Gradient descent learning of radial basis neural networks

An axiomatic approach for building RBF neural networks and a supervised learning algorithm based on gradient descent for their training are presented, which results in a broad variety of admissible RBF models, including those employing Gaussian radial basis functions.

Abstract

This paper presents an axiomatic approach for building RBF neural networks and also proposes a supervised learning algorithm based on gradient descent for their training. This approach results in a broad variety of admissible RBF models, including those employing Gaussian radial basis functions. The form of the radial basis functions is determined by a generator function. A sensitivity analysis explains the failure of gradient descent learning on RBF networks with Gaussian radial basis functions, which are generated by an exponential generator function. The same analysis verifies that RBF networks generated by a linear generator function are much more suitable for gradient descent learning. Experiments involving such RBF networks indicate that the proposed gradient descent algorithm guarantees fast learning and very satisfactory generalization ability.