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.
arXiv:2606. 04777v1 Announce Type: new Abstract: Clustering is increasingly used to support high-impact decisions, yet standard objectives such as $k$-means can produce clusterings that treat demographic groups unequally.
arXiv:2304. 13917v4 Announce Type: replace Abstract: In recent years, there has been a surge in effort to formalize notions of fairness in machine learning.
arXiv:2609.07974v1 Announce Type: cross Abstract: Fairness in clustering has attracted sustained research interest, motivated by the need to ensure equitable representation of protected groups in mac...
The paper presents new algorithms for fair k‑center clustering in Euclidean spaces, where a dataset is divided into groups and each group has a limit on the number of centers that can be chosen. A parameterized approximation algorithm achieves a 2.732 ratio, which is improved to 2.414 with exponential time in k. By integrating this into a one‑pass streaming framework, the authors obtain streaming approximations of 4.464 (improvable to 3.828) and a polynomial‑time streaming algorithm with a 4.732 ratio, further reduced to 4.42, surpassing previous state‑of‑the‑art results. Experiments confirm that these methods outperform existing approaches in clustering accuracy.
arXiv:2608.24818v1 Announce Type: new Abstract: Neighborhood-based fairness audits evaluate individual fairness by comparing predictions among similar individuals in feature space. Despite their wide...
arXiv:2608.29097v1 Announce Type: cross Abstract: This paper studies the problem of proportionally fair clustering, where the goal is to select $k$ ``centers'' from a metric space that fairly represe...
arXiv:2602. 18201v2 Announce Type: replace Abstract: Unsupervised representations are widely assumed to be neutral with respect to sensitive attributes when those attributes are withheld from training.
arXiv:2609.06394v1 Announce Type: cross Abstract: Massive datasets in modern machine learning have made data reduction a central challenge, particularly for clustering tasks where memory and computat...
arXiv:2606. 17810v1 Announce Type: cross Abstract: In this paper, we establish a set of theoretical impossibility results, termed the No-Free-Fairness theorems, that identify three fundamental sources of disparity in learning systems.
arXiv:2607. 18119v1 Announce Type: cross Abstract: Fair clustering aims to make cluster assignments independent of sensitive attributes, but this goal becomes challenging when multiple sensitive attributes jointly define many subgroups.
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.
arXiv:2608. 04014v1 Announce Type: cross Abstract: The subdominant (minmax) ultrametric is a canonical tree-structured summary of a dissimilarity matrix, arising equivalently as the ultrametric induced by single-linkage clustering.