17 research outputs found
Analysis of Agglomerative Clustering
The diameter -clustering problem is the problem of partitioning a finite
subset of into subsets called clusters such that the maximum
diameter of the clusters is minimized. One early clustering algorithm that
computes a hierarchy of approximate solutions to this problem (for all values
of ) is the agglomerative clustering algorithm with the complete linkage
strategy. For decades, this algorithm has been widely used by practitioners.
However, it is not well studied theoretically. In this paper, we analyze the
agglomerative complete linkage clustering algorithm. Assuming that the
dimension is a constant, we show that for any the solution computed by
this algorithm is an -approximation to the diameter -clustering
problem. Our analysis does not only hold for the Euclidean distance but for any
metric that is based on a norm. Furthermore, we analyze the closely related
-center and discrete -center problem. For the corresponding agglomerative
algorithms, we deduce an approximation factor of as well.Comment: A preliminary version of this article appeared in Proceedings of the
28th International Symposium on Theoretical Aspects of Computer Science
(STACS '11), March 2011, pp. 308-319. This article also appeared in
Algorithmica. The final publication is available at
http://link.springer.com/article/10.1007/s00453-012-9717-