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Discrete Affine Wavelet Transforms For Anaylsis And Synthesis Of Feedfoward Neural Networks

In this paper we show that discrete affine wavelet transforms can provide a tool for the analysis and synthesis of standard feedforward neural networks. It is shown that wavelet frames for L2(IR) can be constructed based upon sigmoids. The spatia-spectral localization property of wavelets can be exploited in defining the topology and determining the weights of a feedforward network. Training a network constructed using the synthesis procedure described here involves minimization of a convex cost functional and therefore avoids pitfalls inherent in standard backpropagation algorithms. Extension of these methods to L2(IRN) is also discussed.