Beta wavelet networks for function approximation

Wavelet neural networks (WNN) have recently attracted great interest, because of their advantages over radial basis function networks (RBFN) as they are universal approximators. In this paper we present a novel wavelet neural network, based on Beta wavelets, for 1-D and 2-D function approximation. Our purpose is to approximate an unknown function f. R-n -> R from scattered samples (x(i),- y(i) = f(x)) i=1.... n, where: we have little a priori knowledge on the unknown function f which lives in some infinite dimensional smooth function space, the function approximation process is performed iteratively: each new measure on the function (xi; f(xi)) is used to compute a new estimate as an approximation of the function f. Simulation results are demonstrated to validate the generalization ability and efficiency of the proposed Beta wavelet network.