An Optimal Radial Basis Function (RBF) Neural Network for Hyper-Surface Reconstruction

Data acqui sit ion of chemical engineering processes is expensive and the collected data are always contaminated with inevitable measuremnt errors . efficient algorithms are required to filter out the noise and capture the true underlying trend hidden in the training data sets . regularization networks, which are the exact solution of multivariate linear regularization problems, provide an appropriate meansto perform such a demanding task . these networks can be represented as a single hidden layer neural network with one neuron for each distinct exemplar. efficient training of a regularization network requiresthe calculation of linear synaptic weights, selection of isotropic spread (delta ) and computation of an optimum level of regularization (lambda*). the latter parameters (delta and lambda*) are highly correlated with each other. a novel method is presented in this article for the development of a convenient procedure for de-correlatingthe above parameters and selecting the optimal values of lambda* and delta* , the plot of lambda* versus a suggests a threshold delta* that can be regarded as the optimal isotropic spread for which the regularization network provides appropriate model for the training data set . it is also shown that the effective degrees of freedom of a regularization network is a function of both regularization levels and isotropic spread. a readilycalculable measure of the approximate degrees of freedom of a regularization network is also in troduced, which may be used to de-couple lambda* and delta .