Input selection for radial basis function networks by constrained optimization

Input selection in the nonlinear function approximation is important and difficult problem. Neural networks provide good generalization in many cases, but their interpretability is usually limited. However, the contributions of input variables in the prediction of output would be valuable information in many real world applications. In this work, an input selection algorithm for Radial basis function networks is proposed. The selection of input variables is achieved using a constrained cost function, in which each input dimension is weighted. The constraints are imposed on the values of weights. The proposed algorithm solves a log-barrier reformulation of the original optimization problem. The input selection algorithm was applied to both simulated and benchmark data and obtained results were compelling.