Building nonlinear data models with self-organizing maps

Abstract

We study the extraction of nonlinear data models in high dimensional spaces with modified self-organizing maps. Our algorithm maps lower dimensional lattice into a high dimensional space without topology violations by tuning the neighborhood widths locally. The approach is based on a new principle exploiting the specific dynamical properties of the first order phase transition induced by the noise of the data. The performance of the algorithm is demonstrated for one- and two-dimensional principal manifolds and for sparse data sets.