Self Organizing Map (SOM) neural network based on novel fuzzy wavelet for nonlinear function approximation

Abstract

In this paper a Fuzzy Wavelet Self Organizing Map (FWSOM) is proposed to approximate arbitrary complex nonlinear functions while improving the approximation error. In this method, the novel fuzzy-wavelet method is combined with an unsupervised competitive Self Organizing Map (SOM) neural network. The proposed method uses two stage approximation processes: In the 1st stage, approximation is obtained from the Kohonen SOM neural network, afterwards in stage 2 with the help of a novel fuzzy-wavelet structure, an accurate and fine approximation is obtained. The advantages of this new method are a more accurate approximation and are optimized network size. In the proposed method, on the basis of Multi Resolution Analysis (MRA) theory, fuzzy concept and neural network parallel processing, we can reach a better approximation with appropriate accuracy and using some methods such as recursive least squares method (ROLS), the backward selection algorithm and clustering idea, highly accurate approximations are obtained. Performance of this proposed methods and the traditional SOM are compared from three viewpoints to evaluate the efficiency of the FWSOM method, and simulation results illustrate the effectiveness of this proposed method.