Some Comparisons of Radial and Kernel Computational Models

Abstrakt

Mathematical properties of two types of computational models popular in neurocomputing, radial-basis function networks (RBF) and kernel models, are compared. Both models have their advantages: RBF networks are known to be universal approximators and they allow higher flexibility in choice of free parameters which leads to smaller model complexity. On the other hand, kernel models benefit from geometrical properties of Hilbert spaces generated by symmetric positive semidefinite kernels. These properties allow applications of maximal margin classification, regularization modeling generalization in learning from data and description of optimal solutions of learning tasks. We investigate these two types of models in the framework of kernel units with fixed and variable widths. We give conditions on kernels with fixed widths implying universal approximation property and describe behavior of kernel stabilizers with changing widths and input dimensions. We illustrate our results by the example of Gaussian kernel networks with fixed and varying widths.