Recurrent wavelet networks

Neural networks have been established as a general approximation tool for fitting nonlinear models for input/output data. On the other hand, the wavelet decomposition is a powerful tool for functional approximation. In this paper we improve upon the connection between these two fields. A fast supervised learning algorithm is presented. Inspired by the real time recurrent learning algorithm (RTRL) of Williams and Zipser (1989), the algorithm learns more rapidly than typical implementation of backpropagation, while achieving improved generalization. Furthermore, unlike most traditional functional approximators, the algorithm is well suited for use in real time adaptive signal processing. As an illustration the algorithm is applied to the prediction of a chaotic time series and identification of a complex nonlinear dynamic system