Zigzag Persistence
Open accessAbstract
We describe a new methodology for studying persistence of topological features across a family of spaces or point-cloud data sets, called zigzag persistence. Building on classical results about quiver representations, zigzag persistence generalises the highly successful theory of persistent homology and addresses several situations which are not covered by that theory. In this paper we develop theoretical and algorithmic foundations with a view towards applications in topological statistics.
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References 13 · Cited by 263
- Authors
- Carlsson, G., & de Silva, V.
- Affiliations
- Stanford University (US)
- Corresponding author
- Carlsson, Gunnar
- ORCID
- Carlsson, Gunnar
- Venue
- Foundations of Computational Mathematics
- Published
- 2010-04-21
- Volume
- 10
- Issue
- 4
- Pages
- 367-405
- ISSN
- 1615-3375 (ISSN-L)
- 1615-3383
- OpenAlex
- W2913946465
- Cited by
- 263
- References
- 13
- Citations by year
- 2026: 18 · 2025: 11 · 2024: 23 · 2023: 21 · 2022: 24 · 2021: 17 · 2020: 19 · 2019: 16 · 2018: 25 · 2017: 11 · 2016: 14 · 2015: 13 · 2014: 18 · 2013: 13 · 2012: 6
- FWCI
- 9.86
- Type
- journal article
- Language
- en
- Open access
- hybrid
- doi.org
- Licence
- cc-by-nc
- Locations
- Foundations of Computational Mathematics (publishedVersion, cc-by-nc)
- Funders
- Pomona College
- Defense Advanced Research Projects Agency (HR0011, HR0011-05-1-0007, HR0011-07-1-0002)
- Topics
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Topological and Geometric Data Analysis
- Physical Sciences › Mathematics › Mathematical Physics › Homotopy and Cohomology in Algebraic Topology
- Physical Sciences › Mathematics › Geometry and Topology › Geometric and Algebraic Topology
- Keywords
- zigzag persistence, persistent homology, quiver representations, topological properties, point cloud data, topological statistics, computational topology
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