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 ℝ n using radial basis function (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 ℝ n can uniformly approximate arbitrarily well over all of ℝ n any continuous real functionalf on ℝ n that meets the condition that |f(x)|→0 as ‖x‖→∞.