The DOI matches its Crossref record; 24 of the 24 references it cites were found in a registry or an index.
Finding the Homology of Submanifolds with High Confidence from Random Samples
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“Niyogi, Smale, and Weinberger in [52] provide sufficient hypotheses which guarantee that this is possible for Riemannian manifolds.”
From Topology and data (2009) · cites this paper as [52]
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“Niyogi, Smale and Weinberger (2008) give conditions which show that with high confidence, a construction based on ϵ balls around a finite sample from a submanifold of Euclidean space computes homology of the submanifold accurately.”
From Topological pattern recognition for point cloud data (2014) · cites this paper as Niyogi, Smale and Weinberger (2008)
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“Their method is to prove that the Čech complex associated to a covering by balls of a fixed radius is homotopy equivalent to the underlying manifold.”
From Topology and data (2009) · cites this paper as [52]
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Cites
Nonlinear Dimensionality Reduction by Locally Linear Embedding
Roweis, S. T., & Saul, L. K. (2000) · Science · doi:10.1126/science.290.5500.2323 · Cited by 14,965
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Elements of Algebraic Topology
Munkres, J. R. (2018) · CRC Press eBooks · doi:10.1201/9780429493911 · Cited by 2,113
Hessian eigenmaps: Locally linear embedding techniques for high-dimensional data
Donoho, D. L., & Grimes, C. (2003) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1031596100 · Cited by 1,704
Zomorodian, A., & Carlsson, G. (2005) · Discrete & Computational Geometry · doi:10.1007/s00454-004-1146-y · Cited by 1,591
Graham, R., Grötschel, M., & Lovász, L. (1995) · Medical Entomology and Zoology · Cited by 1,526
ELEMENTS OF ALGEBRAIC TOPOLOGY
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Beffara, E., Boissonnat, J., Boldo, S., Chazal, F., Gioan, E., Martel, M., Paul, C., Melquiond, G., Alfonsín, J. L. R., Vaux, L., et al. (2013)
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Metadata
- Authors
- Niyogi, P., Smale, S., & Weinberger, S.
- Affiliations
- University of Chicago (US)
- Toyota Technological Institute at Chicago (US)
- Corresponding author
- Niyogi, Partha
- ORCID
- Weinberger, Shmuel
- Venue
- Discrete & Computational Geometry
- Published
- 2008-03
- Volume
- 39
- Issue
- 1-3
- Pages
- 419-441
- ISSN
- 0179-5376 (ISSN-L)
- 1432-0444
- OpenAlex
- W2157878484
- Cited by
- 523
- References
- 24
- Citations by year
- 2026: 17 · 2025: 21 · 2024: 26 · 2023: 25 · 2022: 25 · 2021: 37 · 2020: 32 · 2019: 23 · 2018: 43 · 2017: 24 · 2016: 26 · 2015: 23 · 2014: 31 · 2013: 24 · 2012: 26
- FWCI
- 41.28
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Licence
- www.springer.com/tdm (tdm)
- Locations
- Discrete & Computational Geometry (publishedVersion)
- Topics
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Topological and Geometric Data Analysis
- Physical Sciences › Mathematics › Geometry and Topology › Geometric and Algebraic Topology
- Physical Sciences › Computer Science › Computer Graphics and Computer-Aided Design › 3D Shape Modeling and Analysis
- Keywords
- submanifolds, random samples, topological inference, condition number, curvature, self-intersection, noisy data, high-dimensional data analysis, topological data analysis
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