Manifold Fitting: A Review of Methods and Applications | Paper Citation Record

Observation cef51e0f-cc6c-47c9-963d-849da025b66b · outbound

This paper cites A theory of stratification learning.

Manifold Fitting: A Review of Methods and Applications A theory of stratification learning

Reference 1

Resolution: verified exact; arxiv_id, observed 2026-07-04T09:09:43.250546Z

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Observation ee7f998b-eb80-4d6c-94a1-7ed4800704f5 · outbound

This paper cites Nonasymptotic rates for manifold, tangent space and curvature estimation.

Manifold Fitting: A Review of Methods and Applications Nonasymptotic rates for manifold, tangent space and curvature estimation

Reference 2

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Observation e0bfbd3a-d8e3-4bf2-91ce-063d42ba452a · outbound

This paper cites Non-Parametric Estimation of Manifolds from Noisy Data.

Manifold Fitting: A Review of Methods and Applications Non-Parametric Estimation of Manifolds from Noisy Data

Reference 3

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Observation 25deae64-186b-4605-9495-c805c8a0c346 · outbound

This paper cites Laplacian eigenmaps for dimensionality reduction and data representation.

Manifold Fitting: A Review of Methods and Applications Laplacian eigenmaps for dimensionality reduction and data representation

Reference 4

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Observation e5b3e059-c759-4f73-9dc8-a0859aa8499b · outbound

This paper cites Manifold regularization: A geometric framework for learning from labeled and unlabeled examples.Journal of machine learning research, 7(11), 2006.

Manifold Fitting: A Review of Methods and Applications Manifold regularization: A geometric framework for learning from labeled and unlabeled examples.Journal of machine learning research, 7(11), 2006

Reference 5

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Observation 50e35a25-5e25-43af-88a6-661917f7599f · outbound

This paper cites Manifold reconstruction in arbitrary dimensions using witness complexes.Discrete & Computational Geometry, 42(1):37–70, 2009.

Manifold Fitting: A Review of Methods and Applications Manifold reconstruction in arbitrary dimensions using witness complexes.Discrete & Computational Geometry, 42(1):37–70, 2009

Reference 6

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Observation 6dbe7af6-d89d-4dc5-bbff-3e115e19b90a · outbound

This paper cites Smooth manifold reconstruction from noisy and non-uniform approximation with guarantees.Computational Geometry, 40(2):156–170, 2008.

Manifold Fitting: A Review of Methods and Applications Smooth manifold reconstruction from noisy and non-uniform approximation with guarantees.Computational Geometry, 40(2):156–170, 2008

Reference 7

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Observation 40a5edd1-c6e2-458a-b208-968dc158a5e0 · outbound

This paper cites Estimation of Riemannian quantities from noisy data via density derivatives.arXiv preprint arXiv:2603.27171, 2026.

Manifold Fitting: A Review of Methods and Applications Estimation of Riemannian quantities from noisy data via density derivatives.arXiv preprint arXiv:2603.27171, 2026

Reference 8

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Observation 409df83e-e662-4940-a927-0c245bb6418f · outbound

This paper cites Asymptotic theory for density ridges.The Annals of Statistics, 43(5):1896–1928, 2015.

Manifold Fitting: A Review of Methods and Applications Asymptotic theory for density ridges.The Annals of Statistics, 43(5):1896–1928, 2015

Reference 9

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Observation 0dfbd567-01b2-4f3a-90b5-dba495e9825f · outbound

This paper cites Manifold reconstruction from point samples.

Manifold Fitting: A Review of Methods and Applications Manifold reconstruction from point samples

Reference 10

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Observation 8e452ad9-060a-4904-b7a1-fb71462349c9 · outbound

This paper cites Diffusion maps.Applied and computational harmonic analysis, 21(1): 5–30, 2006.

Manifold Fitting: A Review of Methods and Applications Diffusion maps.Applied and computational harmonic analysis, 21(1): 5–30, 2006

Reference 11

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Observation f3535264-b7c1-4841-bffd-5e80d9444000 · outbound

This paper cites Wind speed and direction estimation using manifold approximation.

Manifold Fitting: A Review of Methods and Applications Wind speed and direction estimation using manifold approximation

Reference 12

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Observation 79bf2b35-c2a4-4244-b46f-5181a36d8b5c · outbound

This paper cites Manifold denoising based on spectral graph wavelets.

Manifold Fitting: A Review of Methods and Applications Manifold denoising based on spectral graph wavelets

Reference 13

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Observation 8fbbda5d-6e31-46be-8c56-6f784a610a44 · outbound

This paper cites Analysis of additive dependencies and concurvities using smallest additive principal components.The Annals of Statistics, 22(4):1635–1668, 1994.

Manifold Fitting: A Review of Methods and Applications Analysis of additive dependencies and concurvities using smallest additive principal components.The Annals of Statistics, 22(4):1635–1668, 1994

Reference 14

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Observation f4c1bd9b-00c0-465e-85fd-1ca6d20e98eb · outbound

This paper cites Donoho and Carrie Grimes.

Manifold Fitting: A Review of Methods and Applications Donoho and Carrie Grimes

Reference 15

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Observation 80fedbb4-a416-4147-9324-01144749073d · outbound

This paper cites Curvature measures.Transactions of the American Mathematical Society, 93(3):418–491, 1959.

Manifold Fitting: A Review of Methods and Applications Curvature measures.Transactions of the American Mathematical Society, 93(3):418–491, 1959

Reference 16

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Observation f9ec9bd3-4860-47f7-aca2-9362c71badbc · outbound

This paper cites A sharp form of Whitney’s extension theorem.Annals of Mathematics, 161(1):509–577, 2005.

Manifold Fitting: A Review of Methods and Applications A sharp form of Whitney’s extension theorem.Annals of Mathematics, 161(1):509–577, 2005

Reference 17

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Observation 70d98440-c9de-4a36-9942-85bd2cc66a49 · outbound

This paper cites Whitney’s extension problem forc m.Annals of Mathematics, 164(1):313–359, 2006.

Manifold Fitting: A Review of Methods and Applications Whitney’s extension problem forc m.Annals of Mathematics, 164(1):313–359, 2006

Reference 18

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Observation 5ac49847-fc7a-4157-80c7-515516688b67 · outbound

This paper cites Testing the manifold hypothesis.Journal of the American Mathematical Society, 29(4):983–1049, 2016.

Manifold Fitting: A Review of Methods and Applications Testing the manifold hypothesis.Journal of the American Mathematical Society, 29(4):983–1049, 2016

Reference 19

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Observation cf52f89a-6282-4a45-9093-1b19616c3421 · outbound

This paper cites Fitting a putative manifold to noisy data.

Manifold Fitting: A Review of Methods and Applications Fitting a putative manifold to noisy data

Reference 20

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Observation a9d783f6-5229-476e-863b-b756bd6702dc · outbound

This paper cites Reconstruction and interpolation of manifolds I: The geometric Whitney problem.Foundations of Computational Mathematics, 20(5):1035–1133, 2020.

Manifold Fitting: A Review of Methods and Applications Reconstruction and interpolation of manifolds I: The geometric Whitney problem.Foundations of Computational Mathematics, 20(5):1035–1133, 2020

Reference 21

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Observation 1e58e7cf-e8e4-4c56-b932-490c6344022d · outbound

This paper cites Reconstruction and interpolation of manifolds II: Inverse problems with partial data for distances observations and for the heat kernel.

Manifold Fitting: A Review of Methods and Applications Reconstruction and interpolation of manifolds II: Inverse problems with partial data for distances observations and for the heat kernel

Reference 22

Resolution: verified exact; arxiv_id, observed 2026-07-04T09:09:43.261425Z

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Observation aa5af77d-f817-4553-b69f-d49588f00d99 · outbound

This paper cites Fitting a manifold of large reach to noisy data.

Manifold Fitting: A Review of Methods and Applications Fitting a manifold of large reach to noisy data

Reference 23

Resolution: verified exact; arxiv_id, observed 2026-07-04T09:09:43.254574Z

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Observation 80700054-2b79-452f-8ae0-48dfca0d1815 · outbound

This paper cites Manifold estimation and singular deconvolution under Hausdorff loss.The Annals of Statistics, 40(2):941–963, 2012.

Manifold Fitting: A Review of Methods and Applications Manifold estimation and singular deconvolution under Hausdorff loss.The Annals of Statistics, 40(2):941–963, 2012

Reference 24

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Observation d160a170-67de-40eb-b1c9-4905234ed441 · outbound

This paper cites Minimax manifold estimation.Journal of Machine Learning Research, 13(43):1263–1291, 2012.

Manifold Fitting: A Review of Methods and Applications Minimax manifold estimation.Journal of Machine Learning Research, 13(43):1263–1291, 2012

Reference 25

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Observation 08a889be-987a-4a25-88ec-e9835221f073 · outbound

This paper cites Nonparametric ridge estimation.The Annals of Statistics, 42(4):1511–1545, 2014.

Manifold Fitting: A Review of Methods and Applications Nonparametric ridge estimation.The Annals of Statistics, 42(4):1511–1545, 2014

Reference 26

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Observation 7dc0cadc-31d5-46d0-99a9-f1839f98aa03 · outbound

This paper cites Generative adversarial nets.Advances in Neural Information Processing Systems, 27, 2014.

Manifold Fitting: A Review of Methods and Applications Generative adversarial nets.Advances in Neural Information Processing Systems, 27, 2014

Reference 27

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Observation 7cd3fda2-ef93-45b8-bbbb-c5eb7ba072d5 · outbound

This paper cites Principal curves.Journal of the American Statistical Association, 84(406): 502–516, 1989.

Manifold Fitting: A Review of Methods and Applications Principal curves.Journal of the American Statistical Association, 84(406): 502–516, 1989

Reference 28

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Observation 0d87ecb4-6779-41ef-840d-65034bd70274 · outbound

This paper cites Graph laplacians and their convergence on random neighborhood graphs.Journal of Machine Learning Research, 8(6), 2007.

Manifold Fitting: A Review of Methods and Applications Graph laplacians and their convergence on random neighborhood graphs.Journal of Machine Learning Research, 8(6), 2007

Reference 29

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Observation bd6f980f-ac72-4aa3-9497-b609884e66d5 · outbound

This paper cites Intrinsic shape analysis: Geodesic PCA for Riemannian manifolds modulo isometric Lie group actions.Statistica Sinica, pages 1–58, 2010.

Manifold Fitting: A Review of Methods and Applications Intrinsic shape analysis: Geodesic PCA for Riemannian manifolds modulo isometric Lie group actions.Statistica Sinica, pages 1–58, 2010

Reference 30

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Observation fa9b45af-3694-43ff-9f89-8d81db8e3cbe · outbound

This paper cites and Marron, J.

Manifold Fitting: A Review of Methods and Applications and Marron, J

Reference 31

Resolution: verified exact; doi, observed 2026-06-26T10:29:18.532426Z

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Observation 8a08bb11-593d-4616-8b52-62bdf1da9a51 · outbound

This paper cites Nanophotonics for light detection and ranging technology.

Manifold Fitting: A Review of Methods and Applications Nanophotonics for light detection and ranging technology

Reference 32

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Observation c6006af0-05d3-4c37-ba87-a710cbac79bb · outbound

This paper cites Two algorithms for constructing a Delaunay triangulation.International Journal of Computer & Information Sciences, 9(3):219–242, 1980.

Manifold Fitting: A Review of Methods and Applications Two algorithms for constructing a Delaunay triangulation.International Journal of Computer & Information Sciences, 9(3):219–242, 1980

Reference 33

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Observation efd77c8b-766b-4df7-b2fe-fcfedc9525bb · outbound

This paper cites Approximate global parametrization of manifolds.Technical Report, 2026.

Manifold Fitting: A Review of Methods and Applications Approximate global parametrization of manifolds.Technical Report, 2026

Reference 34

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Observation 968cbdc5-a4c1-4ee2-a27c-570230de4bf0 · outbound

This paper cites CellScope: High-performance cell atlas workflow with tree-structured representation.Nature Communications, 2025.

Manifold Fitting: A Review of Methods and Applications CellScope: High-performance cell atlas workflow with tree-structured representation.Nature Communications, 2025

Reference 35

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Observation 02105e91-e295-486e-8b4b-7dc4a6bdb76f · outbound

This paper cites Curvature-driven manifold fitting under unbounded isotropic noise.arXiv preprint arXiv:2601.10133, 2026.

Manifold Fitting: A Review of Methods and Applications Curvature-driven manifold fitting under unbounded isotropic noise.arXiv preprint arXiv:2601.10133, 2026

Reference 36

Resolution: verified exact; arxiv_id, observed 2026-07-04T09:09:43.257347Z

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Observation cbcff537-7668-4628-916f-cd3c0a3589bd · outbound

This paper cites Differentiable manifold reconstruction for point cloud denoising.

Manifold Fitting: A Review of Methods and Applications Differentiable manifold reconstruction for point cloud denoising

Reference 37

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Observation 78c740e5-fc75-4f3e-9bc9-1d360a576d56 · outbound

This paper cites UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction.

Manifold Fitting: A Review of Methods and Applications UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction

Reference 38

Resolution: verified exact; local_arxiv, observed 2026-07-04T09:09:43.247793Z

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Observation ece917e4-5224-41c9-b1d4-ea2483d7f55f · outbound

This paper cites Manifold learning: What, how, and why.Annual Review of Statistics and Its Application, 11(1):393–417, 2024.

Manifold Fitting: A Review of Methods and Applications Manifold learning: What, how, and why.Annual Review of Statistics and Its Application, 11(1):393–417, 2024

Reference 39

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Observation 9c7df5d6-030c-4a17-9eaa-709edc36f868 · outbound

This paper cites Manifold Learning Using Kernel Density Estimation and Local Principal Components Analysis.

Manifold Fitting: A Review of Methods and Applications Manifold Learning Using Kernel Density Estimation and Local Principal Components Analysis

Reference 40

Resolution: verified exact; local_arxiv, observed 2026-07-04T09:09:43.249006Z

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Observation e2c054da-d00d-4390-84ad-941a3a2c6f14 · outbound

This paper cites Diffusion maps, spectral clustering and reaction coordinates of dynamical systems.Applied and Computational Harmonic Analysis, 21(1):113–127, 2006.

Manifold Fitting: A Review of Methods and Applications Diffusion maps, spectral clustering and reaction coordinates of dynamical systems.Applied and Computational Harmonic Analysis, 21(1):113–127, 2006

Reference 41

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Observation 0e634612-5748-47f3-8061-f150903208ca · outbound

This paper cites Finding the homology of submanifolds with high confidence from random samples.Discrete & Computational Geometry, 39(1):419–441, 2008.

Manifold Fitting: A Review of Methods and Applications Finding the homology of submanifolds with high confidence from random samples.Discrete & Computational Geometry, 39(1):419–441, 2008

Reference 42

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Observation 4971ae33-07e8-489c-b581-300775ab491e · outbound

This paper cites Locally defined principal curves and surfaces.The Journal of Machine Learning Research, 12:1249–1286, 2011.

Manifold Fitting: A Review of Methods and Applications Locally defined principal curves and surfaces.The Journal of Machine Learning Research, 12:1249–1286, 2011

Reference 43

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Observation b8b82d17-b79d-4349-a74b-8f5d1ea29501 · outbound

This paper cites Principal flows.Journal of the American Statistical Association, 109(505):424–436, 2014.

Manifold Fitting: A Review of Methods and Applications Principal flows.Journal of the American Statistical Association, 109(505):424–436, 2014

Reference 44

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Observation 68d6a6ee-05ac-4779-b407-058c0269e3e4 · outbound

This paper cites Linear convergence of diffusion models under the manifold hypothesis.

Manifold Fitting: A Review of Methods and Applications Linear convergence of diffusion models under the manifold hypothesis

Reference 45

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Observation ffc0e085-d522-46d4-b562-c12fddacecba · outbound

This paper cites Nonlinear dimensionality reduction by locally linear embedding.Science, 290(5500):2323–2326, 2000.

Manifold Fitting: A Review of Methods and Applications Nonlinear dimensionality reduction by locally linear embedding.Science, 290(5500):2323–2326, 2000

Reference 46

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Observation 86ecb6f5-7a0d-4128-9aa7-6f919e8951a0 · outbound

This paper cites From graph to manifold laplacian: The convergence rate.Applied and Computational Harmonic Analysis, 21(1):128–134, 2006.

Manifold Fitting: A Review of Methods and Applications From graph to manifold laplacian: The convergence rate.Applied and Computational Harmonic Analysis, 21(1):128–134, 2006

Reference 47

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Observation 066a3eea-3eb1-43fe-928b-f62cecd47906 · outbound

This paper cites Manifold approximation by moving least-squares projection (MMLS).Constructive Approximation, 52(3):433–478, 2020.

Manifold Fitting: A Review of Methods and Applications Manifold approximation by moving least-squares projection (MMLS).Constructive Approximation, 52(3):433–478, 2020

Reference 48

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Observation 3ec9ed25-d4e8-4118-8de7-75ecd6d8f4df · outbound

This paper cites Principal decomposition with nested submanifolds.arXiv preprint arXiv:2502.10010, 2025.

Manifold Fitting: A Review of Methods and Applications Principal decomposition with nested submanifolds.arXiv preprint arXiv:2502.10010, 2025

Reference 49

Resolution: verified exact; arxiv_id, observed 2026-07-04T09:09:43.243489Z

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Observation 9a725a04-c8d7-45cf-9806-607612372594 · outbound

This paper cites A global geometric framework for nonlinear dimensionality reduction.Science, 290(5500):2319–2323, 2000.

Manifold Fitting: A Review of Methods and Applications A global geometric framework for nonlinear dimensionality reduction.Science, 290(5500):2319–2323, 2000

Reference 50

Resolution: unresolved; no resolver link, observed 2026-06-26T10:27:04.422931Z

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Observation 7c2836a4-db45-4ac2-9f22-de6eb2cab094 · outbound

This paper cites Manifold blurring mean shift algorithms for manifold denoising.

Manifold Fitting: A Review of Methods and Applications Manifold blurring mean shift algorithms for manifold denoising

Reference 51

Resolution: unresolved; no resolver link, observed 2026-06-26T10:27:04.422931Z

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Observation a7a5e6f3-3ffe-4e60-bf51-8b7804a66796 · outbound

This paper cites Analytic extensions of differentiable functions defined in closed sets.Transactions of the American Mathematical Society, 36(1):63–89, 1934.

Manifold Fitting: A Review of Methods and Applications Analytic extensions of differentiable functions defined in closed sets.Transactions of the American Mathematical Society, 36(1):63–89, 1934

Reference 52

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Observation 17f45df4-2118-4e7c-91e9-959f0cfde68b · outbound

This paper cites Differentially private manifold denoising.arXiv preprint arXiv:2604.00942, 2026.

Manifold Fitting: A Review of Methods and Applications Differentially private manifold denoising.arXiv preprint arXiv:2604.00942, 2026

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Resolution: verified exact; arxiv_id, observed 2026-07-04T09:09:43.245121Z

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Observation a4874c67-f758-48a6-a5bc-d9078b0fb517 · outbound

This paper cites A principal submanifold-based approach for clustering and multiscale rna correction.arXiv preprint arXiv:2503.20513, 2026.

Manifold Fitting: A Review of Methods and Applications A principal submanifold-based approach for clustering and multiscale rna correction.arXiv preprint arXiv:2503.20513, 2026

Reference 54

Resolution: verified exact; arxiv_id, observed 2026-07-04T09:09:43.256197Z

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Observation 9e5103b5-f806-4281-8641-0c88b8b019ef · outbound

This paper cites Manifold fitting algorithm of noisy manifold data based on variable-scale spectral graph.Soft Computing, 27(1):471–482, 2023.

Manifold Fitting: A Review of Methods and Applications Manifold fitting algorithm of noisy manifold data based on variable-scale spectral graph.Soft Computing, 27(1):471–482, 2023

Reference 55

Resolution: unresolved; no resolver link, observed 2026-06-26T10:27:04.422931Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8d82ac32-9a3e-4e9c-a7cb-55f6986e793d · outbound

This paper cites Manifold fitting under unbounded noise.Journal of Machine Learning Research, 26(45):1–55, 2025.

Manifold Fitting: A Review of Methods and Applications Manifold fitting under unbounded noise.Journal of Machine Learning Research, 26(45):1–55, 2025

Reference 56

Resolution: unresolved; no resolver link, observed 2026-06-26T10:27:04.422931Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 79a9d065-22c6-42ee-894b-596947ddeeec · outbound

This paper cites Principal boundary on Riemannian manifolds.Journal of the American Statistical Association, 115(531):1435–1448, 2020.

Manifold Fitting: A Review of Methods and Applications Principal boundary on Riemannian manifolds.Journal of the American Statistical Association, 115(531):1435–1448, 2020

Reference 57

Resolution: unresolved; no resolver link, observed 2026-06-26T10:27:04.422931Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a671079c-7c7d-414c-b7d2-22f9412a0e87 · outbound

This paper cites Manifold Fitting.

Manifold Fitting: A Review of Methods and Applications Manifold Fitting

Reference 58

Resolution: verified exact; arxiv_id, observed 2026-07-04T09:09:43.253221Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 811f4b2c-0d5b-445c-82e7-3ddd0a53c565 · outbound

This paper cites Single-cell analysis via manifold fitting: A framework for RNA clustering and beyond.Proceedings of the National Academy of Sciences, 121(37):e2400002121, 2024.

Manifold Fitting: A Review of Methods and Applications Single-cell analysis via manifold fitting: A framework for RNA clustering and beyond.Proceedings of the National Academy of Sciences, 121(37):e2400002121, 2024

Reference 59

Resolution: unresolved; no resolver link, observed 2026-06-26T10:27:04.422931Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0c8d98a4-d2b9-4c97-9e2c-a51d030b49c6 · outbound

This paper cites Manifold fitting with CycleGAN.Proceedings of the National Academy of Sciences, 121(5):e2311436121, 2024.

Manifold Fitting: A Review of Methods and Applications Manifold fitting with CycleGAN.Proceedings of the National Academy of Sciences, 121(5):e2311436121, 2024

Reference 60

Resolution: unresolved; no resolver link, observed 2026-06-26T10:27:04.422931Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 20adf3c5-5067-42f0-8676-ea5609b2b5e0 · outbound

This paper cites Random fixed boundary flows.Journal of the American Statistical Association, 119(547):2356–2368, 2024.

Manifold Fitting: A Review of Methods and Applications Random fixed boundary flows.Journal of the American Statistical Association, 119(547):2356–2368, 2024

Reference 61

Resolution: unresolved; no resolver link, observed 2026-06-26T10:27:04.422931Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 42aaffb0-a643-4fd2-a819-142143e02dd1 · outbound

This paper cites Principal sub-manifolds.Statistica Sinica, 36(3):1–41, 2026.

Manifold Fitting: A Review of Methods and Applications Principal sub-manifolds.Statistica Sinica, 36(3):1–41, 2026

Reference 62

Resolution: unresolved; no resolver link, observed 2026-06-26T10:27:04.422931Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1b278cec-1767-460a-819a-476b5ad9cab0 · outbound

This paper cites Principal manifolds and nonlinear dimensionality reduction via tangent space alignment.SIAM Journal on Scientific Computing, 26(1):313–338, 2004.

Manifold Fitting: A Review of Methods and Applications Principal manifolds and nonlinear dimensionality reduction via tangent space alignment.SIAM Journal on Scientific Computing, 26(1):313–338, 2004

Reference 63

Resolution: unresolved; no resolver link, observed 2026-06-26T10:27:04.422931Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 026745ae-1da7-4ce5-8f4c-dca3d53f6af2 · outbound

This paper cites an unresolved cited work.

Manifold Fitting: A Review of Methods and Applications Unresolved cited work

Reference 64

Resolution: unresolved; no resolver link, observed 2026-06-26T10:27:04.422931Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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