The estimation theory and optimization algorithm for the number of hidden units in the higher-order feedforward neural network

Estimation theory for the number of the hidden units in the higher-order feedforward neural network has been investigated in this paper and the authors have demonstrated that: for an arbitrary function Y defined on the set S⊂R^d with (m+1)m/2 elements, the second-order three-layer feedforward neural network with m hidden units can realize function Y sufficiently. With the theories discussed in Kayama et al. (1990), the algorithm for obtaining the optimal number of hidden units has been improved in this paper. Finally, the estimation theory and the developed method are applied to the problems of the prediction of time series and system identification by higher-order neural network, the simulation results show these methods are very effective