison results show that our approach provides quicker and more accurate results in all the considered situations.
Eric Moreau - One of the best experts on this subject based on the ideXlab platform.
-
Joint Eigenvalue Decomposition Algorithms Based on First-Order Taylor Expansion
IEEE Transactions on Signal Processing, 2020Co-Authors: Rémi André, Xavier Luciani, Eric MoreauAbstract:In this paper, we propose a new approach to compute the Joint Eigenvalue Decomposition (JEVD) of real or complex matrix sets. JEVD aims to find a common basis of eigenvectors to a set of matrices. JEVD problem is encountered in many signal processing applications. In particular, recent and efficient algorithms for the Canonical Polyadic Decomposition (CPD) of multiway arrays resort to a JEVD step. The suggested method is based on multiplicative updates. It is distinguishable by the use of a first-order Taylor Expansion to compute the inverse of the updating matrix. We call this approach Joint Eigenvalue Decomposition based on Taylor Expansion (JDTE). This approach is derived in two versions based on simultaneous and sequential optimization schemes respectively. Here, simultaneous optimization means that all entries of the updating matrix are simultaneously optimized at each iteration. To the best of our knowledge, such an optimization scheme had never been proposed to solve the JEVD problem in a multiplicative update procedure. Our numerical simulations show that, in many situations involving complex matrices, the proposed approach improves the eigenvectors estimation while keeping a limited computational cost. Finally, these features are highlighted in a practical context of source separation through the CPD of telecommunication signals.
-
A COUPLED JOINT Eigenvalue Decomposition ALGORITHM FOR CANONICAL POLYADIC Decomposition OF TENSORS
2016Co-Authors: Rémi André, Xavier Luciani, Eric MoreauAbstract:In this paper we propose a novel algorithm to compute the joint Eigenvalue Decomposition of a set of squares matrices. This problem is at the heart of recent direct canonical polyadic Decomposition algorithms. Contrary to the existing approaches the proposed algorithm can deal equally with real or complex-valued matrices without any modifications. The algorithm is based on the algebraic polar Decomposition which allows to make the optimization step directly with complex parameters. Furthermore, both factorization matrices are estimated jointly. This " coupled " approach allows us to limit the numerical complexity of the algorithm. We then show with the help of numerical simulations that this approach is suitable for tensors canonical polyadic Decomposition.
-
a fast algorithm for joint Eigenvalue Decomposition of real matrices
European Signal Processing Conference, 2015Co-Authors: Rémi André, Xavier Luciani, Tual Trainini, Eric MoreauAbstract:We introduce an original algorithm to perform the joint eigen value Decomposition of a set of real matrices. The proposed algorithm is iterative but does not resort to any sweeping procedure such as classical Jacobi approaches. Instead we use a first order approximation of the inverse of the matrix of eigen vectors and at each iteration the whole matrix of eigenvectors is updated. This algorithm is called Joint Eigenvalue Decomposition using Taylor Expansion and has been designed in order to decrease the overall numerical complexity of the procedure (which is a trade off between the number of iterations and the cost of each iteration) while keeping the same level of performances. Numerical comparisons with reference algorithms show that this goal is achieved.
-
EUSIPCO - A fast algorithm for joint Eigenvalue Decomposition of real matrices
2015 23rd European Signal Processing Conference (EUSIPCO), 2015Co-Authors: Rémi André, Xavier Luciani, Tual Trainini, Eric MoreauAbstract:We introduce an original algorithm to perform the joint eigen value Decomposition of a set of real matrices. The proposed algorithm is iterative but does not resort to any sweeping procedure such as classical Jacobi approaches. Instead we use a first order approximation of the inverse of the matrix of eigen vectors and at each iteration the whole matrix of eigenvectors is updated. This algorithm is called Joint Eigenvalue Decomposition using Taylor Expansion and has been designed in order to decrease the overall numerical complexity of the procedure (which is a trade off between the number of iterations and the cost of each iteration) while keeping the same level of performances. Numerical comparisons with reference algorithms show that this goal is achieved.
Hirokazu Kobayashi - One of the best experts on this subject based on the ideXlab platform.
-
hybrid freeman Eigenvalue Decomposition method with extended volume scattering model
IEEE Geoscience and Remote Sensing Letters, 2013Co-Authors: Gulab Singh, Yoshio Yamaguchi, Sang-eun Park, Yi Cui, Hirokazu KobayashiAbstract:In this letter, an advanced version of the hybrid Freeman/Eigenvalue Decomposition technique for land parameter extraction is presented with an illustrative example of application. The motivation arises from Decomposition problems in obtaining a meaningful volume scattering estimation, so that the technique can be used for both oriented objects and vegetation/forest areas. The idea is to improve the accuracy of the required parameter extraction. Two strategies are adopted to increase the applicability of a hybrid Freeman/Eigenvalue Decomposition technique: One is the unitary transformation of the coherency matrix; the other is to use an extended volume scattering model. The extension of the volume scattering model plays an essential role for the hybrid Freeman/Eigenvalue Decomposition technique. Since the volume scattering power is evaluated by assuming that the $HV$ component is caused by vegetation only in the existing technique, an extended volume scattering power approach is utilized. It is shown that vegetation areas and oriented objects such as urban building areas are well discriminated by the proposed technique as compared to the existing techniques.
-
Hybrid Freeman/Eigenvalue Decomposition Method With Extended Volume Scattering Model
IEEE Geoscience and Remote Sensing Letters, 2013Co-Authors: Gulab Singh, Yoshio Yamaguchi, Sang-eun Park, Yi Cui, Hirokazu KobayashiAbstract:In this letter, an advanced version of the hybrid Freeman/Eigenvalue Decomposition technique for land parameter extraction is presented with an illustrative example of application. The motivation arises from Decomposition problems in obtaining a meaningful volume scattering estimation, so that the technique can be used for both oriented objects and vegetation/forest areas. The idea is to improve the accuracy of the required parameter extraction. Two strategies are adopted to increase the applicability of a hybrid Freeman/Eigenvalue Decomposition technique: One is the unitary transformation of the coherency matrix; the other is to use an extended volume scattering model. The extension of the volume scattering model plays an essential role for the hybrid Freeman/Eigenvalue Decomposition technique. Since the volume scattering power is evaluated by assuming that the $HV$ component is caused by vegetation only in the existing technique, an extended volume scattering power approach is utilized. It is shown that vegetation areas and oriented objects such as urban building areas are well discriminated by the proposed technique as compared to the existing techniques.