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.

Open PDF

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

Tags

DTIC Thesaurus Topics

  • Air Force
  • Applied Mathematics
  • Beam Steering
  • Chebyshev Polynomials
  • Coefficients
  • Construction
  • Detection
  • Direction Finding
  • Mathematics
  • Neural Networks
  • Periodic Functions
  • Phased Arrays
  • Polynomials
  • Statistical Samples
  • Training
  • Translations
  • Universities

Readers

  • Calculus or Mathematical Analysis
  • Neural Network Machine Learning.

Technology Areas

  • AI & ML
  • AI & ML - Machine Learning Algorithms
  • AI & ML - Neural Networks