Peeling metric spaces of strict negative type

Steve Huntsman
Proceedings of the 1st Conference on Topology, Algebra, and Geometry in Data Science(TAG-DS 2025), PMLR 321:30-44, 2026.

Abstract

We describe a unified and computationally tractable framework for finding outliers in, and maximum-diversity subsets of, finite metric spaces of strict negative type. Examples of such spaces include finite subsets of Euclidean space and finite subsets of a sphere without antipodal points. The latter accounts for state-of-the-art text embeddings, and we apply our framework in this context to sketch a hallucination mitigation strategy and separately to a class of path diversity optimization problems with a real-world example.

Cite this Paper

BibTeX
@InProceedings{pmlr-v321-huntsman26a, title = {Peeling metric spaces of strict negative type}, author = {Huntsman, Steve}, booktitle = {Proceedings of the 1st Conference on Topology, Algebra, and Geometry in Data Science(TAG-DS 2025)}, pages = {30--44}, year = {2026}, editor = {Bernardez Gil, Guillermo and Black, Mitchell and Cloninger, Alexander and Doster, Timothy and Emerson, Tegan and Garcı́a-Rodondo, Ińes and Holtz, Chester and Kotak, Mit and Kvinge, Henry and Mishne, Gal and Papillon, Mathilde and Pouplin, Alison and Rainey, Katie and Rieck, Bastian and Telyatnikov, Lev and Yeats, Eric and Wang, Qingsong and Wang, Yusu and Wayland, Jeremy}, volume = {321}, series = {Proceedings of Machine Learning Research}, month = {01--02 Dec}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v321/main/assets/huntsman26a/huntsman26a.pdf}, url = {https://proceedings.mlr.press/v321/huntsman26a.html}, abstract = {We describe a unified and computationally tractable framework for finding outliers in, and maximum-diversity subsets of, finite metric spaces of strict negative type. Examples of such spaces include finite subsets of Euclidean space and finite subsets of a sphere without antipodal points. The latter accounts for state-of-the-art text embeddings, and we apply our framework in this context to sketch a hallucination mitigation strategy and separately to a class of path diversity optimization problems with a real-world example.} }
Endnote
%0 Conference Paper %T Peeling metric spaces of strict negative type %A Steve Huntsman %B Proceedings of the 1st Conference on Topology, Algebra, and Geometry in Data Science(TAG-DS 2025) %C Proceedings of Machine Learning Research %D 2026 %E Guillermo Bernardez Gil %E Mitchell Black %E Alexander Cloninger %E Timothy Doster %E Tegan Emerson %E Ińes Garcı́a-Rodondo %E Chester Holtz %E Mit Kotak %E Henry Kvinge %E Gal Mishne %E Mathilde Papillon %E Alison Pouplin %E Katie Rainey %E Bastian Rieck %E Lev Telyatnikov %E Eric Yeats %E Qingsong Wang %E Yusu Wang %E Jeremy Wayland %F pmlr-v321-huntsman26a %I PMLR %P 30--44 %U https://proceedings.mlr.press/v321/huntsman26a.html %V 321 %X We describe a unified and computationally tractable framework for finding outliers in, and maximum-diversity subsets of, finite metric spaces of strict negative type. Examples of such spaces include finite subsets of Euclidean space and finite subsets of a sphere without antipodal points. The latter accounts for state-of-the-art text embeddings, and we apply our framework in this context to sketch a hallucination mitigation strategy and separately to a class of path diversity optimization problems with a real-world example.
APA
Huntsman, S.. (2026). Peeling metric spaces of strict negative type. Proceedings of the 1st Conference on Topology, Algebra, and Geometry in Data Science(TAG-DS 2025), in Proceedings of Machine Learning Research 321:30-44 Available from https://proceedings.mlr.press/v321/huntsman26a.html.

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