Approximation by nonlinear wavelet networks

By combining the class of feedforward neural networks and results from the wavelet theory, a class of networks call wavelet networks that can be used to approximate any nonlinear function is proposed. A stochastic gradient procedure for black-box identification of nonlinear static systems based on this class of networks is developed. This method was inspired by both the neural networks and the wavelet decomposition. The basic idea is to replace the neurons by more powerful computing units obtained by cascading an affine transform and a multidimensional wavelet. Then these affine transforms and the synaptic weights must be identified from possibly noise corrupted input/output data. It is pointed out that for comparable number of adjusted coefficients, the complexity of input/output map realized by the wavelet network is much smaller than that realized by the wavelet decomposition, since many more units are needed in the latter case