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.
This work was supported by Ministry of Education, Youth and Sports of the Czech Republic through the project 1M0572 and by Grant Agency of the Czech Republic through the project 102/09/1278.
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Tichavský, P., Yeredor, A., Koldovský, Z. (2012). On Computation of Approximate Joint Block-Diagonalization Using Ordinary AJD. In: Theis, F., Cichocki, A., Yeredor, A., Zibulevsky, M. (eds) Latent Variable Analysis and Signal Separation. LVA/ICA 2012. Lecture Notes in Computer Science, vol 7191. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28551-6_21
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DOI: https://doi.org/10.1007/978-3-642-28551-6_21
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