On computation of approximate joint block-diagonalization using ordinary AJD

Authors:
Petr Tichavský;Arie Yeredor;Zbyněk Koldovský
Affiliations:
Institute of Information Theory and Automation, Praha 8, Czech Republic;Dept. of Electrical Engineering - Systems, School of Electrical Engineering, Tel-Aviv University, Tel-Aviv, Israel;Institute of Information Theory and Automation, Praha 8, Czech Republic
Venue:
LVA/ICA'12 Proceedings of the 10th international conference on Latent Variable Analysis and Signal Separation
Year:
2012

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Abstract

Approximate joint block diagonalization (AJBD) of a set of matrices has applications in blind source separation, e.g., when the signal mixtures contain mutually independent subspaces of dimension higher than one. The main message of this paper is that certain ordinary approximate joint diagonalization (AJD) methods (which were originally derived for "degenerate" subspaces of dimension 1) can also be used successfully for AJBD, but not all are suitable equally well. In particular, we prove that when the set is exactly jointly block-diagonalizable, perfect block-diagonalization is attainable by the recently proposed AJD algorithm "U-WEDGE" (uniformly weighted exhaustive diagonalization with Gaussian iteration) - but this basic consistency property is not shared by some other popular AJD algorithms. In addition, we show using simulation, that in the more general noisy case, the subspace identification accuracy of U-WEDGE compares favorably to competitors.