A novel two stage algorithm for construction of RBF neural models based on A-optimality criterion

This paper concerns the nonlinear system modelling using Radial Basis Function (RBF) neural networks. RBF neural models can be constructed through a subset selection procedure where the nonlinear parameters associated to the hidden nodes are fixed, thus only significant hidden nodes are selected for inclusion in the final model. However, due to existence of noise on data, this procedure often leads to an over-fitted model with unsatisfactory generalisation performance. Bayesian regularisation and leave-one-out cross validation can be incorporated to tackle this issue, but the algorithm stability is an issue that needs to be addressed. This paper proposes a new method which not only improves the compactness of the resultant RBF neural model, but also the accuracy of estimated model coefficients. This is achieved by effectively incorporating the A-optimality design criterion into a recently proposed two-stage subset selection, while the computational efficiency is still retained from the original two-stage selection method by introducing a residual matrix. Experimental results on two simulation benchmarks are included to illustrate the effectiveness of the proposed approach.