The principle of F-projection, in sequential function estimation, provides a theoretical foundation for a class of gaussian radial basis function networks known as the resource allocating networks (RAN). The ad hoc rules for adaptively changing the size of RAN architectures can be justified from a geometric growth criterion defined in the function space. In this paper, we show that the same arguments can be used to arrive at a pruning with replacement rule for RAN architectures with a limited number of units. We illustrate the algorithm on the laser time series prediction problem of the Santa Fe competition and show that results similar to those of the winners of the competition can be obtained with pruning and replacement.

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