Regularization in the Selection of Radial Basis Function Centers

Subset selection and regularization are two well-known techniques that can improve the generalization performance of nonparametric linear regression estimators, such as radial basis function networks. This paper examines regularized forward selection (RFS)—a combination of forward subset selection and zero-order regularization. An efficient implementation of RFS into which either delete-1 or generalized cross-validation can be incorporated and a reestimation formula for the regularization parameter are also discussed. Simulation studies are presented that demonstrate improved generalization performance due to regularization in the forward selection of radial basis function centers.