Ripser: efficient computation of Vietoris–Rips persistence barcodes
We present an algorithm for the computation of Vietoris–Rips persistence barcodes and describe its implementation in the software Ripser. The method relies on implicit representations of the coboundary operator and the filtration order of the simplices, avoiding the explicit construction and storage...
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| Vydáno v: | Journal of applied and computational topology Ročník 5; číslo 3; s. 391 - 423 |
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| Médium: | Journal Article |
| Jazyk: | angličtina |
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Cham
Springer International Publishing
01.09.2021
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| ISSN: | 2367-1726, 2367-1734 |
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| Abstract | We present an algorithm for the computation of Vietoris–Rips persistence barcodes and describe its implementation in the software Ripser. The method relies on implicit representations of the coboundary operator and the filtration order of the simplices, avoiding the explicit construction and storage of the filtration coboundary matrix. Moreover, it makes use of apparent pairs, a simple but powerful method for constructing a discrete gradient field from a total order on the simplices of a simplicial complex, which is also of independent interest. Our implementation shows substantial improvements over previous software both in time and memory usage. |
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| AbstractList | We present an algorithm for the computation of Vietoris–Rips persistence barcodes and describe its implementation in the software Ripser. The method relies on implicit representations of the coboundary operator and the filtration order of the simplices, avoiding the explicit construction and storage of the filtration coboundary matrix. Moreover, it makes use of apparent pairs, a simple but powerful method for constructing a discrete gradient field from a total order on the simplices of a simplicial complex, which is also of independent interest. Our implementation shows substantial improvements over previous software both in time and memory usage. |
| Author | Bauer, Ulrich |
| Author_xml | – sequence: 1 givenname: Ulrich surname: Bauer fullname: Bauer, Ulrich email: mail@ulrich-bauer.org organization: Technical University of Munich (TUM) |
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| Cites_doi | 10.1145/1998196.1998229 10.1007/978-3-319-42545-0 10.1007/s00454-004-1146-y 10.1090/mbk/069 10.1007/s00454-011-9344-x 10.1109/TPAMI.2014.2346172 10.1109/HPTCDL.2014.10 10.1016/j.comgeo.2012.02.010 10.21105/joss.02614 10.1145/1137856.1137877 10.1016/j.jsc.2016.03.008 10.1016/j.crma.2005.04.036 10.1090/S0002-9947-05-04079-1 10.1007/BF01447877 10.1145/3330345.3332147 10.1007/s00454-002-2885-2 10.1090/memo/0923 10.1515/9781400882588-013 10.1016/0022-0000(79)90042-4 10.1007/s00454-010-9319-3 10.1142/S0219498815500668 10.1090/S0002-9939-1956-0078686-7 10.1137/1.9781611973198.4 10.1145/3350755.3400244 10.1088/0266-5611/27/12/124003 10.1007/PL00000526 10.1016/j.entcs.2014.06.011 10.1006/aima.1997.1650 10.1007/978-1-4613-9586-7_3 10.1140/epjds/s13688-017-0109-5 |
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| Keywords | 55N31 . 55-04 Persistent homology . Vietoris-Rips complexes . Topological data analysis . Discrete Morse theory |
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| References_xml | – reference: Morozov, D., Nigmetov, A.: Towards lockfree persistent homology. In: Proceedings of the 32nd ACM Symposium on Parallelism in Algorithms and Architectures, SPAA ’20, pp. 555–557. Association for Computing Machinery (2020) – reference: Olver, S., Townsend, A.: A practical framework for infinite-dimensional linear algebra. In: Proceedings of the 1st First Workshop for High Performance Technical Computing in Dynamic Languages, HPTCDL ’14, pp. 57–62. IEEE Press (2014) – reference: Chazal, F., de Silva, V., Glisse, M., Oudot, S.: The Structure and Stability of Persistence Modules. SpringerBriefs in Mathematics. Springer (2016) – reference: The GUDHI Project. GUDHI User and Reference Manual. GUDHI Editorial Board, 2015. Software available at http://gudhi.gforge.inria.fr – reference: KruskalJBJrOn the shortest spanning subtree of a graph and the traveling salesman problemProc. Am. Math. 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