Joint Block-Diagonalization

Joint Block-Diagonalization deals with the problem of finding a (here orthogonal/hermitian) basis in which a set of linear transformations is block-diagonal. It thereby extends classical diagonalization and block-diagonalization problems to the case of multiple matrices. This plays an important role in applications to blind source separation or blind deconvolution for example. For more details, please refer to our manuscript. MATLAB-implementations of the algorithms as well as the tests for block-diagonalizability are included.

References

  • The Jacobi-based algorithm is proposed in C. Févotte, F.J. Theis: Orthonormal approximate joint block- diagonalization. Technical Report GET/Télécom Paris 2007D007 (2007)
  • For joint diagonalization, the proposed algorithm uses Cardoso's diagonalization algorithm based on iterative Given's rotations, see J.-F. Cardoso and A. Souloumiac, 'Jacobi angles for simultaneous diagonalization',SIAM J. Mat. Anal. Appl., vol 17(1), pp. 161-164, 1995.
example usage of JBD

Downloads

  • download JBD code (zipped Matlab files including documentation via 'help filename' and examples)
  • tech report with details about the algorithm

If we knew what we were doing,
it wouldn't be called research, would it?
Albert Einstein (1879-1955)

Theoretical and applied signal processing to enhance the understanding of neurophysical and biomedical data sets.

Fabian Theis
Bernstein Center for Computational Neuroscience
MPI for Dynamics and Self-Organisation
Bunsenstr. 10
37073 Göttingen
Germany
Tel: +49 551 5176 418
Fax: +49 551 5176 439

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