STOCHASTIC CHOICE OF BASIS FUNCTIONS IN ADAPTIVE FUNCTION APPROXIMATION AND THE FUNCTIONAL-LINK NET

A theoretical justification for the random vector version of the funct ional-link (RVFL) net is presented in this paper, based on a general a pproach to adaptive function approximation, The approach consists of f ormulating a Limit-integral representation of the function to be appro ximated and subsequently evaluating that integral with the Monte-Carlo method, Two main results are: 1) the RVFL is a universal approximator for continuous functions on bounded finite dimensional sets, and 2) t he RVFL is an efficient universal approximator with the rate of approx imation error convergence to zero of order O(C/root n), where n is num ber of basis functions and with C independent of n, Similar results ar e also obtained for neural nets with hidden nodes implemented as produ cts of univariate functions or radial basis functions, Some possible w ays of enhancing the accuracy of multivariate function approximations are discussed.