On the minimal teaching sets of two-dimensional threshold functions
Combinatorics
2015-01-27 v2 Machine Learning
Number Theory
Abstract
It is known that a minimal teaching set of any threshold function on the twodimensional rectangular grid consists of 3 or 4 points. We derive exact formulae for the numbers of functions corresponding to these values and further refine them in the case of a minimal teaching set of size 3. We also prove that the average cardinality of the minimal teaching sets of threshold functions is asymptotically 7/2. We further present corollaries of these results concerning some special arrangements of lines in the plane.
Cite
@article{arxiv.1307.1058,
title = {On the minimal teaching sets of two-dimensional threshold functions},
author = {Max A. Alekseyev and Marina G. Basova and Nikolai Yu. Zolotykh},
journal= {arXiv preprint arXiv:1307.1058},
year = {2015}
}
Comments
11 pages, 4 figures