Une représentation visuelle des classes empiétantes: les pyramides. (A visual representation of overlapping classes: the pyramids). (French) Zbl 0592.62052

Diday, E.

RAIRO, Autom. Prod. Inf. Ind. 20, 475-526 (1986).

Summary: The problem of overlapping clusters is frequently encountered in practice. Pyramids allow a visual representation of such clusters and constitute a natural extension of hierarchies; they give more information than hierarchies. They induce a special dissimilarity index called ”pyramidal index” closer to the data than ultrametrics. This set of indices (which use the notion of order on the single objects) is in bijection with the set of pyramids and contains the set of ultrametrics.
Constructive procedures for the representation of a pyramid are given; the problem of optimal choice of a pyramid is discussed and more specifically the concept of ”dominant” and ”sub-dominant” pyramids. It is shown how hierarchies may be enriched by ”pyramization” and how it is possible to ”hierarchize” a pyramid.
Among other results, we show that it is possible to obtain a computer program which gives a representation which is more or less a hierarchy or a pyramid depending on a given threshold. We give different other types of representations of a pyramidal index (planer, polygonal, ”thick tree” and ”guirlande”).

MSC:

62H30	Classification and discrimination; cluster analysis (statistical aspects)
62-07	Data analysis (statistics) (MSC2010)

Keywords:

pattern recognition; overlapping clusters; hierarchies; ultrametrics; pyramids