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.

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A b s t r a c t . We discuss two problems in the context of building environment models from multiple range images. The first problem is how to find the correspondences between surfaces viewed in images and surfaces stored in the environment model. The second problem is how to fuse descriptions of different parts of the same surface patch. One conclusion quickly reached is that in order to solve the image-model correspondence problem in a reasonable time the environment model must be divided into parts.

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In this paper, different methods for training radial basis function (RBF) networks for regression problems are described and illustrated. Then, using data from the DELVE archive, they are empirically compared with each other and with some other well known methods for machine learning. Each of the RBF methods performs well on at least one DELVE task, but none are as consistent as the best of the other non-RBF methods.