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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Bibliographic Details
Published inDiscrete & computational geometry Vol. 50; no. 2; pp. 330 - 353
Main Authors Mischaikow, Konstantin, Nanda, Vidit
Format Journal Article
LanguageEnglish
Published Boston Springer US 01.09.2013
Springer Nature B.V
Subjects
Algorithms
Cells
Combinatorial analysis
Combinatorics
Computational efficiency
Computational geometry
Computational Mathematics and Numerical Analysis
Computers
Filtration
Homology
Mathematics
Mathematics and Statistics
Preprocessing
Preserving
Computational topology
Discrete Morse theory
Persistent homology
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ISSN0179-5376
1432-0444
DOI10.1007/s00454-013-9529-6

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Summary: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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ISSN:0179-5376
1432-0444
DOI:10.1007/s00454-013-9529-6