Topological Data Analysis in Finsler Spaces
Differential Geometry
2025-09-23 v2 Geometric Topology
Abstract
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.
Keywords
Cite
@article{arxiv.2509.12660,
title = {Topological Data Analysis in Finsler Spaces},
author = {Rafael Cavalcanti and Nelson Leal and Danilo Barros de Souza and Serafim Rodrigues and Mathieu Desroches},
journal= {arXiv preprint arXiv:2509.12660},
year = {2025}
}
Comments
6 figures, 24 pages