Wavelet neural networks employing over-complete number of compactly supported non-orthogonal wavelets and their applications

This paper proposes two types of new neuron models, WS neuron (wavelet synapse neuron) and WA neuron (wavelet activation function neuron), which are obtained by modifying a traditional neuron model with non-orthogonal wavelet bases, while Boubez et al. (1993) employed orthonormal wavelets. Four types of typical wavelet neural networks employing WS and/or WA neurons are discussed. The simplest wavelet neural network exhibits much higher ability of generalization and much shorter time for learning rather than a three-layered feedforward neural network. Furthermore the wavelet neural network is guaranteed to give the global minimum. Other three wavelet neural networks are examined for predicting chaotic behaviour of a nonlinear dynamical system. The performance in learning speed and prediction of wavelet neural networks are more significant than a four-layered feedforward neural network