A novel locally regularized automatic construction method for RBF neural models

This paper investigates automatic construction of radial basis function (RBF) neural models for nonlinear dynamic systems. The main objective is to automatically and effectively produce a parsimonious RBF neural model that generalizes well. This is achieved by proposing a locally regularized automatic construction (LRAC) method which combines a recently proposed fast recursive algorithm (FRA) with the leave-one-out (LOO) cross-validation criterion. The new method offers distinctive advantages over existing approaches. Firstly, it uses an error criterion where the original model parameters are regularized, in contrast to orthogonal least square (OLS) based approaches where transformed model parameters are regularized. This enables the determination of the significance of each original candidate center and produces a compact neural model. Further, it can automatically determine the network size by the iteratively minimizing a LOO mean-square-error (MSE) without the need to specify any additional termination criterion. Finally, by defining a proper regression context, the whole network construction process can be concisely formulated and easily implemented with significantly reduced computation. An analysis of computational complexity confirms the efficiency of the proposed method, and simulation results reveal its effectiveness in comparison with alternative approaches for producing sparse RBF neural models.