Second-Order Learning in Self-Organizing Maps

Abstract

Kohonen's self-organizing map (SOM) has immense potential as a universal tool of nonlinear data analysis. From the practical point of view, control parameters like the learning rate and the neighborhood width need special attention in order to exploit the possibilities of the approach. In Kohonen's self-organizing feature map, the control parameters are the learning rate ɛ and the neighborhood width σ. The learning rate controls the plasticity of the map since it defines the attention that a neuron attributes to a single stimulus. By an individual tuning of the neural attention, the magnification factor of the map can be controlled locally, such as to achieve maps minimizing particular error criteria. In another approach, the plasticity of the map is improved by a heuristical scheme for choosing optimal learning step lengths. One of the most prominent applications of the SOM is dimension reduction of noisy data. Mathematically, this corresponds to the problem of extracting principal curves (PC) or principal manifolds (PM) in the general case—from higher dimensional data distributions.