A fast algorithm for joint diagonalization with non-orthogonal transformations and its application to blind source separation
- A new efficient algorithm is presented for joint diagonalization of several matrices. The algorithm is based on the Frobenius-norm formulation of the joint diagonalization problem, and addresses diagonalization with a general, non- orthogonal transformation. The iterative scheme of the algorithm is based on a multiplicative update which ensures the invertibility of the diagonalizer. The algorithm's efficiency stems from the special approximation of the cost function resulting in a sparse, block-diagonal Hessian to be used in the computation of the quasi-Newton update step. Extensive numerical simulations illustrate the performance of the algorithm and provide a comparison to other leading diagonalization methods. The results of such comparison demonstrate that the proposed algorithm is a viable alternative to existing state-of-the-art joint diagonalization algorithms. The practical use of our algorithm is shown for blind source separation problems
Author details: | Andreas Ziehe, Pavel LaskovGND, G Nolte, Klaus-Robert Müller |
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Publication type: | Article |
Language: | English |
Year of first publication: | 2004 |
Publication year: | 2004 |
Release date: | 2017/03/24 |
Source: | Journal of machine learning research. - 5 (2004), S. 777 - 800 |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
Peer review: | Referiert |