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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... (Update)
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0.2: Second-Order Learning in Self-Organizing Maps - Der, Herrmann (1999) (Correct)
0.2: Nonlinear Principal Component Analysis - Der, Steinmetz, Balzuweit.. (1998) (Correct)
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BibTeX entry: (Update)
@inproceedings{ der96building,
author = "Ralf Der and Gerd Balzuweit and J. Michael Herrmann",
title = "Building Nonlinear Data Models with Self-Organizing Maps",
booktitle = "{ICANN}",
pages = "821--826",
year = "1996",
url = "citeseer.ist.psu.edu/631733.html" }
Citations (may not include all citations):1213 The Self-Organizing Map (context) - Kohonen - 1995
401 An Introduction to Wavelets (context) - Chui - 1992
94 Neural Computation and Self-Organizing Maps (context) - Ritter, Martinetz et al. - 1992
56 Journal of the American Statistical Association (context) - Hastie, Stuetzle et al. - 1989
29 Self-Organization as an Iterative Kernel Smoothing Process (context) - Mulier, Cherkassky - 1995
5 Self-Organizing Feature Maps with Self-Organizing Neighborho.. - Herrmann - 1995
5 Critical Phenomena in Self-Organized Feature Maps: A Ginzbur.. (context) - Der and, Herrmann - 1994
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