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Fréchet Means for Distributions of Persistence Diagrams
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“The resulting metric space is simpler to work with computationally, and all the existence results from Mileyko et al. (2011) are also shown to hold in Turner et al. (2014).”
From Topological pattern recognition for point cloud data (2014) · cites this paper as Turner et al. (2014)
In the citing paper
“Turner, Mileyko, Mukherjee and Harer (2014) made this existence theorem algorithmic, but for a somewhat different choice of metric and metric space.”
From Topological pattern recognition for point cloud data (2014) · cites this paper as Turner, Mileyko, Mukherjee and Harer (2014)
Citations
Cites
Metric Spaces of Non-Positive Curvature
Bridson, M. R., & Haefliger, A. (1999) · Grundlehren der mathematischen Wissenschaften · doi:10.1007/978-3-662-12494-9 · Cited by 4,569
Algorithms for the Assignment and Transportation Problems
Munkres, J. R. (1957) · Journal of the Society for Industrial and Applied Mathematics · doi:10.1137/0105003 · Cited by 4,001
Penrose, M. (2003) · doi:10.1093/acprof:oso/9780198506263.001.0001 · Cited by 2,480
Computational topology an introduction
Edelsbrunner, H., & Harer, J. (2010) · Cited by 1,718
Self-citationRicci curvature for metric-measure spaces via optimal transport
Lott, J. A., & Villani, C. (2009) · Annals of Mathematics · doi:10.4007/annals.2009.169.903 · Cited by 1,281
Molchanov, I. S. (2017) · Probability theory and stochastic modelling · doi:10.1007/978-1-4471-7349-6 · Cited by 626
Finding the homology of submanifolds with high confidence from random samples
Niyogi, P., Smale, S., & Weinberger, S. (2008) · Discrete & Computational Geometry · doi:10.1007/s00454-008-9053-2 · Cited by 523
A.D. Alexandrov spaces with curvature bounded below
Burago, Y. D., Gromov, M. L., & Perel'man, G. Y. (1992) · Russian Mathematical Surveys · doi:10.1070/rm1992v047n02abeh000877 · Cited by 413
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
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
Self-citation
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1 of the 25 references couldn’t be matched to a known paper.
Research works printed but not linked: 2
- Gromov, M.: Hyperbolic groups. In: Gersten, S.M. (ed.) Essays in Group Theory. Mathematical Sciences Research Institute Publications, vol. 8, pp. 75–263. Springer, New York (1987)
- Lunagómez, S., Mukherjee, S., Wolpert, R.L.: Geometric representations of hypergraphs for prior specification and posterior sampling (2009). http://arxiv.org/abs/0912.3648 · arXiv
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Analyse biogéométrique de l'évolution des protéines et des traits d'histoire de vie
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Metadata
- Authors
- Turner, K., Mileyko, Y., Mukherjee, S., & Harer, J.
- Affiliations
- University of Chicago (US)
- University of Hawaiʻi at Mānoa (US)
- Duke University (US)
- Corresponding author
- Turner, Katharine
- Venue
- Discrete & Computational Geometry
- Published
- 2014-07
- Volume
- 52
- Issue
- 1
- Pages
- 44-70
- ISSN
- 0179-5376 (ISSN-L)
- 1432-0444
- OpenAlex
- W2047158247
- Cited by
- 207
- References
- 25
- Citations by year
- 2026: 6 · 2025: 7 · 2024: 20 · 2023: 29 · 2022: 20 · 2021: 30 · 2020: 25 · 2019: 16 · 2018: 14 · 2017: 8 · 2016: 10 · 2015: 11 · 2014: 6
- FWCI
- 12.07
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Licence
- www.springer.com/tdm (tdm)
- Locations
- Discrete & Computational Geometry (publishedVersion)
- ANU Open Research (Australian National University) (submittedVersion)
- Funders
- National Science Foundation (1049290)
- National Institutes of Health
- Defense Advanced Research Projects Agency
- Defense Threat Reduction Agency (HDTRA1)
- Air Force Office of Scientific Research (FA9550-, FA9550-10-1-, FA9550‐10‐1‐0436)
- Topics
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Topological and Geometric Data Analysis
- Physical Sciences › Mathematics › Applied Mathematics › Geometric Analysis and Curvature Flows
- Physical Sciences › Mathematics › Applied Mathematics › Point processes and geometric inequalities
- Keywords
- Fréchet mean, persistence diagrams, persistence landscapes, topological data analysis, law of large numbers, Gaussian random fields, local minima
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