Efficient Computation of Image Persistence
Algebraic Topology
2022-01-13 v1 Computational Geometry
Abstract
We present an algorithm for computing the barcode of the image of a morphisms in persistent homology induced by an inclusion of filtered finite-dimensional chain complexes. These algorithms make use of the clearing optimization and can be applied to inclusion-induced maps in persistent absolute homology and persistent relative cohomology for filtrations of pairs of simplicial complexes. They form the basis for our implementation for Vietoris-Rips complexes in the framework of the software Ripser.
Cite
@article{arxiv.2201.04170,
title = {Efficient Computation of Image Persistence},
author = {Ulrich Bauer and Maximilian Schmahl},
journal= {arXiv preprint arXiv:2201.04170},
year = {2022}
}
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16 pages