Use of the q-Gaussian Function in Radial Basis Function Networks

Radial Basis Function Networks (RBFNs) have been successfully employed in several function approximation and pattern recognition problems. In RBFNs, radial basis functions are used to compute the activation of artificial neurons. The use of different radial basis functions in RBFN has been reported in the literature. Here, the use of the q-Gaussian function as a radial basis function in RBFNs is investigated. An interesting property of the q-Gaussian function is that it can continuously and smoothly reproduce different radial basis functions, like the Gaussian, the Inverse Multiquadratic, and the Cauchy functions, by changing a real parameter q. In addition, the mixed use of different shapes of radial basis functions in only one RBFN is allowed. For this purpose, a Genetic Algorithm is employed to select the number of hidden neurons, and center, width and q parameter of the q-Gaussian radial basis function associated with each radial unit. The RBF Network with the q-Gaussian RBF is compared to RBF Networks with Gaussian, Cauchy, and Inverse Multiquadratic RBFs in problems in the Medical Informatics domain.