A Fast Algorithm for Joint Diagonalization with Non-orthogonal Transformations and its Application to Blind Source Separation

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A Fast Algorithm for Joint Diagonalization with Non-orthogonal Transformations and its Application to Blind Source Separation (2004)

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by Andreas Ziehe , Pavel Laskov , Guido Nolte , Klaus-Robert Müller

Venue:	JOURNAL OF MACHINE LEARNING RESEARCH
Citations:	45 - 5 self

BibTeX

@ARTICLE{Ziehe04afast,
    author = {Andreas Ziehe and Pavel Laskov and Guido Nolte and Klaus-Robert Müller},
    title = {A Fast Algorithm for Joint Diagonalization with Non-orthogonal Transformations and its Application to Blind Source Separation},
    journal = {JOURNAL OF MACHINE LEARNING RESEARCH},
    year = {2004},
    volume = {5},
    pages = {801--818}
}

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Abstract

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.

Keyphrases

non-orthogonal transformation joint diagonalization fast algorithm blind source separation multiplicative update diagonalization method special approximation extensive numerical simulation several matrix block-diagonal hessian new efficient algorithm frobenius-norm formulation viable alternative joint diagonalization problem iterative scheme cost function quasi-newton update step comparison demonstrate state-of-the-art joint diagonalization algorithm

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