Geometry and Dress groups with non-symmetric cost functions
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908814827061248 |
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| author | Barth, Lukas Silvester Joharinad, Parvaneh Jost, Jürgen Wenzel, Walter |
| author_facet | Barth, Lukas Silvester Joharinad, Parvaneh Jost, Jürgen Wenzel, Walter |
| contents | A metric relation by definition is symmetric. Since many data sets are non-symmetric, in this paper we develop a systematic theory of non-symmetric cost functions. Betweenness relations play an important role. We also introduce the notion of a Dress group in the non-symmetric setting and indicate a notion of curvature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_00590 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Geometry and Dress groups with non-symmetric cost functions Barth, Lukas Silvester Joharinad, Parvaneh Jost, Jürgen Wenzel, Walter Metric Geometry Information Theory Category Theory Group Theory 51F99, 51D99, 37B99, 20C99, 18F99 F.4.2; F.4.3 A metric relation by definition is symmetric. Since many data sets are non-symmetric, in this paper we develop a systematic theory of non-symmetric cost functions. Betweenness relations play an important role. We also introduce the notion of a Dress group in the non-symmetric setting and indicate a notion of curvature. |
| title | Geometry and Dress groups with non-symmetric cost functions |
| topic | Metric Geometry Information Theory Category Theory Group Theory 51F99, 51D99, 37B99, 20C99, 18F99 F.4.2; F.4.3 |
| url | https://arxiv.org/abs/2506.00590 |