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Block Jacobi-type methods for non-orthogonal joint diagonalisation

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Shen,  H
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;

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Hüper,  K
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;

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Citation

Shen, H., & Hüper, K. (2009). Block Jacobi-type methods for non-orthogonal joint diagonalisation. Proceedings of the 34th International Conference on Acoustics, Speech, and Signal Processing (ICASSP09), 3285-3288.


Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-C53D-A
Abstract
In this paper, we study the problem of non-orthogonal joint diagonalisation of a set of real symmetric matrices via simultaneous conjugation. A family of block Jacobi-type methods are proposed to optimise two popular cost functions for the non-orthogonal joint diagonalisation, namely, the off-norm function and the log-likelihood function. By exploiting the appropriate underlying manifold, namely the so-called oblique manifold, rigorous analysis shows that, under the exact non-orthogonal joint diagonalisation setting, the proposed methods converge locally quadratically fast to a joint diagonaliser. Finally, performance of our methods is investigated by numerical experiments for both exact and approximate non-orthogonal joint diagonalisation.