Simplexes, Multi-Dimensional Scaling and Self-Organized Mapping.

Wlodzislaw Duch and Antoine Naud.
Department of Informatics,   Nicolaus Copernicus University,
Grudziadzka 5, 87-100 Torun, Poland.

Proc. of the 8th joint EPS-APS International Conference on Physics Computing '96, Kraków 17-21.9.1996, pp. 367-370

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

Paper in PDF format, 152 KB

Projects on similar subject and BACK to the on-line publications of W. Duch.