Annealing robust fuzzy basis function for modelling with noise and outliers

Abstract

In this paper, an annealing robust fuzzy basis function (ARFBF) is proposed to improve the problems of the fuzzy basis function (FBF) for modelling with noise and outliers. Firstly, the repeated support vector regression (RSVR) approach is proposed to determine the initial structure of ARFBF. Because a RSVR approach is equivalent to solving twice linear constrained quadratic programming problem under a fixed structure of SVR, the number of hidden nodes, the initial parameters and the initial weights of ARFBF are easily obtained in the RSVR. Secondly, the results of RSVR are used as initial structure in the ARFBF. At the same time, an annealing robust learning algorithm (ARLA) is used as the learning algorithm for ARFBF, and applied to adjust the parameters as well as weights of ARFBF. That is, an ARLA is proposed to overcome the problems of initialisation and the cutoff points in the robust learning algorithm. Hence, when an initial structure of ARFBF is determined by a RSVR approach, the ARFBF with ARLA has faster convergence speed and is robust against outliers. Simulation results are provided to show the validity and applicability of the proposed ARFBF.