ABSTRACT
The radial basis function neural network (RBF NN) is extended to the elliptical receptive fields of neurons. It is shown that an optimal response function of the elliptical basis function neural network (EBF NN) is the conditional average of the dependent variable with respect to the independent one. An analytical form of the conditional average is calculated for a special case when the probability density function (p.d.f.) is represented as a sum of K multidimensional Gaussian functions.
Learning algorithms are derived from relative entropy discrepancy measure between representative and empirical p.d.f. The training is done in batch and adaptive mode.
Two-dimensional examples of approximated regression curves are presented and a comparison between radial and elliptical basis function NN is made.
