A framework for multiscale and hybrid RKHS-based approximators

A generalized framework for deriving multiscale and hybrid functionally exp anded approximators that are linear in the adjustable weights is presented. The basic idea here is to define one or more appropriate function spaces a nd then to impose a geometric structure on these to obtain reproducing kern el Hilbert spaces (RKHSs) [1], The weight identification problem is formula ted as a minimum norm optimization problem that produces an approximation n etwork structure that comprises a linear weighted sum of displaced reproduc ing kernels fed by the input signals, Examples of the application of this f ramework are discussed, Results of numerical experiments are presented.