An interpretation of radial basis function networks as zero-mean Gaussian process emulators in cluster space

Emulators provide approximations to computationally expensive functions and are widely used in diverse domains, despite the ever increasing speed of computational devices. In this paper we establish a connection between two independently developed emulation methods: radial basis function networks and Gaussian process emulation. The methodological relationship is established by starting from the observation that the concept of correlation between random variables in Gaussian process emulation can be interpreted as a correlation function applied to points in input space. This correlation function is then extended to apply to clusters, i.e. to sets of points. It is then shown that the extended Gaussian process emulation method is equivalent to radial basis function networks, provided that the prior mean in Gaussian process emulation is chosen zero. This elegant connection might increase understanding of the principles of both types of emulation, and might act as a catalyst for mutually beneficial research in emulation domains that were hitherto considered independent.