Trees and Hierarchical Structures

The "e;raison d'etre"e; of hierarchical dustering theory stems from one basic phe- nomenon: This is the notorious non-transitivity of similarity relations. In spite of the fact that very often two objects may be quite similar to a third without being that similar to each other, one still wants to dassify objects according to their similarity. This should be achieved by grouping them into a hierarchy of non-overlapping dusters such that any two objects in ~ne duster appear to be more related to each other than they are to objects outside this duster. In everyday life, as well as in essentially every field of scientific investigation, there is an urge to reduce complexity by recognizing and establishing reasonable das- sification schemes. Unfortunately, this is counterbalanced by the experience of seemingly unavoidable deadlocks caused by the existence of sequences of objects, each comparatively similar to the next, but the last rather different from the first.