Hierarchical RBF networks and local parameter estimate

The method presented here is aimed to a direct fast setting of the parameters of a RBF network for function approximation. It is based on a hierarchical gridding of the input space; additional layers of Gaussians at lower scales are added where the residual error is higher. The number of the Gaussians of each layer and their variance are computed from considerations grounded in the linear filtering theory. The weight of each Gaussian is estimated through a maximum a posteriori estimate carried out locally on a sub-set of the data points. The method shows a high accuracy in the reconstruction, it can deal with non-evenly spaced data points and can be fully parallelizable. Results on the econstruction of both synthetic and real data are presented and discussed.