Faster RBF Network Learning Utilizing Singular Regions

There are two ways to learn radial basis function (RBF) networks: one-stage and two-stage learnings. Recently a very powerful one-stage learning method called RBF-SSF has been proposed, which can stably find a series of excellent solutions, making good use of singular regions, and can monotonically decrease training error along with the increase of hidden units. RBF-SSF was built by applying the SSF (singularity stairs following) paradigm to RBF networks; the SSF paradigm was originally and successfully proposed for multilayer perceptrons. Although RBF-SSF has the strong capability to find excellent solutions, it required a lot of time mainly because it computes the Hessian. This paper proposes a faster version of RBF-SSF called RBF-SSF(pH) by introducing partial calculation of the Hessian. The experiments using two datasets showed RBF-SSF(pH) ran as fast as usual one-stage learning methods while keeping the excellent solution quality.