PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Partitioning points by parallel planes
Martin Anthony
Discrete Mathematics Volume 282, Number 1-3, pp. 17-21, 2004. ISSN 0012-365X

Abstract

A new upper bound is given on the number of ways in which a set of N points in R^n can be partitioned by k parallel hyperplanes. This bound improves upon a result of Olafsson and Abu-Mostafa (IEEE Trans. Pattern Anal. Machine Intell. 10 (2) (1988) 277); it agrees with the known (tight) result for the case k=1; and it is, for fixed k and n, tight to within a constant. A previously published claimed improvement to the bound of Olafsson and Abu-Mostafa is shown to be incorrect.

EPrint Type:Article
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Computational, Information-Theoretic Learning with Statistics
ID Code:116
Deposited By:Martin Anthony
Deposited On:22 May 2004