Decision region approximation by polynomials or neural networks

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

doi:10.1109/18.568700

Decision region approximation by polynomials or neural networks

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

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

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).

Original language	English
Pages (from-to)	903-907
Number of pages	5
Journal	IEEE Transactions on Information Theory
Volume	43
Issue number	3
DOIs	https://doi.org/10.1109/18.568700
Publication status	Published - 1997

Access to Document

10.1109/18.568700

Cite this

@article{123d434c6fce437d908415210d3a0320,

title = "Decision region approximation by polynomials or neural networks",

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 = "Classification, Decision region, Neural networks, Polynomials, Rate of approximation",

author = "Blackmore, {Kim L.} and Williamson, {Robert C.} and Mareels, {Iven M.Y.}",

year = "1997",

doi = "10.1109/18.568700",

language = "English",

volume = "43",

pages = "903--907",

journal = "IEEE Transactions on Information Theory",

issn = "0018-9448",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

number = "3",

}

TY - JOUR

T1 - Decision region approximation by polynomials or neural networks

AU - Blackmore, Kim L.

AU - Williamson, Robert C.

AU - Mareels, Iven M.Y.

PY - 1997

Y1 - 1997

N2 - 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).

AB - 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).

KW - Classification

KW - Decision region

KW - Neural networks

KW - Polynomials

KW - Rate of approximation

UR - http://www.scopus.com/inward/record.url?scp=0031139265&partnerID=8YFLogxK

U2 - 10.1109/18.568700

DO - 10.1109/18.568700

M3 - Article

SN - 0018-9448

VL - 43

SP - 903

EP - 907

JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

IS - 3

ER -

Decision region approximation by polynomials or neural networks

Abstract

Access to Document

Other files and links

Fingerprint

Cite this