Growing radial basis function network models

In this paper a learning algorithm for creating a Growing Radial Basis Function Network (RBFN) Model is presented and analyzed. The main concept of this algorithm is that the number of the Radial Basis Function (RBF) units is gradually increased at each learning step of the algorithm and the model is gradually improved, until a predetermined (desired) approximation error is achieved. The important point here is that at each step of increasing the number of the RBF units, an optimization algorithm is run to optimize the parameters of only this unit, while keeping the parameters of all the previously optimized RBF units. Such strategy, even if being suboptimal, leads to significant reduction in the number of the parameters that have to be optimized at each step. A modified constraint version of the particle swarm optimization (PSO) algorithm with inertia weight is develop and used in this paper. It allows for obtaining optimal solutions with clear practical meaning. A synthetic nonlinear test example is used in the paper to analyze the performance of the proposed learning algorithm for creating the Growing RBFN model. A comparison with the standard algorithm for simultaneous optimization of all parameters of the classical RBFN model with fixed number of units is also done. It shows that the learning of the Growing RBFN model leads to a more stable and in many cases more accurate solution.

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], [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]. Then the aggregation of all the local models as a weighted sum of their output produces the nonlinear output of the RBFN.