Kohonen's algorithm for the numerical parametrisation of manifolds

Alder, M., Togneri, R., Lai, E. and Attikiouzel, Y. (1990) Kohonen's algorithm for the numerical parametrisation of manifolds. Pattern Recognition Letters, 11 (5). pp. 313-319.

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.

Item Type:	Journal Article
Publisher:	Elsevier B.V.
Copyright:	© 1990 Published by Elsevier B.V.
URI:	http://researchrepository.murdoch.edu.au/id/eprint/20835

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