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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Semi-Supervised Learning on Riemannian Manifolds
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Self-citationSurface Reconstruction by Voronoi Filtering
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Stability of persistence diagrams
Cohen-Steiner, D., Edelsbrunner, H., & Harer, J. (2005) · Proceedings of the twenty-first annual symposium on Computational geometry · doi:10.1145/1064092.1064133 · Cited by 251
A SIMPLE ALGORITHM FOR HOMEOMORPHIC SURFACE RECONSTRUCTION
Amenta, N., Choi, S., Dey, T. K., & Leekha, N. (2002) · International Journal of Computational Geometry & Applications · doi:10.1142/s0218195902000773 · Cited by 229
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Computing Betti Numbers via Combinatorial Laplacians
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Manifold reconstruction from point samples
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Carlsson, G. (2009) · Bulletin of the American Mathematical Society · doi:10.1090/s0273-0979-09-01249-x · Cited by 2,302
“Further, even if one could assume that the data lies along a manifold, one is usually not in a position to verify that the stringent hypotheses of [52] are satisfied.”
BackgroundStability 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
Wasserman, L. (2017) · Annual Review of Statistics and Its Application · doi:10.1146/annurev-statistics-031017-100045 · Cited by 519
Towards a theoretical foundation for Laplacian-based manifold methods
Belkin, M., & Niyogi, P. (2007) · Journal of Computer and System Sciences · doi:10.1016/j.jcss.2007.08.006 · Cited by 464
Self-citationTesting the manifold hypothesis
Fefferman, C., Mitter, S., & Narayanan, H. (2016) · Journal of the American Mathematical Society · doi:10.1090/jams/852 · Cited by 430
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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