Simplexes Multi Dimensional Scaling and Self Organized Mapping

Abstract The self organizingmap 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 dimensions minimizing the error func tion 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 su cient to obtain quick convergence with minimal topological distortions