Search

Your search keyword '"Belouchrani, Adel"' showing total 2 results
Start Over Author "Belouchrani, Adel" Topic algorithms Topic covariance matrices
2 results on '"Belouchrani, Adel"'

1. A New Algorithm for Complex Non-Orthogonal Joint Diagonalization Based on Shear and Givens Rotations.

Author

Mesloub, Ammar, Abed-Meraim, Karim, and Belouchrani, Adel

Subjects
ALGORITHMS, ORTHOGONAL systems, MATRICES (Mathematics), COMPARATIVE studies, SHEAR (Mechanics)
Abstract

This paper introduces a new algorithm to approximate non-orthogonal joint diagonalization (NOJD) of a set of complex matrices. This algorithm is based on the Frobenius norm formulation of the joint diagonalization (JD) problem and takes advantage from combining Givens and Shear rotations to attempt the approximate JD. It represents a non-trivial generalization of the JDi (Joint Diagonalization) algorithm (Souloumiac 2009) to the complex case. The JDi is first slightly modified then generalized to the CJDi (i.e., Complex JDi) using complex to real matrix transformation. Several methods already exist in the literature. Consequently, we provide herein a brief overview of existing NOJD algorithms. Then we provide an extensive comparative study to illustrate the effectiveness and stability of the CJDi with respect to various system parameters and application contexts. [ABSTRACT FROM AUTHOR]

Published
2014
Full Text
View/download PDF

2. Low complexity adaptive algorithms for Principal and Minor Component Analysis

Author

Thameri, Messaoud, Abed-Meraim, Karim, and Belouchrani, Adel

Subjects
*PRINCIPAL components analysis, *ALGORITHMS, *ESTIMATION theory, *COVARIANCE matrices, *DATA transmission systems, *SIGNAL processing
Abstract

Abstract: This article introduces new low cost algorithms for the adaptive estimation and tracking of principal and minor components. The proposed algorithms are based on the well-known OPAST method which is adapted and extended in order to achieve the desired MCA or PCA (Minor or Principal Component Analysis). For the PCA case, we propose efficient solutions using Givens rotations to estimate the principal components out of the weight matrix given by OPAST method. These solutions are then extended to the MCA case by using a transformed data covariance matrix in such a way the desired minor components are obtained from the PCA of the new (transformed) matrix. Finally, as a byproduct of our PCA algorithm, we propose a fast adaptive algorithm for data whitening that is shown to overcome the recently proposed RLS-based whitening method. [Copyright &y& Elsevier]

Published
2013
Full Text
View/download PDF

Catalog

Books, media, physical & digital resources
See catalog results