Abstract
One of the main properties of the feature maps generated by Kohonen's self-organizing net is their preservation of the topology of the target object. However, since the net and the target object in general have different topological structures, there are usually also certain distortions of topology in the feature maps. For a better understanding of such distortions we present a continuous model for the Kohonen net based on topology theory. This model stresses the description of the topological behavior of the feature maps while suppressing the statistical aspects. From the point of view of this model a well-trained Kohonen net describes a matching between the net and the object, whereby both of them are usually partitioned into universally connected parts, and the topology distortion occurs on the boundary of the parts. Simulations demonstrate that the topology distortions within the feature maps normally take a regular structure and provide useful information about the target object.
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References
Alder MD, Togneri R, Attikiouzel Y (1991) Dimension of the speech space. IEE Proc Commun Speech Vision 138:123–127
Bauer H-U, Pawelzik KR (1992) Quantifying the neighborhood preservation of self-organizing feature maps. IEEE Trans Neural Networks 3:570–579
Erwin E, Obermayer K, Schulten K (1992) Self-organizing maps: stationary states, metastability and convergence rate. Biol Cybern 67:35–45
Fritzke B (1991) Let it grow — self-organizing feature maps with problem dependent cell structure. In: Proceedings of the International Conference on Artificial Neural Networks (Espoo, Finland). North-Holland, Amsterdam, pp 403–408
Gasteiger J, Li X (1993) The mapping of molecular electrostatic potentials by Kohonen-networks: investigations of neurotransmitters and their agonists. In: Ziessow D (eds) Software development in chemistry, Vol 7. GDCh, Frankfurt am Main, pp 1–14
Kangas JA, Kohonen T, Laaksonen JT (1990) Variants of self-organizing maps. IEEE Trans Neural Networks 1:93–99
Kohonen T (1982) Analysis of a simple self-organizing process. Biol Cybern 44:135–140
Kohonen T (1988) The “neural” phonetic typewriter. Computer 21:11–22
Kohonen T (1990) The self-organizing map. Proc IEEE 78:1464–1480
Ritter HJ, Martinetz TM, Schulten KJ (1989) Topology conserving maps for learning visu-motor-coordination. Neural Networks 2:159–168
Tavan R, Grubmüller H, Kühnel H (1990) Self-organization of associative memory and pattern classification: recurrent signal processng of topological feature maps. Biol Cybern 64:95–105
Togneri R, Alder MD, Attikiouszel Y (1991) Dimension and structure of the speech space. IEE Proc Commun Speech Vision 138:207–214
Zupan J, Gasteiger J (1993) Neural network for chemists: an introduction. VCH, Weinheim
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Li, X., Gasteiger, J. & Zupan, J. On the topology distortion in self-organizing feature maps. Biol. Cybern. 70, 189–198 (1993). https://doi.org/10.1007/BF00200832
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DOI: https://doi.org/10.1007/BF00200832