Multidimensional Wavelet Neural Network Theory And Applications, In The Eeg Inverse Problem

"Curse of dimensionality"has always been a difficult problem in both research and application fields of wavelet networks, which greatly prohibits the application of wavelet network in high dimensional cases. Up to now, there's no practical way good enough to solve it. In this paper, we profoundly analysis the structure similarity of wavelet networks(WNN) and radial basis function networks(RBFN). Then, based on RBF network model and the theory of single-scaling wavelet frame, we constructed a multi-dimensional(multi-input multi-output) single-scaling radial wavelet network by reducing the redundancy among bases as much as possible. The sparseness of available training samples is analyzed and a parameter λ called similarity threshold is introduced to help to eliminate duplicate nodes in the hidden layer. Finally, Gram- Schmidt algorithm is used to orthonormalize and further select optimal wavelets. Satisfactory results are got in the implementation of this method to inverse EEG problem.