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Comparison between Beta Wavelets Neural Networks, RBF Neural Networks and Polynomial Approximation for 1D, 2D Functions Approximation
| Citations: | 2 - 0 self |
BibTeX
@MISC{Bellil_comparisonbetween,
author = {Wajdi Bellil and Chokri Ben Amar and Adel M. Alimi},
title = {Comparison between Beta Wavelets Neural Networks, RBF Neural Networks and Polynomial Approximation for 1D, 2D Functions Approximation},
year = {}
}
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Abstract
Abstract—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 (x i; f(x i)) 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. I.
Keyphrases
rbf neural network function approximation polynomial approximation beta wavelet neural network unknown function 2-d function approximation priori knowledge simulation result beta wavelet network new measure beta wavelet novel wavelet neural network new estimate wavelet neural network generalization ability infinite dimensional smooth function space function approximation process keywords beta wavelet network
