Fréchet Means for Distributions of Persistence Diagrams
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The L2 Wasserstein metric on B∞ results in a metric space that 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).
“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)
Turner, Mileyko, Mukherjee and Harer (2014) made the existence theorem algorithmic, but for a somewhat different choice of metric and metric space.
“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)
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Topology Data Analysis Using Mean Persistence Landscapes in Financial Crashes
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k-means clustering for persistent homology
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Optimization of Spectral Wavelets for Persistence-Based Graph Classification
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An Overview of the Topology ToolKit
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Topological data analysis reveals differences between simulated galaxies and dark matter haloes
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- 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 · 2013: 4 · 2012: 1
- 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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