Stochastic choice of basis functions in adaptive function approximation and the functional-link net

A theoretical justification for the random vector version of the functional-link (RVFL) net is presented in this paper, based on a general approach to adaptive function approximation. The approach consists of formulating a limit-integral representation of the function to be approximated and subseque...

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Bibliographic Details
Published in:IEEE transactions on neural networks 1995-11, Vol.6 (6), p.1320-1329
Main Authors: Igelnik, B., Yoh-Han Pao
Format: Article
Language:English
Subjects:
Approximation error
Convergence
Function approximation
Hypercubes
Integral equations
Neural networks
Random variables
Stochastic processes
Writing
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Summary:A theoretical justification for the random vector version of the functional-link (RVFL) net is presented in this paper, based on a general approach to adaptive function approximation. The approach consists of formulating a limit-integral representation of the function to be approximated 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) the RVFL is an efficient universal approximator with the rate of approximation error convergence to zero of order O(C//spl radic/n), where n is number of basis functions and with C independent of n. Similar results are also obtained for neural nets with hidden nodes implemented as products of univariate functions or radial basis functions. Some possible ways of enhancing the accuracy of multivariate function approximations are discussed.< >
ISSN:1045-9227
1941-0093
DOI:10.1109/72.471375