This paper presents an axiomatic approach for constructing radial basis function (RBF) neural networks. This approach results in a broad variety of admissible RBF models, including those employing Gaussian RBFs. The form of the RBFs is determined by a generator function. New RBF models can be developed according to the proposed approach by selecting generator functions other than exponential ones, which lead to Gaussian RBFs. This paper also proposes a supervised learning algorithm based on gradient descent for training reformulated RBF neural networks constructed using the proposed approach. A sensitivity analysis of the proposed algorithm relates the properties of RBFs with the convergence of gradient descent learning. Experiments involving a variety of reformulated RBF networks generated by linear and exponential generator functions indicate that gradient descent learning is simple, easily implementable, and produces RBF networks that perform considerably better than conventional RBF models trained by existing algorithms.
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