Theory of Refinement in Agglomerative Hierarchical Clustering

抄録

The theory of refinement in agglomerative clustering is studied. Although a simple relation holds as the necessary and sufficient condition so that a method generates refinements of clusters of the single linkage method, whether or not generalizations hold without the single linkage is unknown. Here a counterexample is shown between the average linkage and the complete linkage, which shows this theory is far from trivial. Observation of this theory leads us to a family of new methods using convex closures. Problems to be solved for the convex closure methods are discussed.