Relaxed conditions for radial-basis function networks to be universal approximators.
In this paper, we investigate the universal approximation property of Radial Basis Function (RBF) networks. We show that RBFs are not required to be integrable for the REF networks to be universal approximators. Instead, RBF networks can uniformly approximate any continuous function on a compact set provided that the radial basis activation function is continuous almost everywhere, locally essentially bounded, and not a polynomial. The approximation in L(p)(micro)(1 < or = p < infinity) space is also discussed. Some experimental results are reported to illustrate our findings.
Liao
Yi
Y
Operations Research and Industrial Engineering, North Carolina State University, Raleigh, NC 27695-7906, USA. yliao2@eos.ncsu.edu
Fang
Shu-Cherng
SC
Nuttle
Henry L W
HL
D016571:Neural Networks, Computer