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Nonorthogonal approximate joint diagonalization with well-conditioned diagonalizers

Zhou, Guoxu, Xie, Shengli, Yang, Zuyuan and Zhang, Jun 2009, Nonorthogonal approximate joint diagonalization with well-conditioned diagonalizers, IEEE Transactions on neural networks, vol. 20, no. 11, pp. 1810-1819, doi: 10.1109/TNN.2009.2030586.

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Title Nonorthogonal approximate joint diagonalization with well-conditioned diagonalizers
Author(s) Zhou, Guoxu
Xie, Shengli
Yang, Zuyuan
Zhang, Jun
Journal name IEEE Transactions on neural networks
Volume number 20
Issue number 11
Start page 1810
End page 1819
Total pages 10
Publisher IEEE
Place of publication Piscataway, N. J.
Publication date 2009
ISSN 1045-9227
1941-0093
Summary To make the results reasonable, existing joint diagonalization algorithms have imposed a variety of constraints on diagonalizers. Actually, those constraints can be imposed uniformly by minimizing the condition number of diagonalizers. Motivated by this, the approximate joint diagonalization problem is reviewed as a multiobjective optimization problem for the first time. Based on this, a new algorithm for nonorthogonal joint diagonalization is developed. The new algorithm yields diagonalizers which not only minimize the diagonalization error but also have as small condition numbers as possible. Meanwhile, degenerate solutions are avoided strictly. Besides, the new algorithm imposes few restrictions on the target set of matrices to be diagonalized, which makes it widely applicable. Primary results on convergence are presented and we also show that, for exactly jointly diagonalizable sets, no local minima exist and the solutions are unique under mild conditions. Extensive numerical simulations illustrate the performance of the algorithm and provide comparison with other leading diagonalization methods. The practical use of our algorithm is shown for blind source separation (BSS) problems, especially when ill-conditioned mixing matrices are involved.
Language eng
DOI 10.1109/TNN.2009.2030586
Field of Research 080109 Pattern Recognition and Data Mining
Socio Economic Objective 890205 Information Processing Services (incl. Data Entry and Capture)
HERDC Research category C1.1 Refereed article in a scholarly journal
Copyright notice ©2009, IEEE
Persistent URL http://hdl.handle.net/10536/DRO/DU:30059308

Document type: Journal Article
Collections: School of Information Technology
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Every reasonable effort has been made to ensure that permission has been obtained for items included in DRO. If you believe that your rights have been infringed by this repository, please contact drosupport@deakin.edu.au.