Approximating nonlinear functions via neural networks based on discrete affine wavelet transformations

Based on the discrete affine wavelet transforms, we develop a new "basis" for wavelet networks for better approximating non-smooth nonlinear functions. It is shown that the wavelet formalism supports a theoretical framework, and it is possible to perform both analysis and synthesis of feedforward neural networks. Using the spatio-spectral localization properties of wavelets, we can synthesize a feedforward network to reduce the training problem to one of convex optimization problem. Specifically, we have developed the algorithm for approximation of high-dimensional nonlinear functions. Finally, the inverted pendulum stabilizing problem is studied via the proposed wavelet neural networks in order to illustrate the usefulness of the developed theoretical framework.<>