Constructing principal manifolds in sparse data sets by self-organizing maps with self-regulating neighborhood width

R. Der; G. Balzuweit; M. Herrmann

doi:10.1109/ICNN.1996.548940

Constructing principal manifolds in sparse data sets by self-organizing maps with self-regulating neighborhood width

R. Der
, G. Balzuweit
, M. Herrmann

School of Informatics

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

Abstract

We study the extraction of principal manifolds (PMs) in high-dimensional spaces with modified self-organizing feature maps. Our algorithm embeds a lower-dimensional lattice into a high-dimensional space without topology violations by tuning the neighborhood widths locally. Topology preservation, however, is not sufficient for determining PMs. It still allows for considerable deviations from the PM and is rather unreliable in the case of sparse data sets. These two problems are solved by the introduction of a new principle exploiting the specific dynamical properties of the first-order phase transition induced by dimensional conflicts

Original language	English
Title of host publication	Neural Networks, 1996., IEEE International Conference on
Publisher	Institute of Electrical and Electronics Engineers
Pages	480-483
Number of pages	5
Volume	1
ISBN (Print)	0-7803-3210-5
DOIs	https://doi.org/10.1109/ICNN.1996.548940
Publication status	Published - 1 Jun 1996

Keywords / Materials (for Non-textual outputs)

data handling
learning (artificial intelligence)
network topology
self-organising feature maps
wavelet transforms
first-order phase transition
high-dimensional space
lower-dimensional lattice
neighborhood width
parameter learning
principal manifolds
self-organizing maps
sparse data sets
topology preserving map
Data mining
Fluctuations
Informatics
Information representation
Lattices
Neurons
Phase measurement
Scattering
Self organizing feature maps
Topology

Access to Document

10.1109/ICNN.1996.548940

http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=548940

Cite this

@inproceedings{f8dae3fef026429ea5590ab7f191c3cd,

title = "Constructing principal manifolds in sparse data sets by self-organizing maps with self-regulating neighborhood width",

abstract = "We study the extraction of principal manifolds (PMs) in high-dimensional spaces with modified self-organizing feature maps. Our algorithm embeds a lower-dimensional lattice into a high-dimensional space without topology violations by tuning the neighborhood widths locally. Topology preservation, however, is not sufficient for determining PMs. It still allows for considerable deviations from the PM and is rather unreliable in the case of sparse data sets. These two problems are solved by the introduction of a new principle exploiting the specific dynamical properties of the first-order phase transition induced by dimensional conflicts",

keywords = "data handling, learning (artificial intelligence), network topology, self-organising feature maps, wavelet transforms, first-order phase transition, high-dimensional space, lower-dimensional lattice, neighborhood width, parameter learning, principal manifolds, self-organizing maps, sparse data sets, topology preserving map, Data mining, Fluctuations, Informatics, Information representation, Lattices, Neurons, Phase measurement, Scattering, Self organizing feature maps, Topology",

author = "R. Der and G. Balzuweit and M. Herrmann",

year = "1996",

month = jun,

day = "1",

doi = "10.1109/ICNN.1996.548940",

language = "English",

isbn = "0-7803-3210-5",

volume = "1",

pages = "480--483",

booktitle = "Neural Networks, 1996., IEEE International Conference on",

publisher = "Institute of Electrical and Electronics Engineers",

address = "United States",

}

Constructing principal manifolds in sparse data sets by self-organizing maps with self-regulating neighborhood width. / Der, R.; Balzuweit, G.; Herrmann, M.
Neural Networks, 1996., IEEE International Conference on. Vol. 1 Institute of Electrical and Electronics Engineers, 1996. p. 480-483.

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

TY - GEN

T1 - Constructing principal manifolds in sparse data sets by self-organizing maps with self-regulating neighborhood width

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AU - Balzuweit, G.

AU - Herrmann, M.

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N2 - We study the extraction of principal manifolds (PMs) in high-dimensional spaces with modified self-organizing feature maps. Our algorithm embeds a lower-dimensional lattice into a high-dimensional space without topology violations by tuning the neighborhood widths locally. Topology preservation, however, is not sufficient for determining PMs. It still allows for considerable deviations from the PM and is rather unreliable in the case of sparse data sets. These two problems are solved by the introduction of a new principle exploiting the specific dynamical properties of the first-order phase transition induced by dimensional conflicts

AB - We study the extraction of principal manifolds (PMs) in high-dimensional spaces with modified self-organizing feature maps. Our algorithm embeds a lower-dimensional lattice into a high-dimensional space without topology violations by tuning the neighborhood widths locally. Topology preservation, however, is not sufficient for determining PMs. It still allows for considerable deviations from the PM and is rather unreliable in the case of sparse data sets. These two problems are solved by the introduction of a new principle exploiting the specific dynamical properties of the first-order phase transition induced by dimensional conflicts

KW - data handling

KW - learning (artificial intelligence)

KW - network topology

KW - self-organising feature maps

KW - wavelet transforms

KW - first-order phase transition

KW - high-dimensional space

KW - lower-dimensional lattice

KW - neighborhood width

KW - parameter learning

KW - principal manifolds

KW - self-organizing maps

KW - sparse data sets

KW - topology preserving map

KW - Data mining

KW - Fluctuations

KW - Informatics

KW - Information representation

KW - Lattices

KW - Neurons

KW - Phase measurement

KW - Scattering

KW - Self organizing feature maps

KW - Topology

U2 - 10.1109/ICNN.1996.548940

DO - 10.1109/ICNN.1996.548940

M3 - Conference contribution

SN - 0-7803-3210-5

VL - 1

SP - 480

EP - 483

BT - Neural Networks, 1996., IEEE International Conference on

PB - Institute of Electrical and Electronics Engineers

ER -

Constructing principal manifolds in sparse data sets by self-organizing maps with self-regulating neighborhood width

Abstract

Keywords / Materials (for Non-textual outputs)

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Cite this