On the kernel widths in radial-basis function networks

RBFN (Radial-Basis Function Networks) represent an attractive alternative to other neural network models. Their learning is usually split into an unsupervised part, where center and widths of the basis functions are set, and a linear supervised part for weight computation. Although available literature on RBFN learning widely covers how basis function centers and weights must be set, little effort has been devoted to the learning of basis function widths. This paper addresses this topic: it shows the importance of a proper choice of basis function widths, and how inadequate values can dramatically influence the approximation performances of the RBFN. It also suggests a one-dimensional searching procedure as a compromise between an exhaustive search on all basis function widths, and a non-optimal a priori choice.