Nonlinear regression using RBFN with linear submodels

Radial basis function networks (RBFNs) have been widely used for function approximation and pattern classification as an alternative to conventional artificial neural networks. In this paper, RBFN with local linear functions is developed and applied to mapping nonlinear functions and modeling air pollutant emission. This extended version of the traditional RBFN has a linear function of inputs as a connecting weight, which is functionally equivalent to the first-order Sugeno fuzzy model. There are three kinds of parameters determined through proper training algorithms: the centers and spreads of each radial basis function, and the connection weights. The extended RBFN (ERBFN) is trained by a hybrid learning algorithm, which uses an iterative nonlinear optimization technique to obtain the center and spread of each radial basis function and the least squares method to obtain the connection weights. To avoid capturing a local optimum, the nonlinear parameters are initialized using a modified K-means clustering method, which has cluster-merging characteristic so as to automatically determine the number of basis functions. The proposed ERBFN method was applied to the approximation of three different functional forms and to the modeling of a real process. The results confirm that the proposed methodology gives considerably better performance and shows faster learning in comparison to previous methods.