AI · 8 min read · April 28, 2026
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.
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.