On Monotonic Radial Basis Function Networks.

Abstract

This article deals with monotonicity conditions for radial basis function (RBF) networks. Two architectures of RBF networks are considered-1) unnormalized network with a local character of the basis function and 2) a normalized network where the value of RBF is taken relatively with respect to the others. Different approaches are followed for each of them. For the former, monotonicity is enforced in prescribed points whereas for the latter sufficient monotonicity conditions are formulated. In both cases, the monotonicity conditions are expressed as linear constraints on the network weights that enable efficient solving of the related optimization problems. Many illustrative examples are presented to show the advantages of incorporating prior information in the form of monotonicity.