Optimising the widths of radial basis functions

In the context of regression analysis with penalised linear models (such as RBF networks) certain model selection criteria can be differentiated to yield a re-estimation formula for the regularisation parameter such that an initial guess can be iteratively improved until a local minimum of the criterion is reached. In this paper we discuss some enhancements of this general approach including improved computational efficiency, detection of the global minimum and simultaneous optimisation of the basis function widths. The benefits of these improvements are demonstrated on a practical problem