A method for finding the optimal number of learning samples and hidden units for function approximation with a feedforward network

Abstract

This paper presents a methodology to estimate the optimal number oflearning samples and the number of hidden units needed to obtaina desired accuracy of a function approximation by a feedforward network.The representation error and the generalization error, componentsof the total approximation error are analyzed and the approximationaccuracy of a feedforward network is investigated as a function ofthe number of hidden units and the number of learning samples. Basedon the asymptotical behaviour of the approximation error, an asymptoticalmodel of the error function (AMEF) is introduced of which the parameterscan be determined experimentally. In combination with knowledge aboutthe computational complexity of the learning rule an optimal learningset size and number of hidden units can be found resulting in a minimumcomputation time for a given desired precision of the approximation.