An algebraic method for approximate rank one factorization of rank deficient matrices

Franz J. Király; Andreas Ziehe; Klaus Robert Müller

doi:10.1007/978-3-642-28551-6_34

An algebraic method for approximate rank one factorization of rank deficient matrices

Franz J. Király, Andreas Ziehe, Klaus Robert Müller

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

1 Citation (Scopus)

Abstract

In this paper we consider the problem of finding approximate common rank one factors for a set of matrices. Instead of jointly diagonalizing the matrices, we perform calculations directly in the problem intrinsic domain: we present an algorithm, AROFAC, which searches the approximate linear span of the matrices using an indicator function for the rank one factors, finding specific single sources. We evaluate the feasibility of this approach by discussing simulations on generated data and a neurophysiological dataset. Note however that our contribution is intended to be mainly conceptual in nature.

Original language	English
Title of host publication	Latent Variable Analysis and Signal Separation - 10th International Conference, LVA/ICA 2012, Proceedings
Pages	272-279
Number of pages	8
DOIs	https://doi.org/10.1007/978-3-642-28551-6_34
Publication status	Published - 2012
Externally published	Yes
Event	10th International Conference on Latent Variable Analysis and Signal Separation, LVA/ICA 2012 - Tel Aviv, Israel Duration: 2012 Mar 12 → 2012 Mar 15

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	7191 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Other

Other	10th International Conference on Latent Variable Analysis and Signal Separation, LVA/ICA 2012
Country/Territory	Israel
City	Tel Aviv
Period	12/3/12 → 12/3/15

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

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10.1007/978-3-642-28551-6_34

Cite this

Király, F. J., Ziehe, A., & Müller, K. R. (2012). An algebraic method for approximate rank one factorization of rank deficient matrices. In Latent Variable Analysis and Signal Separation - 10th International Conference, LVA/ICA 2012, Proceedings (pp. 272-279). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7191 LNCS). https://doi.org/10.1007/978-3-642-28551-6_34

An algebraic method for approximate rank one factorization of rank deficient matrices. / Király, Franz J.; Ziehe, Andreas; Müller, Klaus Robert.
Latent Variable Analysis and Signal Separation - 10th International Conference, LVA/ICA 2012, Proceedings. 2012. p. 272-279 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7191 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Király, FJ, Ziehe, A & Müller, KR 2012, An algebraic method for approximate rank one factorization of rank deficient matrices. in Latent Variable Analysis and Signal Separation - 10th International Conference, LVA/ICA 2012, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 7191 LNCS, pp. 272-279, 10th International Conference on Latent Variable Analysis and Signal Separation, LVA/ICA 2012, Tel Aviv, Israel, 12/3/12. https://doi.org/10.1007/978-3-642-28551-6_34

Király FJ, Ziehe A, Müller KR. An algebraic method for approximate rank one factorization of rank deficient matrices. In Latent Variable Analysis and Signal Separation - 10th International Conference, LVA/ICA 2012, Proceedings. 2012. p. 272-279. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-642-28551-6_34

Király, Franz J. ; Ziehe, Andreas ; Müller, Klaus Robert. / An algebraic method for approximate rank one factorization of rank deficient matrices. Latent Variable Analysis and Signal Separation - 10th International Conference, LVA/ICA 2012, Proceedings. 2012. pp. 272-279 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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An algebraic method for approximate rank one factorization of rank deficient matrices

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