Exact classification with two-layered perceptrons

P.J. Zwietering, E.H.L. Aarts, J. Wessels

Research output: Contribution to journalArticleScientificpeer-review

Abstract

We study the capabilities of two-layered perceptrons for classifying exactly a given subset. Both necessary and sufficient conditions are derived for subsets to be exactly classifiable with two-layered perceptrons that use the hard-limiting response function. The necessary conditions can be viewed as generalizations of the linear-separability condition of one-layered perceptrons and confirm the conjecture that the capabilities of two-layered perceptrons are more limited than those of three-layered perceptrons. The sufficient conditions show that the capabilities of two-layered perceptrons extend beyond the exact classification of convex subsets. Furthermore, we present an algorithmic approach to the problem of verifying the sufficiency condition for a given subset.
Original languageEnglish
Pages (from-to)143-156
Number of pages14
JournalInternational Journal of Neural Systems
Volume3
Issue number2
DOIs
Publication statusPublished - 1992
Externally publishedYes

Fingerprint

Neural networks

Cite this

Zwietering, P.J. ; Aarts, E.H.L. ; Wessels, J. / Exact classification with two-layered perceptrons. In: International Journal of Neural Systems. 1992 ; Vol. 3, No. 2. pp. 143-156.
@article{dfed8d6400df4af6977f9d8b4b7bd6b7,
title = "Exact classification with two-layered perceptrons",
abstract = "We study the capabilities of two-layered perceptrons for classifying exactly a given subset. Both necessary and sufficient conditions are derived for subsets to be exactly classifiable with two-layered perceptrons that use the hard-limiting response function. The necessary conditions can be viewed as generalizations of the linear-separability condition of one-layered perceptrons and confirm the conjecture that the capabilities of two-layered perceptrons are more limited than those of three-layered perceptrons. The sufficient conditions show that the capabilities of two-layered perceptrons extend beyond the exact classification of convex subsets. Furthermore, we present an algorithmic approach to the problem of verifying the sufficiency condition for a given subset.",
author = "P.J. Zwietering and E.H.L. Aarts and J. Wessels",
year = "1992",
doi = "10.1142/S0129065792000127",
language = "English",
volume = "3",
pages = "143--156",
journal = "International Journal of Neural Systems",
issn = "0129-0657",
publisher = "World Scientific Publishing Co. Pte Ltd",
number = "2",

}

Exact classification with two-layered perceptrons. / Zwietering, P.J.; Aarts, E.H.L.; Wessels, J.

In: International Journal of Neural Systems, Vol. 3, No. 2, 1992, p. 143-156.

Research output: Contribution to journalArticleScientificpeer-review

TY - JOUR

T1 - Exact classification with two-layered perceptrons

AU - Zwietering, P.J.

AU - Aarts, E.H.L.

AU - Wessels, J.

PY - 1992

Y1 - 1992

N2 - We study the capabilities of two-layered perceptrons for classifying exactly a given subset. Both necessary and sufficient conditions are derived for subsets to be exactly classifiable with two-layered perceptrons that use the hard-limiting response function. The necessary conditions can be viewed as generalizations of the linear-separability condition of one-layered perceptrons and confirm the conjecture that the capabilities of two-layered perceptrons are more limited than those of three-layered perceptrons. The sufficient conditions show that the capabilities of two-layered perceptrons extend beyond the exact classification of convex subsets. Furthermore, we present an algorithmic approach to the problem of verifying the sufficiency condition for a given subset.

AB - We study the capabilities of two-layered perceptrons for classifying exactly a given subset. Both necessary and sufficient conditions are derived for subsets to be exactly classifiable with two-layered perceptrons that use the hard-limiting response function. The necessary conditions can be viewed as generalizations of the linear-separability condition of one-layered perceptrons and confirm the conjecture that the capabilities of two-layered perceptrons are more limited than those of three-layered perceptrons. The sufficient conditions show that the capabilities of two-layered perceptrons extend beyond the exact classification of convex subsets. Furthermore, we present an algorithmic approach to the problem of verifying the sufficiency condition for a given subset.

U2 - 10.1142/S0129065792000127

DO - 10.1142/S0129065792000127

M3 - Article

VL - 3

SP - 143

EP - 156

JO - International Journal of Neural Systems

JF - International Journal of Neural Systems

SN - 0129-0657

IS - 2

ER -