Wavelets and Neural Networks
Abstract
During our previous work, we had established a very dose connection between polynomial approximation and approximation by neural networks. In fact, we had developed a unified theory of the approximation properties of neural networks, radial basis function (RBF) networks, and generalized regularization networks. Our networks provided an optimal approximation to a class of functions, where the only known a priori assumption was the number of continuous derivatives. The networks did not require ally training in the classical sense, but were given explicitly in terms of the coefficients of the target function in certain orthogonal expansions. Our current objectives are the following. Modify the formulas for the networks, so that the networks can be obtained in terms of the values of the target function at judiciously chosen points. Develop polynomial wavelets with an eventual objective of integrating these with the theory of 'generalized translation networks' which we had previously developed.
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 01, 1999
- Accession Number
- ADA385766
Entities
People
- H. N. Mhaskar
Organizations
- California State University, Los Angeles