Nonlinear function approximation using radial basis function neural networks

Radial basis function neural networks (RBFNN) which are best suited for nonlinear function approximation, have been successfully applied to a wide range of areas including system modeling. The two-stage training procedure adapted in numerous RBFNN applications usually provides satisfactory network performance. Though this method is proven to allow faster training and improves convergence, the initial stage of selecting the network centers pose a problem of creating a larger architecture than what is required. This limitation holds true in applications with large data samples. Various techniques have been developed to choose a sufficient number of centers to suit the network structure. Orthogonal least squares and input clustering are two of such methods that show considerable results of which can provide an amicable solution to the above problem. This paper presents a comparative study on the performance achieved by the two techniques demonstrated when applying the RBFNN in modeling of nonlinear functions and an investigation based on their capabilities in handling over-parameterization problems.