Building nonlinear data models with self-organizing maps

Ralf Der; Gerd Balzuweit; Michael Herrmann

doi:10.1007/3-540-61510-5_138

Building nonlinear data models with self-organizing maps

Ralf Der, Gerd Balzuweit, Michael Herrmann

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

Abstract / Description of output

We study the extraction of nonlinear data models in high dimensional spaces with modified self-organizing maps. Our algorithm maps lower dimensional lattice into a high dimensional space without topology violations by tuning the neighborhood widths locally. The approach is based on a new principle exploiting the specific dynamical properties of the first order phase transition induced by the noise of the data. The performance of the algorithm is demonstrated for one- and two-dimensional principal manifolds and for sparse data sets.

Original language	English
Title of host publication	Artificial Neural Networks — ICANN 96
Subtitle of host publication	1996 International Conference Bochum, Germany, July 16–19, 1996 Proceedings
Editors	Christoph Malsburg, Werner Seelen, Jan C. Vorbrüggen, Bernhard Sendhoff
Place of Publication	Berlin, Heidelberg
Publisher	Springer
Pages	821-826
Number of pages	6
ISBN (Electronic)	978-3-540-68684-2
ISBN (Print)	978-3-540-61510-1
DOIs	https://doi.org/10.1007/3-540-61510-5_138
Publication status	Published - 1996

Publication series

Name	Lecture Notes in Computer Science
Publisher	Springer Berlin Heidelberg
Volume	1112
ISSN (Print)	0302-9743

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10.1007/3-540-61510-5_138

http://link.springer.com/chapter/10.1007%2F3-540-61510-5_138

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Der, R., Balzuweit, G., & Herrmann, M. (1996). Building nonlinear data models with self-organizing maps. In C. Malsburg, W. Seelen, J. C. Vorbrüggen, & B. Sendhoff (Eds.), Artificial Neural Networks — ICANN 96: 1996 International Conference Bochum, Germany, July 16–19, 1996 Proceedings (pp. 821-826). (Lecture Notes in Computer Science; Vol. 1112). Springer. https://doi.org/10.1007/3-540-61510-5_138

Der, Ralf ; Balzuweit, Gerd ; Herrmann, Michael. / Building nonlinear data models with self-organizing maps. Artificial Neural Networks — ICANN 96: 1996 International Conference Bochum, Germany, July 16–19, 1996 Proceedings. editor / Christoph Malsburg ; Werner Seelen ; Jan C. Vorbrüggen ; Bernhard Sendhoff. Berlin, Heidelberg : Springer, 1996. pp. 821-826 (Lecture Notes in Computer Science).

@inproceedings{6af2dd2746d34df29d8151ed8ab20c00,

title = "Building nonlinear data models with self-organizing maps",

abstract = "We study the extraction of nonlinear data models in high dimensional spaces with modified self-organizing maps. Our algorithm maps lower dimensional lattice into a high dimensional space without topology violations by tuning the neighborhood widths locally. The approach is based on a new principle exploiting the specific dynamical properties of the first order phase transition induced by the noise of the data. The performance of the algorithm is demonstrated for one- and two-dimensional principal manifolds and for sparse data sets.",

author = "Ralf Der and Gerd Balzuweit and Michael Herrmann",

year = "1996",

doi = "10.1007/3-540-61510-5_138",

language = "English",

isbn = "978-3-540-61510-1",

series = "Lecture Notes in Computer Science",

publisher = "Springer",

pages = "821--826",

editor = "Christoph Malsburg and Werner Seelen and Vorbr{\"u}ggen, {Jan C.} and Bernhard Sendhoff",

booktitle = "Artificial Neural Networks — ICANN 96",

address = "United Kingdom",

}

Der, R, Balzuweit, G & Herrmann, M 1996, Building nonlinear data models with self-organizing maps. in C Malsburg, W Seelen, JC Vorbrüggen & B Sendhoff (eds), Artificial Neural Networks — ICANN 96: 1996 International Conference Bochum, Germany, July 16–19, 1996 Proceedings. Lecture Notes in Computer Science, vol. 1112, Springer, Berlin, Heidelberg, pp. 821-826. https://doi.org/10.1007/3-540-61510-5_138

Building nonlinear data models with self-organizing maps. / Der, Ralf; Balzuweit, Gerd; Herrmann, Michael.
Artificial Neural Networks — ICANN 96: 1996 International Conference Bochum, Germany, July 16–19, 1996 Proceedings. ed. / Christoph Malsburg; Werner Seelen; Jan C. Vorbrüggen; Bernhard Sendhoff. Berlin, Heidelberg: Springer, 1996. p. 821-826 (Lecture Notes in Computer Science; Vol. 1112).

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

TY - GEN

T1 - Building nonlinear data models with self-organizing maps

AU - Der, Ralf

AU - Balzuweit, Gerd

AU - Herrmann, Michael

PY - 1996

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N2 - We study the extraction of nonlinear data models in high dimensional spaces with modified self-organizing maps. Our algorithm maps lower dimensional lattice into a high dimensional space without topology violations by tuning the neighborhood widths locally. The approach is based on a new principle exploiting the specific dynamical properties of the first order phase transition induced by the noise of the data. The performance of the algorithm is demonstrated for one- and two-dimensional principal manifolds and for sparse data sets.

AB - We study the extraction of nonlinear data models in high dimensional spaces with modified self-organizing maps. Our algorithm maps lower dimensional lattice into a high dimensional space without topology violations by tuning the neighborhood widths locally. The approach is based on a new principle exploiting the specific dynamical properties of the first order phase transition induced by the noise of the data. The performance of the algorithm is demonstrated for one- and two-dimensional principal manifolds and for sparse data sets.

U2 - 10.1007/3-540-61510-5_138

DO - 10.1007/3-540-61510-5_138

M3 - Conference contribution

SN - 978-3-540-61510-1

T3 - Lecture Notes in Computer Science

SP - 821

EP - 826

BT - Artificial Neural Networks — ICANN 96

A2 - Malsburg, Christoph

A2 - Seelen, Werner

A2 - Vorbrüggen, Jan C.

A2 - Sendhoff, Bernhard

PB - Springer

CY - Berlin, Heidelberg

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Der R, Balzuweit G, Herrmann M. Building nonlinear data models with self-organizing maps. In Malsburg C, Seelen W, Vorbrüggen JC, Sendhoff B, editors, Artificial Neural Networks — ICANN 96: 1996 International Conference Bochum, Germany, July 16–19, 1996 Proceedings. Berlin, Heidelberg: Springer. 1996. p. 821-826. (Lecture Notes in Computer Science). doi: 10.1007/3-540-61510-5_138

Building nonlinear data models with self-organizing maps

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