A framework for multiscale and hybrid RKHS-based approximators

A generalized framework for deriving multiscale and hybrid functionally expanded approximators that are linear in the adjustable weights is presented. The basic idea here is to define one or more appropriate function spaces and then to impose a geometric structure on these to obtain reproducing kernel Hilbert spaces (RKHSs). The weight identification problem is formulated as a minimum norm optimization problem that produces an approximation network structure that comprises a linear weighted sum of displaced reproducing kernels fed by the input signals. Examples of the application of this framework are discussed. Results of numerical experiments are presented.