Morse Theory for Filtrations and Efficient Computation of Persistent Homology

Konstantin Mischaikow; Vidit Nanda

doi:10.1007/s00454-013-9529-6

Morse Theory for Filtrations and Efficient Computation of Persistent Homology

Konstantin Mischaikow, Vidit Nanda

Research output: Contribution to journal › Article › peer-review

169 Scopus citations

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.

Original language	English (US)
Pages (from-to)	330-353
Number of pages	24
Journal	Discrete and Computational Geometry
Volume	50
Issue number	2
DOIs	https://doi.org/10.1007/s00454-013-9529-6
State	Published - Sep 2013

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Geometry and Topology
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics

Keywords

Computational topology
Discrete Morse theory
Persistent homology

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10.1007/s00454-013-9529-6

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title = "Morse Theory for Filtrations and Efficient Computation of Persistent Homology",

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.",

keywords = "Computational topology, Discrete Morse theory, Persistent homology",

author = "Konstantin Mischaikow and Vidit Nanda",

note = "Funding Information: The authors were partially supported by NSF Grants DMS-0915019 and CBI-0835621 and by contracts from DARPA and AFOSR. ",

year = "2013",

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doi = "10.1007/s00454-013-9529-6",

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T1 - Morse Theory for Filtrations and Efficient Computation of Persistent Homology

AU - Mischaikow, Konstantin

AU - Nanda, Vidit

N1 - Funding Information: The authors were partially supported by NSF Grants DMS-0915019 and CBI-0835621 and by contracts from DARPA and AFOSR.

PY - 2013/9

Y1 - 2013/9

N2 - 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.

AB - 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.

KW - Computational topology

KW - Discrete Morse theory

KW - Persistent homology

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AN - SCOPUS:84881611962

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JO - Discrete and Computational Geometry

JF - Discrete and Computational Geometry

IS - 2

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Morse Theory for Filtrations and Efficient Computation of Persistent Homology

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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