Networks that approximate vector-valued mappings

A network architecture capable of approximating an arbitrary pattern of vectors by a linear superposition of nonlinear vector fields is proposed. The authors´ approach is based on a direct extension of the method of basis functions to the representation of vector-valued mappings. In the proposed network architecture, vector approximation is represented as a form of auto-association. The output field must reproduce as closely as possible the set of input vectors. It is shown that, with a simple and relatively small set of connection weights, it is possible to represent a broad spectrum of vector patterns and to generate a functionally meaningful decomposition of these patterns into zero-curl and zero-divergence components