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Block Jacobi-type methods for non-orthogonal joint diagonalisation

2009

Conference Paper

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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.

Author(s): Shen, H. and Hüper, K.
Book Title: ICASSP09
Journal: Proceedings of the 34th International Conference on Acoustics, Speech, and Signal Processing (ICASSP09)
Pages: 3285-3288
Year: 2009
Month: April
Day: 0
Publisher: IEEE Service Center

Department(s): Empirical Inference
Bibtex Type: Conference Paper (inproceedings)

DOI: 10.1109/ICASSP.2009.4960326
Event Name: 34th International Conference on Acoustics, Speech, and Signal Processing
Event Place: Taipei, Taiwan

Address: Piscataway, NJ, USA
Digital: 0
Institution: Institute of Electrical and Electronics Engineers
Language: en
Organization: Max-Planck-Gesellschaft
School: Biologische Kybernetik

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BibTex

@inproceedings{5632,
  title = {Block Jacobi-type methods for non-orthogonal joint diagonalisation},
  author = {Shen, H. and H{\"u}per, K.},
  journal = {Proceedings of the 34th International Conference on Acoustics, Speech, and Signal Processing (ICASSP09)},
  booktitle = {ICASSP09},
  pages = {3285-3288},
  publisher = {IEEE Service Center},
  organization = {Max-Planck-Gesellschaft},
  institution = {Institute of Electrical and Electronics Engineers},
  school = {Biologische Kybernetik},
  address = {Piscataway, NJ, USA},
  month = apr,
  year = {2009},
  month_numeric = {4}
}