Wavelet neural networks for function learning
- 1 June 1995
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Signal Processing
- Vol. 43 (6) , 1485-1497
- https://doi.org/10.1109/78.388860
Abstract
A wavelet-based neural network is described. The structure of this network is similar to that of the radial basis function (RBF) network, except that in the present paper the radial basis functions are replaced by orthonormal scaling functions that are not necessarily radial-symmetric. The efficacy of this type of network in function learning and estimation is demonstrated through theoretical analysis and experimental results. In particular, it has been shown that the wavelet network has universal and L/sup 2/ approximation properties and is a consistent function estimator. Convergence rates associated with these properties are obtained for certain function classes where the rates avoid the "curse of dimensionality". In the experiments, the wavelet network performed well and compared favorably to the MLP and RBF networks.<>Keywords
This publication has 16 references indexed in Scilit:
- Regression modeling in back-propagation and projection pursuit learningIEEE Transactions on Neural Networks, 1994
- Pointwise convergence of wavelet expansionsBulletin of the American Mathematical Society, 1994
- Analysis and synthesis of feedforward neural networks using discrete affine wavelet transformationsIEEE Transactions on Neural Networks, 1993
- Approximation of the delta function by waveletsJournal of Approximation Theory, 1992
- Nonseparable multidimensional perfect reconstruction filter banks and wavelet bases for R/sup n/IEEE Transactions on Information Theory, 1992
- Wavelet networksIEEE Transactions on Neural Networks, 1992
- Networks for approximation and learningProceedings of the IEEE, 1990
- Layered Neural Networks with Gaussian Hidden Units as Universal ApproximationsNeural Computation, 1990
- A theory for multiresolution signal decomposition: the wavelet representationPublished by Institute of Electrical and Electronics Engineers (IEEE) ,1989
- Fast Learning in Networks of Locally-Tuned Processing UnitsNeural Computation, 1989