Selection of Radial Basis Functions via Genetic Algorithms in Pattern Recognition Problems

The mixed use of different shapes of radial basis functions (RBFs) in RBF networks is investigated in this paper. For this purpose, we propose the use of the q-Gaussian function, which reproduces different RBFs by changing a real parameter q, in RBF networks. In the proposed methodology, the centers of the radial units are determined by the k-means algorithm. Then, a genetic algorithm is employed to select the number of hidden neurons, type and width of each RBF associated with each radial unit. In order to test the performance of the proposed methodology, an experimental study with two pattern recognition problems is presented. The RBF network with the q-Gaussian RBF is compared to RBF networks with Gaussian, Cauchy, and inverse multiquadratic RBFs.