SHATTERING ALL SETS OF K POINTS IN GENERAL POSITION REQUIRES (K-1) 2 PARAMETERS/

Authors
SONTAG ED
Citation
Ed. Sontag, SHATTERING ALL SETS OF K POINTS IN GENERAL POSITION REQUIRES (K-1) 2 PARAMETERS/, Neural computation, 9(2), 1997, pp. 337-348
Citations number
10
Categorie Soggetti
Computer Sciences","Computer Science Artificial Intelligence",Neurosciences
Journal title
Neural computation → ACNP
ISSN journal
08997667
Volume
9
Issue
2
Year of publication
1997
Pages
337 - 348
Database
ISI
SICI code
0899-7667(1997)9:2<337:SASOKP>2.0.ZU;2-C
Abstract
For classes of concepts defined by certain classes of analytic functio ns depending on n parameters, there are nonempty open sets of samples of length 2n + 2 that cannot be shattered. A slighly weaker result is also proved for piecewise-analytic functions. The special case of neur al networks is discussed.