Year: 2019
Type: preprint
Abstract: In topological data analysis, the matching distance is a computationally tractable metric on multi-filtered simplicial complexes. We design efficient algorithms for approximating the matching distance of two bi-filtered complexes to any desired precision ε>0. Our approach is based on a quad-tree refinement strategy introduced by Biasotti et al., but we recast their approach entirely in geometric terms. This point of view leads to several novel observations resulting in a practically faster algorithm. We demonstrate this speed-up by experimental comparison and provide our code in a public repository which provides the first efficient publicly available implementation of the matching distance.
Source: arXiv (Cornell University)
Authors: Kerber, Michael, Nigmetov, Arnur
Institution: Graz University of Technology
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Funder: Austrian Science Fund
OpenAlex ID: W2996737098