Peeling metric spaces of strict negative type
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914267888877568 |
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| author | Huntsman, Steve |
| author_facet | Huntsman, Steve |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_19565 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Peeling metric spaces of strict negative type Huntsman, Steve Metric Geometry 51F99, 51K05 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. |
| title | Peeling metric spaces of strict negative type |
| topic | Metric Geometry 51F99, 51K05 |
| url | https://arxiv.org/abs/2509.19565 |