On Gaussian radial basis function approximations: interpretation, extensions, and learning strategies

We focus on an interpretation of Gaussian radial basis functions (GRBF) which motivates extensions and learning strategies. Specifically, we show that GRBF regression equations naturally result from representing the input-output joint probability density function by a finite mixture of Gaussian. Corollaries of this interpretation are: some special forms of GRBF representations can be traced back to the type of Gaussian mixture used; previously proposed learning methods based on input-output clustering have a new learning; and estimation techniques for finite mixtures (namely the EM algorithm and model selection criteria) can be invoked to learn GRBF regression equations.