The paper investigates whether the impossibility results for flat clustering—specifically Kleinberg’s axioms of scale invariance, richness, and consistency—extend to hierarchical clustering. It demonstrates that, unlike the flat case, there exist uncountably many hierarchical clustering methods that satisfy 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 method shares a common backbone of well‑separated clusters.
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: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
arXiv:2607. 10305v1 Announce Type: cross Abstract: Byzantine-robust aggregation rules such as multi-Krum assume a central coordinator, and decentralising them is obstructed by the rules themselves: they are globally coupled, non-associative, and discontinuous, so an ulpscale perturbation can flip the selected subset, moving the output by a non-vanishing amount.
By Ryan Gillespie
The paper investigates hierarchical clustering under an individual fairness constraint that limits relative distortion within local k‑nearest neighborhoods. It formulates this as a feasibility problem over dominated ultrametrics, characterizes the minimal multiplicative slack needed, identifies a sharp local threshold, proves stability under bounded perturbations, establishes monotonicity in k, and demonstrates a Θ(log n) separation between local and global realizability. Experiments on synthetic and real‑world datasets corroborate the theoretical findings.
By Binita Maity, Shrutimoy Das