Hierarchical Clustering Given Confidence Intervals of Metric Distances

This paper considers metric the exact dissimilarities between pairs of points are not unknown but known to belong to some interval. 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 dissimilarities. Our construction of hierarchical clustering methods is based on defining admissible methods to be those methods that satisfy the axioms of value-nodes in a metric space with two nodes are clustered together at the convex combination of the upper and lower bounds determined by a parameter-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 bounds in the space of admissible methods. Practical implications are explored by clustering moving points via snapshots and by clustering coauthorship networks representing collaboration between researchers from different communities. The proposed clustering methods succeed in identifying underlying hierarchical clustering structures via the maximum and minimum distances in all snapshots, as well as in differentiating collaboration patterns in journal publications between different research communities based on bounds of network distances.