ABSTRACT
In the previous chapter, we showed that the learning of shape and orientation parameters of a basis function significantly improves the approximation capability of a Gaussian basis function. This intuitively comfortable fact was illustrated by considering a variety of examples from a variety of disciplines such as continuous function approximation, dynamic system modeling and system identification, nonlinear signal processing, and time series prediction. Although the RBF learning algorithms presented in Chapter 3 are shown to work very well for different test examples, there remain several challenging issues concerning the complexity and convergence of the RBF model. The nonlinear RBF model is global. This has both advantages and disadvantages, but ultimately for very high-dimensioned problems, it is likely defeated by the curse of high dimensionality (computation burden and convergence difficulties, mainly). Although successes have been many, the computational cost associated with learning these parameters and the convergence of nonlinear estimation algorithms remain obstacles that limit applicability to problems of low to moderate dimensionality.
