Local Training for Radial Basis Function Networks: Towards Solving the Hidden Unit Problem

Abstract

This work examines training methods for radial basis function networks (RBFNs). First, the theoretical and practical motivation for RBFNs is reviewed, as are two currently popular training methods. Next a new training method is developed using well known results from functional analysis. This method trains each kidden unit individually, and is thus called the local training method. The structure of the method allows analysis of individual hidden units; moreover a covariance-related quantity is defined that gives insight into how many hidden units to employ. Two examples illustrate the usefulness of the method. Lastly, an ad hoc method to further improve RBFN performance is demonstrated.