Automatic variable selection in RBF network and its application to neurofuzzy GMDH

The radial basis function (RBF) network is a technique for interpolating data in high dimensional spaces. The network has an architecture that uses a single internal layer of locally tuned processing units. The networks are universal approximation schemes, as they can approximate any continuous nonlinear function to any desired degree of accuracy. It is important, but difficult to select the necessary input variables to the network among many variables because we do not have knowledge about the target system. The computation to find the optimal combination of variables is intense. We consider the method to automatically select the optimal combination of variables in one learning iteration. We propose a combined algorithm of the affine scaling interior point method and the gradient projection method for the automatic selection of the optimal combination of variables. This method simultaneously enables the learning of model parameters and the selection of variables. Furthermore, the proposed method is applied to the neurofuzzy GMDH algorithm with successive determination of variables. Numerical examples show the validity of the method