2016/10/13 by Weiyu Huang, Alejandro Ribeiro, Huang, Weiyu +1 · 1 voice
Computer Science · Physics and Astronomy · #Advanced Clustering Algorithms Research #Complex Network Analysis Techniques #FOS: Computer and information sciences #FOS: Physical sciences #Physics and Society (physics.soc-ph) #Social and Information Networks (cs.SI) #Topological and Geometric Data Analysis #cs.SI #physics.soc-ph
paper · pdf · doi:10.48550/arxiv.1610.04274
openalex publication_date 2016/10/13 · arxiv published 2016/10/13 · arxiv updated 2016/10/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 of hierarchical clustering methods is based on defining admissible methods to be those methods that abide to the axioms of value - nodes in a metric space with two nodes are clustered together at the convex combination of the distance bounds between them - and transformation - when both distance bounds are reduced, the output may become more clustered but not less. Two admissible methods are constructed and are shown to provide universal upper and lower bounds in the space of admissible methods. Practical implications are explored by clustering moving points via snapshots and by clustering networks representing brain structural connectivity using the lower and upper bounds of the network distance. The proposed clustering methods succeed in identifying underlying clustering structures via the maximum and minimum distances in all snapshots, as well as in differentiating brain connectivity networks of patients from those of healthy controls.