Gaussian radial basis functions and inner-product spaces

Abstract

An approximation result is given concerning gaussian radial basis functions in a general inner-product space. Applications are described concerning the classification of the elements of disjoint sets of signals, and also the approximation of continuous real functions defined on all of IRn using RBF networks. More specifically, it is shown that an important large class of classification problems involving signals can be solved using a structure consisting of only a generalized RBF network followed by a quantizer. It is also shown that gaussian radial basis functions defined on IRn can uniformly approximate arbitrarily well over all of IRn any continuous real functional f on IRn that meets the condition that |f(x)| → 0 as ||x|| → ∞.