‘Partition of Unity’ RBF Networks are Universal Function Approximators

Abstract

Networks with ’Partition of Unity’ Gaussian radial basis functions (RBF) have achieved considerable attention for their capability to incorporate rule-based knowledge into the network and to extract rule-based knowledge from the network (Tresp et. al., 1993). On the other hand, RBF networks are known for fast adaptation as being used for function approximation. Combining these properties, e. g. prestructuring the network with domain knowledge and refining it with rapid training, is a desirable goal. However, the capability of ’Partition of Unity’ RBF networks to approximate arbitrary functions arbitrarily close on a bounded domain, the essential requirement for universal function approximators, could not be guaranteed so far.