Annealing robust radial basis function networks for function approximation with outliers

Abstract

In this paper, the annealing robust radial basis function networks (ARRBFNs) are proposed to improve the problems of the robust radial basis function networks (RBFNs) for function approximation with outliers. Firstly, a support vector regression (SVR) approach is proposed to determine an initial structure of ARRBFNs in this paper. Because an SVR approach is equivalent to solving a linear constrained quadratic programming problem under a fixed structure of SVR, the number of hidden nodes, initial parameters and initial weights of the ARRBFNs are easily obtained. Secondly, the results of SVR are used as the initial structure in ARRBFNs. At the same time, an annealing robust learning algorithm (ARLA) is used as the learning algorithm for ARRBFNs, and applied to adjust the parameters as well as weights of ARRBFNs. That is, an ARLA is proposed to overcome the problems of initialization and the cut-off points in the robust learning algorithm. Hence, when an initial structure of ARRBFNs is determined by an SVR approach, the ARRBFNs with ARLA have fast convergence speed and are robust against outliers. Simulation results are provided to show the validity and applicability of the proposed ARRBFNs.