Incremental RBF network models for nonlinear approximation and classification

In this paper a multistep learning algorithm for creating a novel incremental Radial Basis Function Network (RBFN) Model is presented and analyzed. The proposed incremental RBFN model has a composite structure that consists of one initial linear sub-model and a number of incremental sub-models, each of them being able to gradually decrease the overall approximation error of the model, until a desired accuracy is achieved. The identification of the entire incremental RBFN model is divided into a series of identifications steps applied to smaller size sub-models. At each identification step the Particle Swarm Optimization algorithm (PSO) with constraints is used to optimize the small number of parameters of the respective sub-model. A synthetic nonlinear test example is used in the paper to analyze the performance of the proposed multistep learning algorithm for the incremental RBFN model. A real wine quality data set is also used to illustrate the usage of the proposed incremental model for solving nonlinear classification problems. A brief comparison with the classical single RBFN model with large number of parameters is conducted in the paper and shows the merits of the incremental RBFN model in terms of efficiency and accuracy.

I. Introduction

Radial Basis Function (RBF) Networks have been widely used in the last decade as a power tool in modeling and simulation, because they are proven to be universal approximators of nonlinear input-output relationships with any complexity [1], [2], [3]. In fact, the RBF Network (RBFN) is a composite multi-input, single output model, consisting of a predetermined number of RBFs, each of them performing the role of a local model [3], [4]. Then the aggregation of all the local models as a weighted sum of their output produces the nonlinear output of the RBFN.