PUB - Publikationen an der Universität Bielefeld

Branching structures, alias topological tree structures are fundamental to any hierarchical classification that aims to relate objects according to their similarities or dissimilarities. This paper provides a rigorous treatment of these structures, and continues previous work of Colonius and Schulze on H-structures. Thus extensive use is made of the so-called neighbors relation associated with a dissimilarity index. Arbitrary dissimilarity data are then analyzed by comparing their neighbors relations with ideal, that is, tree-like relations: if it matches an ideal relation, then one can readily construct a tree representing the data that is optimal in a certain sense. Finally, some algorithms are proposed for fitting observed data to tree-like data.