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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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