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http://dx.doi.org/10.5831/HMJ.2013.35.4.729

THE CAPABILITY OF LOCALIZED NEURAL NETWORK APPROXIMATION  

Hahm, Nahmwoo (Department of Mathematics, Incheon National University)
Hong, Bum Il (Department of Applied Mathematics, Kyung Hee University)
Publication Information
Honam Mathematical Journal / v.35, no.4, 2013 , pp. 729-738 More about this Journal
Abstract
In this paper, we investigate a localized approximation of a continuously differentiable function by neural networks. To do this, we first approximate a continuously differentiable function by B-spline functions and then approximate B-spline functions by neural networks. Our proofs are constructive and we give numerical results to support our theory.
Keywords
localized approximation; neural network; B-spline;
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Times Cited By KSCI : 1  (Citation Analysis)
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1 C. K. Chui, X. Li and H. N. Mhaskar, Limitations of the approximation capabilities of neural networks with one hidden layer, Adv. Comput. Math., 5 (1996), 233-243.   DOI   ScienceOn
2 B. Gao and Y. Xu, Univariant approximation by superpositions of a sigmoidal function, J. Math. Anal. Appl., 178 (1993), 221-226.   DOI   ScienceOn
3 N. Hahm and B. I. Hong, Extension of localised approximation by neural networks, Bull. Austral. Math. Soc., 59 (1999), 121-131.   DOI
4 N. Hahm and B. I. Hong, An approximation by neural networks with a fixed weight, Comput. Math. Appl., 47 (2004), 1897-1903.   DOI   ScienceOn
5 N. Hahm and B. I. Hong, Approximation order to a function in $L_{p}$ space by generalized translation networks, Honam Math. J. 28(1) (2006), 125-133.
6 N. Hahm and B. I. Hong, A simultaneous neural network approximation with the squashing function, Honam Math. J. 31(2) (2009), 147-156.   과학기술학회마을   DOI   ScienceOn
7 B. I. Hong and N. Hahm, Approximation order to a function in C(R) by superposition of a sigmoidal function, Appl. Math. Lett., 15 (2002), 591-597.   DOI   ScienceOn
8 B. L. Kalman and S. C. Kwasny, Why Tanh : Choosing a sigmoidal function, Int. Joint Conf. on Neural Networks 4 (1992), 578-581.
9 M. Leshno, V. Lin, A. Pinkus and S. Schocken, Multilayered feedforward networks with a nonpolynomial activation function can approximate any function, Neural Networks, 6 (1993), 61-80.
10 G. Lewicki and G. Marino, Approximation of functions of finite variation by superpositions of a sigmoidal function, Appl. Math. Lett. 17 (2004), 1147-1152.   DOI   ScienceOn
11 H. N. Mhaskar and N. Hahm, Neural networks for functional approximation and system identification, Neural Comput., 9 (1997), 143-159.   DOI   ScienceOn
12 L. L. Schumaker, Spline Functions : Basic Theory, Cambridge University Press, Cambridge, 2007.