Neighborhoods and trajectories in Kohonen maps
Alexander Grunewald · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1992
The Kohonen map is a basic paradigm of unsupervised learning. Quite a few descriptions exist of the possibility to expand other paradigms, and to describe their output behavior, for example, the functions that can be learned and the trajectories in the output space. The main parameters of Kohonen maps are the underlying topology and the metric used. In this paper the concepts of nearest neighbor, neighbor, neighborhood and underlying topology are formalized in a set-theoretic manner and thus expanded. Similarly, the concept of metric is enhanced by the introduction of similarity measures. A theorem on continuity of output is proved for such measures.