The paper investigates whether the three axioms of scale invariance, richness, and consistency—known to be mutually exclusive for flat clustering—can be jointly satisfied by hierarchical clustering. It demonstrates that, unlike the flat case, there exist uncountably many hierarchical clustering methods that meet all three axioms, termed admissible methods. The authors construct several such methods, explore a refinement partial order among them, and show that while the set of admissible methods is diverse, every admissible method shares a common backbone of well‑separated clusters.
By Daichi Kuroda, Maximilien Dreveton, Matthias Grossglauser, Patrick Thiran
arXiv:2604. 23628v2 Announce Type: replace-cross Abstract: Hierarchical clustering is a fundamental task in data analysis, but classical methods have long lacked a principled objective function.
By Ryuki Tsukuba, Kazutoshi Ando
Consider the following variation on the Hierarchical Clustering problem: Usually, while building a hierarchical clustering, one recursively partitions the data until each cluster becomes a singleton. We relax the halting condition of the recursive process to stop whenever the remaining cluster is a graph belonging to a class $\mathcal{F}$.
arXiv:2607. 13217v1 Announce Type: cross Abstract: Consider the following variation on the Hierarchical Clustering problem: Usually, while building a hierarchical clustering, one recursively partitions the data until each cluster becomes a singleton.
By Micha{\l} Szyfelbein, Dariusz Dereniowski
arXiv:2606. 18972v1 Announce Type: cross Abstract: Extracting a flat clustering solution from a hierarchy is a common task in practical cluster analysis and can be formulated as an optimisation problem.
By Connor Simpson, Ricardo J. G. B. Campello
Extracting a flat clustering solution from a hierarchy is a common task in practical cluster analysis and can be formulated as an optimisation problem. Existing approaches focus on finding a single optimal solution.