Approximate joint diagonalization using a natural gradient approach

Arie Yeredor; Andreas Ziehe; Klaus Robert Müller

doi:10.1007/978-3-540-30110-3_12

Approximate joint diagonalization using a natural gradient approach

Arie Yeredor, Andreas Ziehe, Klaus Robert Müller

School of Electrical Engineering

Fraunhofer FIRST

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

40 Scopus citations

Abstract

We present a new algorithm for non-unitary approximate joint diagonalization (AJD), based on a "natural gradient"-type multiplicative update of the diagonalizing matrix, complemented by step-size optimization at each iteration. The advantages of the new algorithm over existing non-unitary AJD algorithms are in the ability to accommodate non-positive-definite matrices (compared to Pham's algorithm), in the low computational load per iteration (compared to Yeredor's AC-DC algorithm), and in the theoretically guaranteed convergence to a true (possibly local) minimum (compared to Ziehe et al.'s FFDiag algorithm).

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	89-96
Number of pages	8
ISBN (Electronic)	3540230564, 9783540230564
DOIs	https://doi.org/10.1007/978-3-540-30110-3_12
State	Published - 2004

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

Access to Document

10.1007/978-3-540-30110-3_12

Cite this

Yeredor, A., Ziehe, A., & Müller, K. R. (2004). Approximate joint diagonalization using a natural gradient approach. 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. 89-96). (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_12

Yeredor, Arie ; Ziehe, Andreas ; Müller, Klaus Robert. / Approximate joint diagonalization using a natural gradient approach. 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. 89-96 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

@inbook{71fa1b1a49d8483e99ae789ba72238d5,

title = "Approximate joint diagonalization using a natural gradient approach",

abstract = "We present a new algorithm for non-unitary approximate joint diagonalization (AJD), based on a {"}natural gradient{"}-type multiplicative update of the diagonalizing matrix, complemented by step-size optimization at each iteration. The advantages of the new algorithm over existing non-unitary AJD algorithms are in the ability to accommodate non-positive-definite matrices (compared to Pham's algorithm), in the low computational load per iteration (compared to Yeredor's AC-DC algorithm), and in the theoretically guaranteed convergence to a true (possibly local) minimum (compared to Ziehe et al.'s FFDiag algorithm).",

author = "Arie Yeredor and Andreas Ziehe and M{\"u}ller, {Klaus Robert}",

year = "2004",

doi = "10.1007/978-3-540-30110-3_12",

language = "אנגלית",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer Verlag",

pages = "89--96",

editor = "Puntonet, {Carlos G.} and Alberto Prieto",

booktitle = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

}

Yeredor, A, Ziehe, A & Müller, KR 2004, Approximate joint diagonalization using a natural gradient approach. 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. 89-96. https://doi.org/10.1007/978-3-540-30110-3_12

Approximate joint diagonalization using a natural gradient approach. / Yeredor, Arie; Ziehe, Andreas; Müller, Klaus Robert.
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. 89-96 (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

TY - CHAP

T1 - Approximate joint diagonalization using a natural gradient approach

AU - Yeredor, Arie

AU - Ziehe, Andreas

AU - Müller, Klaus Robert

PY - 2004

Y1 - 2004

N2 - We present a new algorithm for non-unitary approximate joint diagonalization (AJD), based on a "natural gradient"-type multiplicative update of the diagonalizing matrix, complemented by step-size optimization at each iteration. The advantages of the new algorithm over existing non-unitary AJD algorithms are in the ability to accommodate non-positive-definite matrices (compared to Pham's algorithm), in the low computational load per iteration (compared to Yeredor's AC-DC algorithm), and in the theoretically guaranteed convergence to a true (possibly local) minimum (compared to Ziehe et al.'s FFDiag algorithm).

AB - We present a new algorithm for non-unitary approximate joint diagonalization (AJD), based on a "natural gradient"-type multiplicative update of the diagonalizing matrix, complemented by step-size optimization at each iteration. The advantages of the new algorithm over existing non-unitary AJD algorithms are in the ability to accommodate non-positive-definite matrices (compared to Pham's algorithm), in the low computational load per iteration (compared to Yeredor's AC-DC algorithm), and in the theoretically guaranteed convergence to a true (possibly local) minimum (compared to Ziehe et al.'s FFDiag algorithm).

UR - http://www.scopus.com/inward/record.url?scp=35048855087&partnerID=8YFLogxK

U2 - 10.1007/978-3-540-30110-3_12

DO - 10.1007/978-3-540-30110-3_12

M3 - ???researchoutput.researchoutputtypes.contributiontobookanthology.chapter???

AN - SCOPUS:35048855087

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 89

EP - 96

BT - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

A2 - Puntonet, Carlos G.

A2 - Prieto, Alberto

PB - Springer Verlag

ER -

Yeredor A, Ziehe A, Müller KR. Approximate joint diagonalization using a natural gradient approach. 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. 89-96. (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_12

Approximate joint diagonalization using a natural gradient approach

Abstract

Publication series

Access to Document

Other files and links

Fingerprint

Cite this