New bounds on the cohesion of complete-link and other linkage methods for agglomeration clustering
This work addresses theoretical gaps in evaluating clustering quality for practitioners, but it is incremental as it builds on existing bounds.
The paper improves bounds on the maximum diameter of clusters produced by complete-link hierarchical clustering in metric spaces, with one new bound separating it from single-link to show complete-link is better for compact clusters, and extends techniques to derive upper bounds for a class including average-link.
Linkage methods are among the most popular algorithms for hierarchical clustering. Despite their relevance the current knowledge regarding the quality of the clustering produced by these methods is limited. Here, we improve the currently available bounds on the maximum diameter of the clustering obtained by complete-link for metric spaces. One of our new bounds, in contrast to the existing ones, allows us to separate complete-link from single-link in terms of approximation for the diameter, which corroborates the common perception that the former is more suitable than the latter when the goal is producing compact clusters. We also show that our techniques can be employed to derive upper bounds on the cohesion of a class of linkage methods that includes the quite popular average-link.