Testing of Clustering (2000)
| Venue: | In Proc. 41th Annu. IEEE Sympos. Found. Comput. Sci |
| Citations: | 51 - 11 self |
BibTeX
@INPROCEEDINGS{Alon00testingof,
author = {Noga Alon and Seannie Dar and Michal Parnas and Dana Ron},
title = {Testing of Clustering},
booktitle = {In Proc. 41th Annu. IEEE Sympos. Found. Comput. Sci},
year = {2000},
pages = {240--250}
}
Years of Citing Articles
OpenURL
Abstract
A set X of points in ! d is (k; b)-clusterable if X can be partitioned into k subsets (clusters) so that the diameter (alternatively, the radius) of each cluster is at most b. We present algorithms that by sampling from a set X , distinguish between the case that X is (k; b)-clusterable and the case that X is ffl-far from being (k; b 0 )-clusterable for any given 0 ! ffl 1 and for b 0 b. In ffl-far from being (k; b 0 )-clusterable we mean that more than ffl \Delta jX j points should be removed from X so that it becomes (k; b 0 )-clusterable. We give algorithms for a variety of cost measures that use a sample of size independent of jX j, and polynomial in k and 1=ffl. Our algorithms can also be used to find approximately good clusterings. Namely, these are clusterings of all but an ffl-fraction of the points in X that have optimal (or close to optimal) cost. The benefit of our algorithms is that they construct an implicit representation of such clusterings in time independ...







