Title: Joint diagonalisation via weighted generalised eigenvalue decomposition

Authors: Jun Liu, Jingli Li

Addresses: LinkQuest Inc., San Diego, CA 92121, USA. ' TopWorx, Louisville, KY 40213, USA

Abstract: In this correspondence, we propose a new approach for joint diagonalisation of multiple matrices. The proposed algorithm performs generalised eigenvalue decomposition (GEVD) of two weighted matrices, and then optimises the weighting factors so that an upper bound of the mean square error (MSE) of the estimates of the mixing matrix is minimised. The proposed scheme can solve the potential problem in the initialisation step of several existing joint diagonalisation algorithms in the presence of repeated eigenvalues. The simulation results indicate that weighted diagonalisation offers competitive performance for joint diagonalisation.

Keywords: joint diagonalisation; generalised eigenvalue decomposition; GEVD; mean square error; MSE; weighted diagonalisation; optimiseation; weighting factors; simulation.

DOI: 10.1504/IJITCC.2011.042128

International Journal of Information Technology, Communications and Convergence, 2011 Vol.1 No.3, pp.318 - 330

Received: 08 May 2021
Accepted: 12 May 2021

Published online: 28 Aug 2011 *

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