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

Andreas Ziehe, Pavel Laskov, Guido Nolte, Klaus Muller

Research output: Contribution to journalArticle

194 Citations (Scopus)

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. The practical use of our algorithm is shown for blind source separation problems.

Original languageEnglish
Pages (from-to)777-800
Number of pages24
JournalJournal of Machine Learning Research
Volume5
Publication statusPublished - 2004 Jul 1
Externally publishedYes

Fingerprint

Blind source separation
Blind Source Separation
Diagonalization
Fast Algorithm
Update
Quasi-Newton
Frobenius norm
Invertibility
Iterative Scheme
Cost Function
Multiplicative
Cost functions
Efficient Algorithms
Numerical Simulation
Formulation
Alternatives
Approximation
Computer simulation
Demonstrate

Keywords

  • Blind source separation
  • Common principle component analysis
  • Independent component analysis
  • Joint diagonalization
  • Levenberg-marquardt algorithm
  • Newton method
  • Nonlinear least squares

ASJC Scopus subject areas

  • Artificial Intelligence
  • Software
  • Control and Systems Engineering
  • Statistics and Probability

Cite this

A fast algorithm for joint diagonalization with non-orthogonal transformations and its application to blind source separation. / Ziehe, Andreas; Laskov, Pavel; Nolte, Guido; Muller, Klaus.

In: Journal of Machine Learning Research, Vol. 5, 01.07.2004, p. 777-800.

Research output: Contribution to journalArticle

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