Abstract
A new adaptive learning algorithm for constructing and training wavelet networks is proposed based on the time-frequency localization properties of wavelet frames and the adaptive projection algorithm. The exponential convergence of the adaptive projection algorithm in finite-dimensional Hilbert spaces is constructively proved, with exponential decay ratios given with high accuracy. The learning algorithm can sufficiently utilize the time-frequency information contained in the training data, iteratively determines the number of the hidden layer nodes and the weights of wavelet networks, and solves the problem of structure optimization of wavelet networks. The algorithm is simple and efficient, as illustrated by examples of signal representation and denoising.
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Zhang, Z., Liu, G. & Liu, F. Construction of a new adaptive wavelet network and its learning algorithm. Sci China Ser F 44, 93–103 (2001). https://doi.org/10.1007/BF02713968
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DOI: https://doi.org/10.1007/BF02713968