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Computing Persistent Homology with Various Coefficient Fields in a Single Pass

Jean-Daniel Boissonnat 1 Clément Maria 1, * 
* Corresponding author
1 DATASHAPE - Understanding the Shape of Data
CRISAM - Inria Sophia Antipolis - Méditerranée , Inria Saclay - Ile de France
Abstract : This article introduces an algorithm to compute the persistent homology of a filtered complex with various coefficient fields in a single matrix reduction. The algorithm is output-sensitive in the total number of distinct persistent homological features in the diagrams for the different coefficient fields. This computation allows us to infer the prime divisors of the torsion coefficients of the integral homology groups of the topological space at any scale, hence furnishing a more informative description of topology than persistence in a single coefficient field. We provide theoretical complexity analysis as well as detailed experimental results. The code is part of the Gudhi software library.
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Submitted on : Thursday, January 9, 2020 - 2:49:27 AM
Last modification on : Saturday, July 23, 2022 - 3:53:11 AM
Long-term archiving on: : Saturday, April 11, 2020 - 10:03:16 AM


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Jean-Daniel Boissonnat, Clément Maria. Computing Persistent Homology with Various Coefficient Fields in a Single Pass. Journal of Applied and Computational Topology, Springer, 2019, 3 (1-2), pp.16. ⟨10.1007/s41468-019-00025-y⟩. ⟨hal-00922572v5⟩



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