Axiomatic hierarchical clustering for intervals of metric distances
Weiyu Huang, Alejandro Ribeiro · 2016
This paper considers metric spaces where distances between a pair of nodes are represented by distance intervals. The goal is to study methods for the determination of hierarchical clusters, i.e., a family of nested partitions indexed by a resolution parameter, induced from the given distance intervals of the metric spaces. Our construction is based on defining admissible methods to be those methods that abide to the axioms of value and transformation. Two admissible methods are constructed and are shown to provide upper and lower bounds in the space of admissible methods. Practical implications are explored by clustering networks representing brain structural connectivity using the lower and upper bounds of the network distance. The proposed clustering methods succeed in differentiating brain connectivity networks of patients from those of healthy controls.