Comparison between Beta Wavelets Neural Networks , RBF Neural Networks and Polynomial Approximation for 1 D , 2 D Functions Approximation

This paper proposes a comparison between wavelet neural networks (WNN), RBF neural network and polynomial approximation in term of 1-D and 2-D functions approximation. We present a novel wavelet neural network, based on Beta wavelets, for 1-D and 2-D functions approximation. Our purpose is to approximate an unknown function f: Rn R from scattered samples (xi; y = f(xi)) i=1....n, where first, we have little a priori knowledge on the unknown function f: it lives in some infinite dimensional smooth function space and second the function approximation process is performed iteratively: each new measure on the function (xi; f(xi)) is used to compute a new estimate ∧ f as an approximation of the function f. Simulation results are demonstrated to validate the generalization ability and efficiency of the proposed Beta wavelet network. Keywords—Beta wavelets networks, RBF neural network, training algorithms, MSE, 1-D, 2D function approximation.