The Experts below are selected from a list of 300 Experts worldwide ranked by ideXlab platform
M.a. Hasan - One of the best experts on this subject based on the ideXlab platform.
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simultaneous minor component extraction via weighted inverse Rayleigh Quotient
International Conference on Acoustics Speech and Signal Processing, 2007Co-Authors: M.a. HasanAbstract:New criteria are proposed for extracting multiple minor components associated with the covariance matrix of an input process. The proposed minor component analysis (MCA) algorithms are based on optimizing a weighted inverse Rayleigh Quotient so that the optimum weights at equilibrium points are exactly the desired eigenvectors of a covariance matrix instead of an arbitrary orthonormal basis of the minor subspace. Variations of the derived MCA learning rules are obtained by imposing orthogonal and quadratic constraints and change of variables. Some of the proposed algorithms can also perform PCA by merely changing the sign of the step-size. These algorithms may be seen as MCA counterparts of Oja's and Xu's systems for computing multiple principal component analysis. Simulation results to demonstrate algorithm performance are also presented.
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Revisiting Weighted Inverse Rayleigh Quotient for Minor Component Extraction
2005 5th International Conference on Information Communications & Signal Processing, 2005Co-Authors: M.a. HasanAbstract:A framework for classes of minor component learning rules is presented. In the proposed rules, eigenvectors of a covariance matrix are simultaneously estimated. The derivation of MCA rules is based on optimizing a weighted inverse Rayleigh Quotient so that the optimum weights at equilibrium points are exactly the desired eigenvectors of a covariance matrix instead of an arbitrary orthonormal basis of the minor subspace. Variations of the derived MCA learning rules are obtained by imposing orthogonal and quadratic constraints and change of variables. Some of the proposed algorithms can also perform PCA by merely changing the sign of the step-size
P. Van Dooren - One of the best experts on this subject based on the ideXlab platform.
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Two-sided Grassmann–Rayleigh Quotient iteration
Numerische Mathematik, 2010Co-Authors: P-a Absil, P. Van DoorenAbstract:The two-sided Rayleigh Quotient iteration proposed by Ostrowski computes a pair of corresponding left–right eigenvectors of a matrix C . We propose a Grassmannian version of this iteration, i.e., its iterates are pairs of p -dimensional subspaces instead of one-dimensional subspaces in the classical case. The new iteration generically converges locally cubically to the pairs of left–right p -dimensional invariant subspaces of C . Moreover, Grassmannian versions of the Rayleigh Quotient iteration are given for the generalized Hermitian eigenproblem, the Hamiltonian eigenproblem and the skew-Hamiltonian eigenproblem.
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Two-sided Grassmann-Rayleigh Quotient iteration
Numerische Mathematik, 2009Co-Authors: Pierre-antoine Absil, P. Van DoorenAbstract:The two-sided Rayleigh Quotient iteration proposed by Ostrowski computes a pair of corresponding left-right eigenvectors of a matrix $C$. We propose a Grassmannian version of this iteration, i.e., its iterates are pairs of $p$-dimensional subspaces instead of one-dimensional subspaces in the classical case. The new iteration generically converges locally cubically to the pairs of left-right $p$-dimensional invariant subspaces of $C$. Moreover, Grassmannian versions of the Rayleigh Quotient iteration are given for the generalized Hermitian eigenproblem, the Hamiltonian eigenproblem and the skew-Hamiltonian eigenproblem.
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A Grassmann-Rayleigh Quotient Iteration for
2002Co-Authors: Pierre-antoine Absil, Robert Mahony, Rodolphe Sepulchre, P. Van DoorenAbstract:The classical Rayleigh Quotient iteration (RQI) allows one to compute a one-dimensional invariant subspace of a symmetric matrix A. Here we propose a generalization of the RQI which computes a p-dimensional invariant subspace of A. Cubic convergence is preserved and the cost per iteration is low compared to other methods proposed in the literature.
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A Grassmann--Rayleigh Quotient Iteration for Computing Invariant Subspaces
SIAM Review, 2002Co-Authors: Pierre-antoine Absil, Robert Mahony, Rodolphe Sepulchre, P. Van DoorenAbstract:The classical Rayleigh Quotient iteration (RQI) allows one to compute a one-dimensional invariant subspace of a symmetric matrix A. Here we propose a generalization of the RQI which computes a p-dimensional invariant subspace of A. Cubic convergence is preserved and the cost per iteration is low compared to other methods proposed in the literature.
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A Grassmann-Rayleigh Quotient iteration for computing invariant subspaces
Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187), 1Co-Authors: Pierre-antoine Absil, Robert Mahony, Rodolphe Sepulchre, P. Van DoorenAbstract:The classical Rayleigh Quotient iteration (RQI) computes a 1-dimensional invariant subspace of a symmetric matrix A with cubic convergence. We propose a generalization of the RQI which computes a p-dimensional invariant subspace of A. The geometry of the algorithm on the Grassmann manifold Gr(p,n) is developed to show cubic convergence and to draw connections with Newton algorithms on Riemannian manifolds.
Lieven De Lathauwer - One of the best experts on this subject based on the ideXlab platform.
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Rayleigh Quotient Methods for Estimating Common Roots of Noisy Univariate Polynomials
Computational Methods in Applied Mathematics, 2018Co-Authors: Alwin Stegeman, Lieven De LathauwerAbstract:Abstract The problem is considered of approximately solving a system of univariate polynomials with one or more common roots and its coefficients corrupted by noise. The goal is to estimate the underlying common roots from the noisy system. Symbolic algebra methods are not suitable for this. New Rayleigh Quotient methods are proposed and evaluated for estimating the common roots. Using tensor algebra, reasonable starting values for the Rayleigh Quotient methods can be computed. The new methods are compared to Gauss–Newton, solving an eigenvalue problem obtained from the generalized Sylvester matrix, and finding a cluster among the roots of all polynomials. In a simulation study it is shown that Gauss–Newton and a new Rayleigh Quotient method perform best, where the latter is more accurate when other roots than the true common roots are close together.
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ICA - A Grassmann-Rayleigh Quotient Iteration for Dimensionality Reduction in ICA
Independent Component Analysis and Blind Signal Separation, 2004Co-Authors: Lieven De Lathauwer, L Hoegaerts, Joos VandewalleAbstract:We derive a Grassmann-Rayleigh Quotient Iteration for the computation of the best rank-(R1, R2, R3) approximation of higher-order tensors. We present some variants that allow for a very efficient estimation of the signal subspace in ICA schemes without prewhitening.
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a grassmann Rayleigh Quotient iteration for dimensionality reduction in ica
International Conference on Independent Component Analysis and Signal Separation, 2004Co-Authors: Lieven De Lathauwer, L Hoegaerts, Joos VandewalleAbstract:We derive a Grassmann-Rayleigh Quotient Iteration for the computation of the best rank-(R1, R2, R3) approximation of higher-order tensors. We present some variants that allow for a very efficient estimation of the signal subspace in ICA schemes without prewhitening.
Chingiz Hajiyev - One of the best experts on this subject based on the ideXlab platform.
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Generalized Rayleigh Quotient based innovation covariance testing applied to sensor/actuator fault detection
Measurement, 2014Co-Authors: Chingiz HajiyevAbstract:Abstract A new approach based on the generalized Rayleigh Quotient for testing the innovation covariance of the Kalman filter is proposed. The optimization process of testing quality is reduced to the classical problem of maximization of the generalized Rayleigh Quotient. In the simulations, the longitudinal and lateral dynamics of the F-16 aircraft model are considered, and the detection procedure of sensor/actuator faults, which affect the innovation covariance, is examined. Comparison of the proposed generalized Rayleigh Quotients based algorithms for testing the innovation covariance is performed in the sense of the fastest detection of a fault and the detected minimum fault rate. Some recommendations for the fastest detection of the fault are given.
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generalized Rayleigh Quotient based innovation covariance testing applied to sensor actuator fault detection
Measurement, 2014Co-Authors: Chingiz HajiyevAbstract:Abstract A new approach based on the generalized Rayleigh Quotient for testing the innovation covariance of the Kalman filter is proposed. The optimization process of testing quality is reduced to the classical problem of maximization of the generalized Rayleigh Quotient. In the simulations, the longitudinal and lateral dynamics of the F-16 aircraft model are considered, and the detection procedure of sensor/actuator faults, which affect the innovation covariance, is examined. Comparison of the proposed generalized Rayleigh Quotients based algorithms for testing the innovation covariance is performed in the sense of the fastest detection of a fault and the detected minimum fault rate. Some recommendations for the fastest detection of the fault are given.
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Generalized Rayleigh Quotient Based Sensor/actuator Fault Detection
IFAC Proceedings Volumes, 2012Co-Authors: Chingiz HajiyevAbstract:Abstract A new approach based on the generalized Rayleigh Quotient for testing the innovation covariance of the Kalman filter is proposed. The optimization process of testing quality is reduced to the classical problem of maximization of the generalized Rayleigh Quotient. The proposed fault detection algorithm is reduced to the comparison of the generalized Rayleigh Quotient, which is calculated using representative sample and found Quotient's bounds, and making a decision on the basis of the presented decision rule. In the simulations, the longitudinal and lateral dynamics of the F-16 aircraft model are considered, and the detection procedure of sensor/actuator faults, which affect the innovation covariance, is examined.
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generalized Rayleigh Quotient based sensor actuator fault detection
IFAC Proceedings Volumes, 2012Co-Authors: Chingiz HajiyevAbstract:Abstract A new approach based on the generalized Rayleigh Quotient for testing the innovation covariance of the Kalman filter is proposed. The optimization process of testing quality is reduced to the classical problem of maximization of the generalized Rayleigh Quotient. The proposed fault detection algorithm is reduced to the comparison of the generalized Rayleigh Quotient, which is calculated using representative sample and found Quotient's bounds, and making a decision on the basis of the presented decision rule. In the simulations, the longitudinal and lateral dynamics of the F-16 aircraft model are considered, and the detection procedure of sensor/actuator faults, which affect the innovation covariance, is examined.
Pierre-antoine Absil - One of the best experts on this subject based on the ideXlab platform.
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Two-sided Grassmann-Rayleigh Quotient iteration
Numerische Mathematik, 2009Co-Authors: Pierre-antoine Absil, P. Van DoorenAbstract:The two-sided Rayleigh Quotient iteration proposed by Ostrowski computes a pair of corresponding left-right eigenvectors of a matrix $C$. We propose a Grassmannian version of this iteration, i.e., its iterates are pairs of $p$-dimensional subspaces instead of one-dimensional subspaces in the classical case. The new iteration generically converges locally cubically to the pairs of left-right $p$-dimensional invariant subspaces of $C$. Moreover, Grassmannian versions of the Rayleigh Quotient iteration are given for the generalized Hermitian eigenproblem, the Hamiltonian eigenproblem and the skew-Hamiltonian eigenproblem.
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A Grassmann-Rayleigh Quotient Iteration for
2002Co-Authors: Pierre-antoine Absil, Robert Mahony, Rodolphe Sepulchre, P. Van DoorenAbstract:The classical Rayleigh Quotient iteration (RQI) allows one to compute a one-dimensional invariant subspace of a symmetric matrix A. Here we propose a generalization of the RQI which computes a p-dimensional invariant subspace of A. Cubic convergence is preserved and the cost per iteration is low compared to other methods proposed in the literature.
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A Grassmann--Rayleigh Quotient Iteration for Computing Invariant Subspaces
SIAM Review, 2002Co-Authors: Pierre-antoine Absil, Robert Mahony, Rodolphe Sepulchre, P. Van DoorenAbstract:The classical Rayleigh Quotient iteration (RQI) allows one to compute a one-dimensional invariant subspace of a symmetric matrix A. Here we propose a generalization of the RQI which computes a p-dimensional invariant subspace of A. Cubic convergence is preserved and the cost per iteration is low compared to other methods proposed in the literature.
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A Grassmann-Rayleigh Quotient iteration for computing invariant subspaces
Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187), 1Co-Authors: Pierre-antoine Absil, Robert Mahony, Rodolphe Sepulchre, P. Van DoorenAbstract:The classical Rayleigh Quotient iteration (RQI) computes a 1-dimensional invariant subspace of a symmetric matrix A with cubic convergence. We propose a generalization of the RQI which computes a p-dimensional invariant subspace of A. The geometry of the algorithm on the Grassmann manifold Gr(p,n) is developed to show cubic convergence and to draw connections with Newton algorithms on Riemannian manifolds.
