Admissible Objectives for Hierarchical Clustering Formally Characterized
Tsukuba and Ando extend the theory of objective functions for hierarchical clustering, characterizing when functions recover ground-truth structures and introducing max-type variants.
Researchers characterize which objective functions for hierarchical clustering recover true structures and introduce max-type alternatives to sum-type formulations.
- — Admissibility ensures objective functions recover consistent hierarchical structures when input data supports them.
- — Sum-type functions with symmetric polynomial scaling up to degree two have necessary and sufficient admissibility conditions.
- — Recursive sparsest cut algorithm achieves O(φ)-approximation for admissible sum-type objectives.
- — Max-type objective functions measure cluster interactions by maximum similarity instead of aggregate.
- — Max-type class admits complete characterization for symmetric polynomial scaling of degree two or less.
- — Results clarify algorithmic guarantees and scope for optimizing hierarchical clustering objectives.
- — Framework extends prior work by Dasgupta and Cohen-Addad on principled clustering objectives.
Astrobobo tool mapping
- Knowledge Capture Record the admissibility conditions for sum-type and max-type objectives as a reference table; note which scaling functions (linear, quadratic, cubic) apply to your domain.
- Focus Brief Summarize the O(φ)-approximation guarantee for sparsest cut and compare it against your current algorithm's empirical performance on benchmark datasets.
- Reading Queue Queue the Cohen-Addad et al. (2019) and Dasgupta (2016) papers to understand the foundational framework before implementing new objectives.
Frequently asked
- Admissibility is a property ensuring that an objective function recovers the true hierarchical structure whenever the input data admits a consistent hierarchical representation. In other words, if a ground-truth hierarchy exists, an admissible objective function will find it as a minimizer, providing theoretical guarantees that the algorithm produces meaningful results.
cite ▸
APA
Ryuki Tsukuba, Kazutoshi Ando. (2026, April 28). Admissible Objectives for Hierarchical Clustering Formally Characterized. Astrobobo Content Engine (rewrite of arxiv/cs.LG). https://astrobobo-content-engine.vercel.app/article/admissible-objectives-for-hierarchical-clustering-formally-characterized-b23526
MLA
Ryuki Tsukuba, Kazutoshi Ando. "Admissible Objectives for Hierarchical Clustering Formally Characterized." Astrobobo Content Engine, 28 Apr 2026, https://astrobobo-content-engine.vercel.app/article/admissible-objectives-for-hierarchical-clustering-formally-characterized-b23526. Based on "arxiv/cs.LG", https://arxiv.org/abs/2604.23628.
BibTeX
@misc{astrobobo_admissible-objectives-for-hierarchical-clustering-formally-characterized-b23526_2026,
author = {Ryuki Tsukuba, Kazutoshi Ando},
title = {Admissible Objectives for Hierarchical Clustering Formally Characterized},
year = {2026},
url = {https://astrobobo-content-engine.vercel.app/article/admissible-objectives-for-hierarchical-clustering-formally-characterized-b23526},
note = {Astrobobo rewrite of arxiv/cs.LG, https://arxiv.org/abs/2604.23628},
}