Vach, Werner; Degens, Paul O. The system of common lower neighbours of a hierarchy. (English) Zbl 0733.92030 Classification and related methods of data analysis, Proc. 1st Conf. IFCS, Aachen/FRG 1987, 165-172 (1988). Summary: [For the entire collection see Zbl 0732.00020.] Each hierarchy can be characterized by its system of common lower neighbours. This corresponds to a special interpretation of a hierarchy as a system of separated sets in contrast to the usual interpretation of a hierarchy as a set of clusters. We give three applications of this alternative interpretation: first a reformulation and two extensions of the betweenness-axiom for consensus hierarchies, second a remarkable improvement of the Average-Linkage- method and third a suggestion of a new interesting class of hierarchical cluster methods. Cited in 1 Document MSC: 91C20 Clustering in the social and behavioral sciences Keywords:common loweer neighbours of a hierarchy; system of separated sets; betweenness-axiom; consensus hierarchies; Average-Linkage-method; hierarchical cluster methods Citations:Zbl 0732.00020 PDFBibTeX XML