Postnonlinear overcomplete blind source separation using sparse sources

Fabian J. Theis; Shun Ichi Amari

doi:10.1007/978-3-540-30110-3_91

Postnonlinear overcomplete blind source separation using sparse sources

Fabian J. Theis, Shun Ichi Amari

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

9 Scopus citations

Abstract

We present an approach for blindly decomposing an observed random vector x into f(As) where f is a diagonal function i.e. f = f₁× ... × f_m with one-dimensional functions f_i and A an m × n matrix. This postnonlinear model is allowed to be overcomplete, which means that less observations than sources (m < n) are given. In contrast to Independent Component Analysis (ICA) we do not assume the sources s to be independent but to be sparse in the sense that at each time instant they have at most m -1 non-zero components (Sparse Component Analysis or SCA). Identifiability of the model is shown, and an algorithm for model and source recovery is proposed. It first detects the postnonlinearities in each component, and then identifies the now linearized model using previous results.

Original language	English
Title of host publication	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Editors	Carlos G. Puntonet, Alberto Prieto
Publisher	Springer Verlag
Pages	718-725
Number of pages	8
ISBN (Electronic)	3540230564, 9783540230564
DOIs	https://doi.org/10.1007/978-3-540-30110-3_91
State	Published - 2004
Externally published	Yes

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	3195
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

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10.1007/978-3-540-30110-3_91

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Theis, F. J., & Amari, S. I. (2004). Postnonlinear overcomplete blind source separation using sparse sources. In C. G. Puntonet, & A. Prieto (Eds.), Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (pp. 718-725). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 3195). Springer Verlag. https://doi.org/10.1007/978-3-540-30110-3_91

Theis, Fabian J. ; Amari, Shun Ichi. / Postnonlinear overcomplete blind source separation using sparse sources. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). editor / Carlos G. Puntonet ; Alberto Prieto. Springer Verlag, 2004. pp. 718-725 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "We present an approach for blindly decomposing an observed random vector x into f(As) where f is a diagonal function i.e. f = f1× ... × fm with one-dimensional functions fi and A an m × n matrix. This postnonlinear model is allowed to be overcomplete, which means that less observations than sources (m < n) are given. In contrast to Independent Component Analysis (ICA) we do not assume the sources s to be independent but to be sparse in the sense that at each time instant they have at most m -1 non-zero components (Sparse Component Analysis or SCA). Identifiability of the model is shown, and an algorithm for model and source recovery is proposed. It first detects the postnonlinearities in each component, and then identifies the now linearized model using previous results.",

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year = "2004",

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Theis, FJ & Amari, SI 2004, Postnonlinear overcomplete blind source separation using sparse sources. in CG Puntonet & A Prieto (eds), Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 3195, Springer Verlag, pp. 718-725. https://doi.org/10.1007/978-3-540-30110-3_91

Postnonlinear overcomplete blind source separation using sparse sources. / Theis, Fabian J.; Amari, Shun Ichi.
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). ed. / Carlos G. Puntonet; Alberto Prieto. Springer Verlag, 2004. p. 718-725 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 3195).

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

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Theis FJ, Amari SI. Postnonlinear overcomplete blind source separation using sparse sources. In Puntonet CG, Prieto A, editors, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Springer Verlag. 2004. p. 718-725. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-540-30110-3_91

Postnonlinear overcomplete blind source separation using sparse sources

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