Sliding Windows and Persistence: An Application of Topological Methods to Signal Analysis
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Cites
Detecting strange attractors in turbulence
Takens, F. (1981) · Lecture Notes in Mathematics · doi:10.1007/bfb0091924 · Cited by 10,459 · see citing works
Carlsson, G. (2009) · Bulletin of the American Mathematical Society · doi:10.1090/s0273-0979-09-01249-x · Cited by 2,302 · cited 1× · see citing works
“gy [12]. Persistent homology is a topological method for measuring the shapes of spaces and the features of functions. One of the most important applications of persistent homology is to point clouds [3], where shape is usually interpreted as the geometry of some implicit underlying object near which the point cloud i…”
MethodZomorodian, A., & Carlsson, G. (2005) · Discrete & Computational Geometry · doi:10.1007/s00454-004-1146-y · Cited by 1,591 · see citing works
Stability of Persistence Diagrams
Cohen-Steiner, D., Edelsbrunner, H., & Harer, J. (2007) · Discrete & Computational Geometry · doi:10.1007/s00454-006-1276-5 · Cited by 1,280 · see citing works
Self-citationOn the Local Behavior of Spaces of Natural Images
Carlsson, G., Ishkhanov, T., de Silva, V., & Zomorodian, A. (2008) · International Journal of Computer Vision · doi:10.1007/s11263-007-0056-x · Cited by 477 · see citing works
Lipschitz Functions Have L p -Stable Persistence
Cohen-Steiner, D., Edelsbrunner, H., Harer, J., & Mileyko, Y. (2010) · Foundations of Computational Mathematics · doi:10.1007/s10208-010-9060-6 · Cited by 284 · see citing works
Self-citationProbability measures on the space of persistence diagrams
Mileyko, Y., Mukherjee, S., & Harer, J. (2011) · Inverse Problems · doi:10.1088/0266-5611/27/12/124007 · Cited by 249 · see citing works
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Cang, Z., Mu, L., & Wei, G.-W. (2018) · PLOS Computational Biology · doi:10.1371/journal.pcbi.1005929 · Cited by 257 · see citing works
Topological pattern recognition for point cloud data
Carlsson, G. (2014) · Acta Numerica · doi:10.1017/s0962492914000051 · Cited by 230 · see citing works
A topological approach for protein classification
Cang, Z., Mu, L., Wu, K., Opron, K., Xia, K., & Wei, G.-W. (2015) · Computational and Mathematical Biophysics · doi:10.1515/mlbmb-2015-0009 · Cited by 93 · see citing works
- Authors
- Perea, J. A., & Harer, J.
- Affiliations
- Duke University (US)
- Venue
- Foundations of Computational Mathematics
- Published
- 2014-05-29
- Volume
- 15
- Issue
- 3
- Pages
- 799-838
- ISSN
- 1615-3375 (ISSN-L)
- 1615-3383
- OpenAlex
- W2102368730
- Cited by
- 306
- References
- 7
- Citations by year
- 2026: 40 · 2025: 31 · 2024: 24 · 2023: 27 · 2022: 24 · 2021: 29 · 2020: 33 · 2019: 24 · 2018: 26 · 2017: 13 · 2016: 19 · 2015: 10 · 2014: 4 · 2013: 2
- FWCI
- 40.45
- Type
- book chapter
- Language
- en
- Open access
- green
- arxiv.org
- Licence
- www.springer.com/tdm (tdm)
- Locations
- Foundations of Computational Mathematics (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Funders
- Defense Advanced Research Projects Agency (D12AP00025-002, D12AP00025)
- Air Force Office of Scientific Research (FA9550-, FA9550‐10‐1‐0436)
- Topics
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Topological and Geometric Data Analysis
- Physical Sciences › Computer Science › Signal Processing › Time Series Analysis and Forecasting
- Physical Sciences › Mathematics › Mathematical Physics › Homotopy and Cohomology in Algebraic Topology
- Keywords
- persistent homology, periodicity detection, time series analysis, persistence diagrams, point clouds, gene expression analysis, embedding dimension
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