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A fast algorithm for joint diagonalization with non-orthogonal transformations and its application to blind source separation

: Ziehe, A.; Laskov, P.; Nolte, G.; Müller, K.-R.

Journal of Machine Learning Research 5 (2004), No.1, pp.777-800
ISSN: 1533-7928
ISSN: 1532-4435
Journal Article
Fraunhofer FIRST ()

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.