Persistent homology for random fields and complexes
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<!-- *** Custom HTML *** --> We discuss and review recent developments in the area of applied algebraic topology, such as persistent homology and barcodes. In particular, we discuss how these are related to understanding more about manifold learning from random point cloud data, the algebraic structure of simplicial complexes determined by random vertices and, in most detail, the algebraic topology of the excursion sets of random fields.
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Adler et al. (2010) defined the analogue of the Euler characteristic for persistent homology and studied it for Gaussian random fields.
“Adler et al. (2010) have defined the analogue of the Euler characteristic for persistent homology and studied it for Gaussian random fields.”
From Topological pattern recognition for point cloud data (2014) · cites this paper as Adler et al. (2010)
In Adler et al. (2010) a result is proved which computes χ_pers for Gaussian random fields.
“in Adler et al. (2010) a result is proved which computes χ pers for Gaussian random fields.”
From Topological pattern recognition for point cloud data (2014) · cites this paper as Adler et al. (2010)
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References 28 · Cited by 91
- Authors
- Adler, R. J., Bobrowski, O., Borman, M. S., Subag, E., & Weinberger, S.
- Affiliations
- Technion – Israel Institute of Technology (IL)
- Venue
- Institute of Mathematical Statistics Collections
- Publisher
- Institute of Mathematical Statistics
- Published
- 2010
- Pages
- 124-143
- ISSN
- 1937-5166 (ISSN-L)
- 1939-4039
- OpenAlex
- W1680861744
- Cited by
- 91
- References
- 28
- Citations by year
- 2025: 3 · 2024: 2 · 2023: 10 · 2022: 3 · 2021: 12 · 2020: 7 · 2019: 8 · 2018: 8 · 2017: 8 · 2016: 7 · 2015: 2 · 2014: 8 · 2013: 4 · 2012: 4
- FWCI
- 7.38
- Type
- book chapter
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Institute of Mathematical Statistics collections (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- Project Euclid (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- 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
- persistent homology, barcodes, random fields, excursion sets, simplicial complexes, manifold learning
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