Kohonen's algorithm for the numerical parametrisation of manifolds

M. Alder; R. Togneri; E. Lai; Y. Attikiouzel

doi:10.1016/0167-8655(90)90040-9

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Kohonen's algorithm for the numerical parametrisation of manifolds

Journal article

Peer reviewed

Kohonen's algorithm for the numerical parametrisation of manifolds

M. Alder, R. Togneri, E. Lai and Y. Attikiouzel

Pattern Recognition Letters, Vol.11(5), pp.313-319

1990

DOI: https://doi.org/10.1016/0167-8655(90)90040-9

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Abstract

T. Kohonen has described an algorithm for fitting a k-dimensional grid of points to a set of points taken from a k-manifold in Rn, for k⩽n. The algorithm is inspired by a neural model and bears some of the marks of its ancestry. In this paper we show that if the process converges, it converges to a locally 1-1 mapping of the grid onto the manifold. Hitherto this result has only been proved for the case where k=1.

Details

Title: Kohonen's algorithm for the numerical parametrisation of manifolds
Authors/Creators: M. Alder (Author/Creator) - The University of Western Australia
R. Togneri (Author/Creator) - The University of Western Australia
E. Lai (Author/Creator)
Y. Attikiouzel (Author/Creator) - The University of Western Australia
Publication Details: Pattern Recognition Letters, Vol.11(5), pp.313-319
Publisher: Elsevier B.V.
Identifiers: 991005544271507891
Murdoch Affiliation: Murdoch University
Language: English
Resource Type: Journal article

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Citation topics: 4 Electrical Engineering, Electronics & Computer Science; 4.17 Computer Vision & Graphics; 4.17.118 Face Recognition
Web Of Science research areas: Computer Science, Artificial Intelligence
ESI research areas: Engineering