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

Franz J. Király, Andreas Ziehe, Klaus Muller

Research output: Chapter in Book/Report/Conference proceedingConference 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 languageEnglish
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Pages272-279
Number of pages8
Volume7191 LNCS
DOIs
Publication statusPublished - 2012 Feb 27
Externally publishedYes
Event10th International Conference on Latent Variable Analysis and Signal Separation, LVA/ICA 2012 - Tel Aviv, Israel
Duration: 2012 Mar 122012 Mar 15

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume7191 LNCS
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other10th International Conference on Latent Variable Analysis and Signal Separation, LVA/ICA 2012
CountryIsrael
CityTel Aviv
Period12/3/1212/3/15

Fingerprint

Algebraic Methods
Factorization
Indicator function
Evaluate
Simulation

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

Cite this

Király, F. J., Ziehe, A., & Muller, K. (2012). An algebraic method for approximate rank one factorization of rank deficient matrices. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 7191 LNCS, 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; Muller, Klaus.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 7191 LNCS 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 proceedingConference contribution

Király, FJ, Ziehe, A & Muller, K 2012, An algebraic method for approximate rank one factorization of rank deficient matrices. in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). vol. 7191 LNCS, 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, Muller K. An algebraic method for approximate rank one factorization of rank deficient matrices. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 7191 LNCS. 2012. p. 272-279. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-642-28551-6_34
Király, Franz J. ; Ziehe, Andreas ; Muller, Klaus. / An algebraic method for approximate rank one factorization of rank deficient matrices. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 7191 LNCS 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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