Reordering Transitions in Self—Organized Feature Maps with Short—Range Neighbourhood

R. Der, M. Herrmann

Research output: Chapter in Book/Report/Conference proceedingChapter


We report a reordering phase transition in Kohonen’s self-organized feature maps with short neighbourhood range. The transition is established for the specific case of mapping a two-dimensional square shaped input distribution onto a square lattice of neurons. Below a critical value of the neighbourhood width σ* ≈ 0.49 the symmetry of the globally ordered state is broken spontaneously. This is predicted theoretically by a stability analysis in terms of a Langevin approach to the dynamics of the system and supported by numerical simulations which clearly show the spontaneous emergence of hexagon-shaped receptive fields below the critical value of σ. Our results show that for a hexagonal lattice of neurons a more reliable mapping is achieved since the phase transition which is accompagnied by faults in the map is avoided
Original languageEnglish
Title of host publicationICANN '94: Proceedings of the International Conference on Artificial Neural Networks Sorrento, Italy, 26--29 May 1994 Volume 1, Parts 1 and 2
EditorsMaria Marinaro, Pietro G. Morasso
Place of PublicationLondon
PublisherSpringer London
Number of pages4
ISBN (Print)978-1-4471-2097-1
Publication statusPublished - 1994

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