Optimizing widths with PSO for center selection of Gaussian radial basis function networks

Abstract

The radial basis function (RBF) centers play different roles in determining the classification capability of a Gaussian radial basis function neural network (GRBFNN) and should hold different width values. However, it is very hard and time-consuming to optimize the centers and widths at the same time. In this paper, we introduce a new insight into this problem. We explore the impact of the definition of widths on the selection of the centers, propose an optimization algorithm of the RBF widths in order to select proper centers from the center candidate pool, and improve the classification performance of the GRBFNN. The design of the objective function of the optimization algorithm is based on the local mapping capability of each Gaussian RBF. Further, in the design of the objective function, we also handle the imbalanced problem which may occur even when different local regions have the same number of examples. Finally, the recursive orthogonal least square (ROLS) and genetic algorithm (GA), which are usually adopted to optimize the RBF centers, are separately used to select the centers from the center candidates with the initialized widths, in order to testify the validity of our proposed width initialization strategy on the selection of centers. Our experimental results show that, compared with the heuristic width setting method, the width optimization strategy makes the selected centers more appropriate, and improves the classification performance of the GRBFNN. Moreover, the GRBFNN constructed by our method can attain better classification performance than the RBF LS-SVM, which is a state-of-the-art classifier.