Approximation by Ridge Functions and Neural Networks

Abstract

We investigate the efficiency of approximation by linear combinations of ridge functions... Thus the theorems we obtain show that this form of ridge approximation has the same efficiency of approximation as other more traditional methods of multivariate approximation such as polynomials splines or wavelets The theorems we obtain can be applied to show that a feed forward neural network with one hidden layer of computational nodes given by certain sigmoidal function sigma will also have this approximation efficiency. Minimal requirements are made of the sigmoidal functions and in particular our results hold for the unit impulse function.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1997
Accession Number
AD1000053

Entities

People

  • Pencho Petrushev

Organizations

  • University of South Carolina

Tags

DTIC Thesaurus Topics

  • Cartesian Coordinates
  • Chebyshev Polynomials
  • Contracts
  • Coordinate Systems
  • Decomposition
  • Fourier Analysis
  • Identities
  • Inequalities
  • Integrals
  • Mathematics
  • Neural Networks
  • Numbers
  • Polynomials
  • Real Numbers
  • Sequences
  • South Carolina
  • Spherical Harmonics

Fields of Study

  • Mathematics

Readers

  • Approximation Theory.
  • Neural Network Machine Learning.

Technology Areas

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