Graphs Implied by the Jardine-Sibson Overlapping Clustering Methods, Bk

A cluster analysis can be Interpreted as a function which maps the input dissimilarity matrix into an output dissimilarity matrix whose elements indicate the dissimilarity between pairs of objects. Some cluster analyses leave invariant the dissimilarities between certain pairs of objects. The set of elements left invariant by the single-linkage clustering method corresponds to the edges in the minimum spanning tree. The properties of the graphs whose edges correspond to the dissimilarities left invariant by the Jardine-Sibson Bk clustering method are examined and algorithms are given for the determination of Bk clusters.