Simplexes, Multi-Dimensional Scaling and Self-Organized Mapping

	              Wlodzislaw Duch and Antoine Naud

	Department of Computer Methods, Nicholas Copernicus University
		ul. Grudziadzka 5, 87-100 Torun, Poland.
	   e-mail: duch @ phys.uni.torun.pl, naud @ phys.uni.torun.pl
	   	  WWW: http://www.phys.uni.torun.pl/kmk

				Abstract
							
The self-organizing map (SOM) of Kohonen is one of the most successful
models of unsupervised learning. Its popularity is partially due to the
visualization (topography preservation) of relations among clusters in
high-dimensional input space. SOM learns slowly, especially in the
initial phase, and the preservation of topography by SOM maps is not
based on any quantitative criteria. We have obtained the best possible
two-dimensional representation of simplexes in spaces of up to 20
dimensions, minimizing the error function measuring the unavoidable
distortion of the original input space topography. This two-dimensional
representation is used to select neurons during initialization of the SOM
network. After such initialization in the learning phase a small radius
of the neighborhood function is sufficient to obtain quick convergence
with minimal topological distortions.


This version: UMK-KMK-TR 2/96 report (1996)
Short version of this paper: Physics Computing 1996, Krakow, Sept. 1996
