RBF Neural Networks Design with Graph Based Structural Information from Dominating Sets

The definition of an appropriate number of Radial Basis Functions and their parameters in Radial Basis Function networks is a non-trivial task. The fitting of its parameters has direct implications on model performance and generalization. Techniques such as cross-validation associated with error metrics, which frequently rely on iterative optimization, have been used to address this problem, requiring significant computational effort and uncertain solutions. We propose a method for determining the number and parameters of Radial Basis Functions based on the Dominating Set of the Gabriel graph, which represents the structure of the input data, such that no exterior/prior parameter estimation or heuristic methods are necessary.