Geometric Kernel Diversity: An Axiomatic Diversity Measure in Euclidean Space
Quantifying the diversity of a set of objects is a fundamental problem in machine learning and statistics. Mironov and Prokhorenkova (2025) recently showed that three axioms-monotonicity, uniqueness, and continuity-are crucial for a reliable diversity measure and that none of the standard metrics in the literature satisfy all three. They also constructed two measures that do satisfy the axioms, but both are NP-hard to compute, leaving open the question of whether efficient axiomatic diversity measures can exist. We study a Euclidean-restricted version of this question. We introduce Geometric Kernel Diversity (GKD), which associates a radial kernel solid with each point and measures the vo...
| Authors | Ditbul Ban, Younghun Roh, Julian Shun et al. |
|---|---|
| Primary category | cs.CG |
| Published | 14 October 2026 |
| Last updated at source | 14 October 2026 |
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