Morse Theory for Filtrations and Efficient Computation of Persistent Homology
We introduce an efficient preprocessing algorithm to reduce the number of cells in a filtered cell complex while preserving its persistent homology groups. The technique is based on an extension of combinatorial Morse theory from complexes to filtrations.
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| Published in | Discrete & computational geometry Vol. 50; no. 2; pp. 330 - 353 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Boston
Springer US
01.09.2013
Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0179-5376 1432-0444 1432-0444 |
| DOI | 10.1007/s00454-013-9529-6 |
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| Abstract | We introduce an efficient preprocessing algorithm to reduce the number of cells in a filtered cell complex while preserving its persistent homology groups. The technique is based on an extension of combinatorial Morse theory from complexes to filtrations. |
|---|---|
| AbstractList | We introduce an efficient preprocessing algorithm to reduce the number of cells in a filtered cell complex while preserving its persistent homology groups. The technique is based on an extension of combinatorial Morse theory from complexes to filtrations.[PUBLICATION ABSTRACT] We introduce an efficient preprocessing algorithm to reduce the number of cells in a filtered cell complex while preserving its persistent homology groups. The technique is based on an extension of combinatorial Morse theory from complexes to filtrations. |
| Author | Nanda, Vidit Mischaikow, Konstantin |
| Author_xml | – sequence: 1 givenname: Konstantin surname: Mischaikow fullname: Mischaikow, Konstantin organization: Department of Mathematics and BioMaPS, Rutgers, The State University of New Jersey – sequence: 2 givenname: Vidit surname: Nanda fullname: Nanda, Vidit email: vnanda@sas.upenn.edu organization: Department of Mathematics, The University of Pennsylvania |
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| Cites_doi | 10.1007/s00454-006-1276-5 10.1007/s00454-008-9073-y 10.1007/BF02165411 10.1016/j.camwa.2010.09.036 10.1006/aima.1997.1650 10.1137/0220067 10.1016/j.crma.2005.04.036 10.1080/10586458.2003.10504498 10.1137/S0895480104445885 10.2307/1968689 10.1090/mbk/069 10.1090/coll/027 10.1090/conm/453/08802 10.1145/1998196.1998229 10.1145/236869.237084 10.1007/978-3-540-71962-5 10.1007/978-3-642-23175-9_7 10.1145/1005285.1005325 10.1007/978-3-662-05148-1_10 10.1016/S0012-365X(99)00258-7 |
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| Keywords | Computational topology Discrete Morse theory Persistent homology |
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| References | Hafner, McCurley (CR12) 1991; 20 Mrozek, Wanner (CR24) 2010; 60 CR19 CR18 Zomorodian (CR34) 2005 CR17 Munkres (CR25) 1984 CR13 Morozov (CR22) 2005 CR11 CR33 Harker, Mischaikow, Mrozek, Nanda (CR14) 2013 CR30 Joswig, Pfetsch (CR15) 2006; 20 Mrozek, Batko (CR23) 2009; 41 CR2 CR4 Cohen-Steiner, Edelsbrunner, Harer (CR3) 2007; 37 CR6 CR5 CR8 CR7 CR28 CR27 CR26 Zomorodian, Carlsson (CR35) 2005; 33 CR21 Carlsson (CR1) 2009; 46 Forman (CR9) 1998; 134 Ghrist (CR10) 2008; 45 Strassen (CR31) 1969; 13 Tucker (CR32) 1936; 37 Kozlov (CR16) 2005; 340 Lewiner, Lopes, Tavares (CR20) 2003; 12 Spanier (CR29) 1966 9529_CR17 M Mrozek (9529_CR23) 2009; 41 V Strassen (9529_CR31) 1969; 13 A Zomorodian (9529_CR34) 2005 9529_CR19 9529_CR18 R Forman (9529_CR9) 1998; 134 EH Spanier (9529_CR29) 1966 M Mrozek (9529_CR24) 2010; 60 9529_CR30 9529_CR11 9529_CR33 9529_CR10 9529_CR13 9529_CR35 9529_CR28 9529_CR27 9529_CR8 9529_CR7 9529_CR6 9529_CR5 D Morozov (9529_CR22) 2005 9529_CR4 JR Munkres (9529_CR25) 1984 9529_CR2 9529_CR1 D Kozlov (9529_CR16) 2005; 340 J Hafner (9529_CR12) 1991; 20 T Lewiner (9529_CR20) 2003; 12 AW Tucker (9529_CR32) 1936; 37 D Cohen-Steiner (9529_CR3) 2007; 37 9529_CR21 S Harker (9529_CR14) 2013 M Joswig (9529_CR15) 2006; 20 9529_CR26 |
| References_xml | – year: 2005 ident: CR22 publication-title: Persistence Algorithm Takes Cubic Time in the Worst Case – ident: CR18 – volume: 46 start-page: 255 issue: 2 year: 2009 end-page: 308 ident: CR1 article-title: Topology and data publication-title: Bull. Am. Math. Soc. (N.S.) – ident: CR4 – ident: CR2 – ident: CR30 – volume: 45 start-page: 61 issue: 1 year: 2008 end-page: 75 ident: CR10 article-title: Barcodes: the persistent topology of data publication-title: Bull. Am. Math. Soc. (N.S.) – volume: 37 start-page: 103 issue: 1 year: 2007 end-page: 120 ident: CR3 article-title: Stability of persistence diagrams publication-title: Discrete Comput. Geom. doi: 10.1007/s00454-006-1276-5 – ident: CR33 – ident: CR6 – volume: 41 start-page: 96 year: 2009 end-page: 118 ident: CR23 article-title: The coreduction homology algorithm publication-title: Discrete Comput. Geom. doi: 10.1007/s00454-008-9073-y – volume: 13 start-page: 354 year: 1969 end-page: 356 ident: CR31 article-title: Gaussian elimination is not optimal publication-title: Numer. Math. doi: 10.1007/BF02165411 – ident: CR8 – volume: 60 start-page: 2812 issue: 10 year: 2010 end-page: 2833 ident: CR24 article-title: Coreduction homology algorithm for inclusions and persistent homology publication-title: Comput. Math. Appl. doi: 10.1016/j.camwa.2010.09.036 – year: 2013 ident: CR14 article-title: Discrete Morse theoretic algorithms for computing homology of complexes and maps publication-title: Found. Comput. Math. – volume: 134 start-page: 90 year: 1998 end-page: 145 ident: CR9 article-title: Morse theory for cell complexes publication-title: Adv. Math. doi: 10.1006/aima.1997.1650 – volume: 20 start-page: 1068 issue: 6 year: 1991 end-page: 1083 ident: CR12 article-title: Asymptotically fast triangularization of matrices over rings publication-title: SIAM J. Comput. doi: 10.1137/0220067 – ident: CR27 – ident: CR21 – ident: CR19 – volume: 340 start-page: 867 year: 2005 end-page: 872 ident: CR16 article-title: Discrete Morse theory for free chain complexes publication-title: C. R. Math. doi: 10.1016/j.crma.2005.04.036 – year: 2005 ident: CR34 publication-title: Topology for Computing, Cambridge Monographs on Applied and Computational Mathematics – ident: CR17 – ident: CR13 – year: 1966 ident: CR29 publication-title: Algebraic Topology – ident: CR11 – volume: 12 start-page: 271 issue: 3 year: 2003 end-page: 286 ident: CR20 article-title: Toward optimality in discrete Morse theory publication-title: Exp. Math. doi: 10.1080/10586458.2003.10504498 – volume: 33 start-page: 249 issue: 2 year: 2005 end-page: 274 ident: CR35 article-title: Computing persistent homology publication-title: Discrete Comput. Geom. – volume: 20 start-page: 11 issue: 1 year: 2006 end-page: 25 ident: CR15 article-title: Computing optimal Morse matchings publication-title: SIAM J. Discrete Math doi: 10.1137/S0895480104445885 – volume: 37 start-page: 92 year: 1936 end-page: 100 ident: CR32 article-title: Cell spaces publication-title: Ann. Math. doi: 10.2307/1968689 – ident: CR5 – ident: CR7 – year: 1984 ident: CR25 publication-title: Elements of Algebraic Topology – ident: CR28 – ident: CR26 – ident: 9529_CR7 doi: 10.1090/mbk/069 – ident: 9529_CR18 doi: 10.1090/coll/027 – ident: 9529_CR6 doi: 10.1090/conm/453/08802 – ident: 9529_CR10 – volume-title: Algebraic Topology year: 1966 ident: 9529_CR29 – volume-title: Topology for Computing, Cambridge Monographs on Applied and Computational Mathematics year: 2005 ident: 9529_CR34 – ident: 9529_CR21 doi: 10.1145/1998196.1998229 – volume: 340 start-page: 867 year: 2005 ident: 9529_CR16 publication-title: C. R. Math. doi: 10.1016/j.crma.2005.04.036 – ident: 9529_CR30 doi: 10.1145/236869.237084 – ident: 9529_CR8 – ident: 9529_CR35 – ident: 9529_CR4 – ident: 9529_CR17 doi: 10.1007/978-3-540-71962-5 – volume-title: Elements of Algebraic Topology year: 1984 ident: 9529_CR25 – volume: 13 start-page: 354 year: 1969 ident: 9529_CR31 publication-title: Numer. Math. doi: 10.1007/BF02165411 – volume: 60 start-page: 2812 issue: 10 year: 2010 ident: 9529_CR24 publication-title: Comput. Math. Appl. doi: 10.1016/j.camwa.2010.09.036 – ident: 9529_CR26 – year: 2013 ident: 9529_CR14 publication-title: Found. Comput. Math. – volume: 20 start-page: 11 issue: 1 year: 2006 ident: 9529_CR15 publication-title: SIAM J. Discrete Math doi: 10.1137/S0895480104445885 – volume: 41 start-page: 96 year: 2009 ident: 9529_CR23 publication-title: Discrete Comput. Geom. doi: 10.1007/s00454-008-9073-y – ident: 9529_CR13 – ident: 9529_CR11 – volume: 20 start-page: 1068 issue: 6 year: 1991 ident: 9529_CR12 publication-title: SIAM J. Comput. doi: 10.1137/0220067 – volume-title: Persistence Algorithm Takes Cubic Time in the Worst Case year: 2005 ident: 9529_CR22 – volume: 37 start-page: 92 year: 1936 ident: 9529_CR32 publication-title: Ann. Math. doi: 10.2307/1968689 – ident: 9529_CR33 doi: 10.1007/978-3-642-23175-9_7 – ident: 9529_CR1 – volume: 37 start-page: 103 issue: 1 year: 2007 ident: 9529_CR3 publication-title: Discrete Comput. Geom. doi: 10.1007/s00454-006-1276-5 – ident: 9529_CR19 – volume: 12 start-page: 271 issue: 3 year: 2003 ident: 9529_CR20 publication-title: Exp. Math. doi: 10.1080/10586458.2003.10504498 – ident: 9529_CR28 doi: 10.1145/1005285.1005325 – volume: 134 start-page: 90 year: 1998 ident: 9529_CR9 publication-title: Adv. Math. doi: 10.1006/aima.1997.1650 – ident: 9529_CR5 doi: 10.1007/978-3-662-05148-1_10 – ident: 9529_CR2 doi: 10.1016/S0012-365X(99)00258-7 – ident: 9529_CR27 |
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| SubjectTerms | Algorithms Cells Combinatorial analysis Combinatorics Computational efficiency Computational geometry Computational Mathematics and Numerical Analysis Computers Filtration Homology Mathematics Mathematics and Statistics Preprocessing Preserving |
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| Title | Morse Theory for Filtrations and Efficient Computation of Persistent Homology |
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