Adaptive radial basis function nonlinearities, and the problem of generalisation

The author and D.S. Broomhead developed (1988) the opinion that most current feedforward layered neural networks perform a curve fitting operation in a high-dimensional space. To create the analogy, it was necessary to generalise earlier papers´ assumptions, and so a mechanism for choosing radial basis functions was needed. The method involves optimisation. It is concluded that nonlinear optimisation of the first layer parameters is beneficial only when a minimal network is required to solve a given problem, since the same generalisation performance can be achieved simply by using more centres and adapting only the final layer by linear optimisation. The processing time is many orders of magnitude longer when full adaptation was used. Nonlinear optimisation cannot be used to improve the generalisation performance of the network. Choice of the nonlinearity is not crucial