Decision region approximation by polynomials or neural networks

Author

Blackmore, Kim L. ; Williamson, Robert C. ; Mareels, Iven M Y

Author_Institution

Commun. Div., Defence Sci. & Technol. Organ., Salisbury, SA, Australia

Volume

43

Issue

3

fYear

1997

fDate

5/1/1997 12:00:00 AM

Firstpage

903

Lastpage

907

Abstract

We give degree of approximation results for decision regions which are defined by polynomial and neural network parametrizations. The volume of the misclassified region is used to measure the approximation error, and results for the degree of L₁ approximation of functions are used. For polynomial parametrizations, we show that the degree of approximation is at least 1, whereas for neural network parametrizations we prove the slightly weaker result that the degree of approximation is at least r, where r can be any number in the open interval (0, 1)

Keywords

approximation theory; decision theory; feedforward neural nets; network parameters; parameter estimation; polynomials; approximation error; approximation results; decision region approximation; misclassified region volume; neural network parametrizations; polynomial parametrizations; polynomials; Algorithm design and analysis; Approximation error; Australia Council; Computer vision; Machine learning; Neural networks; Pattern recognition; Polynomials; Volume measurement;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/18.568700

Filename

568700