Integral transform and its application to neural network approximation

Authors:
Feng-jun Li;Zongben Xu
Affiliations:
Faculty of Science, Institute for Information and System Science, Xi’an Jiaotong University, Xi’an, P.R. China;Faculty of Science, Institute for Information and System Science, Xi’an Jiaotong University, Xi’an, P.R. China
Venue:
ISNN'06 Proceedings of the Third international conference on Advances in Neural Networks - Volume Part I
Year:
2006

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Abstract

Neural networks are widely used to approximate nonlinear functions. In order to study its approximation capability, a theorem of integral representation of functions is developed by using integral transform. Using the developed representation, an approximation order estimation for the bell-shaped neural networks is obtained. The obtained result reveals that the approximation accurately of the bell-shaped neural networks depends not only on the number of hidden neurons, but also on the smoothness of target functions.