Topological Data Analysis in Finsler Spaces
Fuente:
arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866916959722930176 |
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| author | Cavalcanti, Rafael Leal, Nelson de Souza, Danilo Barros Rodrigues, Serafim Desroches, Mathieu |
| author_facet | Cavalcanti, Rafael Leal, Nelson de Souza, Danilo Barros Rodrigues, Serafim Desroches, Mathieu |
| contents | We introduce a new approach to Topological Data Analysis (TDA) based on Finsler metrics and we also generalize the classical concepts of Vietoris-Rips and Cech complexes within this framework. In particular, we propose a class of directionally dependent Finsler metrics and establish key results demonstrating their relevance to TDA. Moreover, we show that several Information Theoretic perspectives on TDA can often be recovered through the lens of Finsler geometry. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_12660 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Topological Data Analysis in Finsler Spaces Cavalcanti, Rafael Leal, Nelson de Souza, Danilo Barros Rodrigues, Serafim Desroches, Mathieu Differential Geometry Geometric Topology We introduce a new approach to Topological Data Analysis (TDA) based on Finsler metrics and we also generalize the classical concepts of Vietoris-Rips and Cech complexes within this framework. In particular, we propose a class of directionally dependent Finsler metrics and establish key results demonstrating their relevance to TDA. Moreover, we show that several Information Theoretic perspectives on TDA can often be recovered through the lens of Finsler geometry. |
| title | Topological Data Analysis in Finsler Spaces |
| topic | Differential Geometry Geometric Topology |
| url | https://arxiv.org/abs/2509.12660 |