Dimensionality Reduction in Basis-function Networks: Exploiting the Link with Fuzzy System

We address the dimensionality problem in the training of basis function networks of various types. Some results which establish the functional equivalence of basis function networks and fuzzy inference systems are discussed, and this equivalence is exploited in the development of a generalised form of basis function network which has in general a lower dimension than the standard form of network. The functional equivalence result allows the employment of training algorithms from both the elds of neural networks and fuzzy systems. We summarise examples of such algorithms and point to their possible use in fuzzy control systems. 1. Summary In this section we summarise the main technical points of the paper. The standard basis function network is described and the problems which arise when the input space has high dimension are highlighted. The Takagi-Sugeno model of fuzzy inference (the TS-model) is then introduced and motivates the establishment of the generalised basis function network (GBFN). The basis functions in the GBFN operate on only a subset of the input variables and the dimensionality problems are therefore considerably alleviated.