Wavelet neural networks for function learning

A wavelet-based neural network is described. The structure of this network is similar to that of the radial basis function (RBF) network, except that in the present paper the radial basis functions are replaced by orthonormal scaling functions that are not necessarily radial-symmetric. The efficacy of this type of network in function learning and estimation is demonstrated through theoretical analysis and experimental results. In particular, it has been shown that the wavelet network has universal and L² approximation properties and is a consistent function estimator. Convergence rates associated with these properties are obtained for certain function classes where the rates avoid the “curse of dimensionality”. In the experiments, the wavelet network performed well and compared favorably to the MLP and RBF networks