Proceedings 41st Annual Symposium on Foundations of Computer Science (2000)

Redondo Beach, California

Nov. 12, 2000 to Nov. 14, 2000

ISSN: 0272-5428

ISBN: 0-7695-0850-2

pp: 240

N. Alon , Dept. of Math., Tel Aviv Univ., Israel

S. Dar , Dept. of Math., Tel Aviv Univ., Israel

M. Parnas , Dept. of Math., Tel Aviv Univ., Israel

D. Ron , Dept. of Math., Tel Aviv Univ., Israel

ABSTRACT

A set X of points in /spl Rfr//sup 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 /spl epsiv/-far from being (k,b')-clusterable for any given 0>/spl epsiv//spl les/1 and for b'/spl ges/b. In /spl epsiv/-far from being (k,b')-clusterable we mean that more than /spl epsiv/.|X| points should be removed from X so that it becomes (k,b')-clusterable. We give algorithms for a variety of cost measures that use a sample of size independent of |X|, and polynomial in k and 1//spl epsiv/. Our algorithms can also be used to find approximately good clusterings. Namely, these are clusterings of all but an /spl epsiv/-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 independent of |X|. That is, without actually having to partition all points in X, the implicit representation can be used to answer queries concerning the cluster any given point belongs to.

INDEX TERMS

pattern clustering; statistical analysis; computational complexity; clustering testing; sampling; cost measures; optimal cost; lower bounds

CITATION

S. Dar, N. Alon, D. Ron and M. Parnas, "Testing of clustering,"

*Proceedings 41st Annual Symposium on Foundations of Computer Science(FOCS)*, Redondo Beach, California, 2000, pp. 240.

doi:10.1109/SFCS.2000.892111

CITATIONS