A New Incremental Strategy for Function Approximation by Radial Basis Function Neural Networks

Abstract

In this paper we present a new incremental learning algorithm for approximating continuous mapping. The algorithm uses radial basis functions as activation functions. The novelty of the algorithm has different aspects: First, the learning procedure is accomplished modifying only the variances of the activation functions instead of the weights on the synapses; Secondly, the variances of the radial basis functions are trained by a two stage strategy, which includes a local optimization of each new neuron variance. An evolutionary optimization algorithm instead of the usual backpropagation algorithm is used to train the variances. The ability of the net to save training time depends on selectively growing the net structure and on the capability of the algorithm to preserve the locality of the activation functions.

Moreover, reported are comparisons with other incremental algorithm in the literature. Such comparisons show that our net perform better both in terms of net size (few hidden neuron are sufficient to reach very good approximations), and in terms of computational time (the training phase is accomplished on a PC computer and require few minutes).