Functional modelling of large scattered data sets using neural networks

We propose a self-organising hierarchical Radial Basis Function (RBF) network for functional modelling of large amounts of scattered unstructured point data. The network employs an error-driven active learning algorithm and a multi-layer architecture, allowing progressive bottom-up reinforcement of local features in subdivisions of error clusters. For each RBF subnet, neurons can be inserted, removed or updated iteratively with full dimensionality adapting to the complexity and distribution of the underlying data. This flexibility is particularly desirable for highly variable spatial frequencies. Experimental results demonstrate that the network representation is conducive to geometric data formulation and simplification, and therefore to manageable computation and compact storage.