A Sufficient Condition for the Correct Recognition of Two Classes in Hierarchical Clustering
R. Henrion, Günter Henrion, Albrecht Gnauck · Acta hydrochimica et hydrobiologica · 1990
Abstract Hierarchical clustering is a widely used instrument for the investigation of multivariate data sets as they arise for instance in the chemistry of waters. Frequently one is confronted to the problem that detected clusters do not correspond sufficiently to classes of objects which a priori had been expected to occur. Then it may be that the chosen clustering algorithm did not work well. However it is more likely that the unsatisfactory recognition of clusters is due to a lack of information in data. For the simplest case of two clusters we shall prove that single, complete and average (weighted and unweighted) linkage guarantee correct recognition, provided that the two expected classes of objects are ‘real clusters’. To this aim a theoretically sufficient condition is developed.