Orthonormal Function Neural Network for Nonlinear System Modeling

Nonlinear system identiication is often solved by determining a set of coeecients for a nite number of xed nonlinear basis functions. However, if the input data is drawn from a high{dimensional space, the number of required basis functions grows exponentially with dimension, and this has led many authors to consider subset model selection techniques. In this paper we describe a one hidden layer neural network which employs a set of signal independent orthonormal expansions, and a scaling derived from an estimate of the vector probability density function of the input data. The orthonormality of the basis functions allows the contribution of each basis function to the model to be calculated independently, since their contribution will be directly related to the magnitude of the corresponding weights in the output layer. The resulting neural network retains the desirable linear in the parameters nature of radial basis function neural networks.