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Error estimates for spectral convergence of the graph Laplacian on
  random geometric graphs towards the Laplace--Beltrami operator

Error estimates for spectral convergence of the graph Laplacian on random geometric graphs towards the Laplace--Beltrami operator

30 January 2018
Nicolas García Trillos
Moritz Gerlach
Matthias Hein
D. Slepčev
ArXivPDFHTML

Papers citing "Error estimates for spectral convergence of the graph Laplacian on random geometric graphs towards the Laplace--Beltrami operator"

50 / 106 papers shown
Title
Convergence of Laplacian Eigenmaps and its Rate for Submanifolds with
  Singularities
Convergence of Laplacian Eigenmaps and its Rate for Submanifolds with Singularities
Masayuki Aino
14
1
0
15 Oct 2021
Neural Operator: Learning Maps Between Function Spaces
Neural Operator: Learning Maps Between Function Spaces
Nikola B. Kovachki
Zong-Yi Li
Burigede Liu
Kamyar Azizzadenesheli
K. Bhattacharya
Andrew M. Stuart
Anima Anandkumar
AI4CE
52
440
0
19 Aug 2021
Clustering dynamics on graphs: from spectral clustering to mean shift
  through Fokker-Planck interpolation
Clustering dynamics on graphs: from spectral clustering to mean shift through Fokker-Planck interpolation
Katy Craig
Nicolas García Trillos
D. Slepčev
11
6
0
18 Aug 2021
Large sample spectral analysis of graph-based multi-manifold clustering
Large sample spectral analysis of graph-based multi-manifold clustering
Nicolas García Trillos
Pengfei He
Chenghui Li
8
6
0
28 Jul 2021
Laplacian-Based Dimensionality Reduction Including Spectral Clustering,
  Laplacian Eigenmap, Locality Preserving Projection, Graph Embedding, and
  Diffusion Map: Tutorial and Survey
Laplacian-Based Dimensionality Reduction Including Spectral Clustering, Laplacian Eigenmap, Locality Preserving Projection, Graph Embedding, and Diffusion Map: Tutorial and Survey
Benyamin Ghojogh
A. Ghodsi
Fakhri Karray
Mark Crowley
15
12
0
03 Jun 2021
Minimax Optimal Regression over Sobolev Spaces via Laplacian
  Regularization on Neighborhood Graphs
Minimax Optimal Regression over Sobolev Spaces via Laplacian Regularization on Neighborhood Graphs
Alden Green
Sivaraman Balakrishnan
R. Tibshirani
13
15
0
03 Jun 2021
Error Bounds of the Invariant Statistics in Machine Learning of Ergodic
  Itô Diffusions
Error Bounds of the Invariant Statistics in Machine Learning of Ergodic Itô Diffusions
He Zhang
J. Harlim
Xiantao Li
18
7
0
21 May 2021
Kernel Two-Sample Tests for Manifold Data
Kernel Two-Sample Tests for Manifold Data
Xiuyuan Cheng
Yao Xie
19
9
0
07 May 2021
Robust Certification for Laplace Learning on Geometric Graphs
Robust Certification for Laplace Learning on Geometric Graphs
Matthew Thorpe
Bao Wang
OOD
AAML
22
1
0
22 Apr 2021
Which Sampling Densities are Suitable for Spectral Clustering on
  Unbounded Domains?
Which Sampling Densities are Suitable for Spectral Clustering on Unbounded Domains?
Henry-Louis de Kergorlay
26
0
0
05 Apr 2021
Measure estimation on manifolds: an optimal transport approach
Measure estimation on manifolds: an optimal transport approach
Vincent Divol
OT
16
21
0
15 Feb 2021
LDLE: Low Distortion Local Eigenmaps
LDLE: Low Distortion Local Eigenmaps
Dhruv Kohli
A. Cloninger
Gal Mishne
11
17
0
26 Jan 2021
Eigen-convergence of Gaussian kernelized graph Laplacian by manifold
  heat interpolation
Eigen-convergence of Gaussian kernelized graph Laplacian by manifold heat interpolation
Xiuyuan Cheng
Nan Wu
63
29
0
25 Jan 2021
Manifold learning with arbitrary norms
Manifold learning with arbitrary norms
Joe Kileel
Amit Moscovich
Nathan Zelesko
A. Singer
44
25
0
28 Dec 2020
Impact of signal-to-noise ratio and bandwidth on graph Laplacian
  spectrum from high-dimensional noisy point cloud
Impact of signal-to-noise ratio and bandwidth on graph Laplacian spectrum from high-dimensional noisy point cloud
Xiucai Ding
Hau‐Tieng Wu
6
13
0
21 Nov 2020
Convergence of Graph Laplacian with kNN Self-tuned Kernels
Convergence of Graph Laplacian with kNN Self-tuned Kernels
Xiuyuan Cheng
Hau‐Tieng Wu
8
23
0
03 Nov 2020
The Mathematical Foundations of Manifold Learning
The Mathematical Foundations of Manifold Learning
Luke Melas-Kyriazi
AI4CE
12
17
0
30 Oct 2020
Product Manifold Learning
Product Manifold Learning
Sharon Zhang
Amit Moscovich
A. Singer
39
14
0
19 Oct 2020
A Linear Transportation $\mathrm{L}^p$ Distance for Pattern Recognition
A Linear Transportation Lp\mathrm{L}^pLp Distance for Pattern Recognition
Oliver M. Crook
Mihai Cucuringu
Tim Hurst
Carola-Bibiane Schönlieb
Matthew Thorpe
K. Zygalakis
25
7
0
23 Sep 2020
Overcoming the curse of dimensionality with Laplacian regularization in
  semi-supervised learning
Overcoming the curse of dimensionality with Laplacian regularization in semi-supervised learning
Vivien A. Cabannes
Loucas Pillaud-Vivien
Francis R. Bach
Alessandro Rudi
6
19
0
09 Sep 2020
Unlabeled Data Help in Graph-Based Semi-Supervised Learning: A Bayesian
  Nonparametrics Perspective
Unlabeled Data Help in Graph-Based Semi-Supervised Learning: A Bayesian Nonparametrics Perspective
D. Sanz-Alonso
Ruiyi Yang
SSL
13
9
0
26 Aug 2020
Posterior Consistency of Semi-Supervised Regression on Graphs
Posterior Consistency of Semi-Supervised Regression on Graphs
Andrea L. Bertozzi
Bamdad Hosseini
Hao Li
Kevin Miller
Andrew M. Stuart
10
10
0
25 Jul 2020
Lipschitz regularity of graph Laplacians on random data clouds
Lipschitz regularity of graph Laplacians on random data clouds
Jeff Calder
Nicolas García Trillos
M. Lewicka
25
30
0
13 Jul 2020
Consistency of Anchor-based Spectral Clustering
Consistency of Anchor-based Spectral Clustering
Henry-Louis de Kergorlay
D. Higham
4
6
0
24 Jun 2020
Construction and Monte Carlo estimation of wavelet frames generated by a
  reproducing kernel
Construction and Monte Carlo estimation of wavelet frames generated by a reproducing kernel
Ernesto De Vito
Ž. Kereta
Valeriya Naumova
Lorenzo Rosasco
Stefano Vigogna
19
3
0
17 Jun 2020
Rates of Convergence for Laplacian Semi-Supervised Learning with Low
  Labeling Rates
Rates of Convergence for Laplacian Semi-Supervised Learning with Low Labeling Rates
Jeff Calder
D. Slepčev
Matthew Thorpe
18
26
0
04 Jun 2020
Spectral convergence of diffusion maps: improved error bounds and an
  alternative normalisation
Spectral convergence of diffusion maps: improved error bounds and an alternative normalisation
Caroline L. Wormell
Sebastian Reich
8
37
0
03 Jun 2020
Doubly-Stochastic Normalization of the Gaussian Kernel is Robust to
  Heteroskedastic Noise
Doubly-Stochastic Normalization of the Gaussian Kernel is Robust to Heteroskedastic Noise
Boris Landa
Ronald R. Coifman
Y. Kluger
15
23
0
31 May 2020
Data-driven Efficient Solvers for Langevin Dynamics on Manifold in High
  Dimensions
Data-driven Efficient Solvers for Langevin Dynamics on Manifold in High Dimensions
Yuan Gao
Jiang Liu
Nan Wu
21
12
0
22 May 2020
Kernel Analog Forecasting: Multiscale Test Problems
Kernel Analog Forecasting: Multiscale Test Problems
Dmitry Burov
D. Giannakis
Krithika Manohar
Andrew M. Stuart
11
22
0
13 May 2020
From graph cuts to isoperimetric inequalities: Convergence rates of
  Cheeger cuts on data clouds
From graph cuts to isoperimetric inequalities: Convergence rates of Cheeger cuts on data clouds
Nicolas García Trillos
Ryan W. Murray
Matthew Thorpe
14
10
0
20 Apr 2020
The SPDE Approach to Matérn Fields: Graph Representations
The SPDE Approach to Matérn Fields: Graph Representations
D. Sanz-Alonso
Ruiyi Yang
6
18
0
16 Apr 2020
Diffusion State Distances: Multitemporal Analysis, Fast Algorithms, and
  Applications to Biological Networks
Diffusion State Distances: Multitemporal Analysis, Fast Algorithms, and Applications to Biological Networks
L. Cowen
K. Devkota
Xiaozhe Hu
James M. Murphy
Kaiyi Wu
9
5
0
07 Mar 2020
Bridging data science and dynamical systems theory
Bridging data science and dynamical systems theory
Tyrus Berry
D. Giannakis
J. Harlim
AI4TS
AI4CE
11
22
0
18 Feb 2020
A continuum limit for the PageRank algorithm
A continuum limit for the PageRank algorithm
Amber Yuan
Jeff Calder
Braxton Osting
34
18
0
24 Jan 2020
Scalability and robustness of spectral embedding: landmark diffusion is
  all you need
Scalability and robustness of spectral embedding: landmark diffusion is all you need
Chao Shen
Hau‐Tieng Wu
45
24
0
03 Jan 2020
Spectral Convergence of Graph Laplacian and Heat Kernel Reconstruction
  in $L^\infty$ from Random Samples
Spectral Convergence of Graph Laplacian and Heat Kernel Reconstruction in L∞L^\inftyL∞ from Random Samples
David B. Dunson
Hau‐Tieng Wu
Nan Wu
12
64
0
11 Dec 2019
Understanding Graph Neural Networks with Generalized Geometric
  Scattering Transforms
Understanding Graph Neural Networks with Generalized Geometric Scattering Transforms
Michael Perlmutter
Alexander Tong
F. Gao
Guy Wolf
M. Hirn
GNN
19
9
0
14 Nov 2019
Spatially regularized active diffusion learning for high-dimensional
  images
Spatially regularized active diffusion learning for high-dimensional images
James M. Murphy
11
12
0
06 Nov 2019
Improved spectral convergence rates for graph Laplacians on
  epsilon-graphs and k-NN graphs
Improved spectral convergence rates for graph Laplacians on epsilon-graphs and k-NN graphs
Jeff Calder
Nicolas García Trillos
35
40
0
29 Oct 2019
PDE-Inspired Algorithms for Semi-Supervised Learning on Point Clouds
PDE-Inspired Algorithms for Semi-Supervised Learning on Point Clouds
Oliver M. Crook
Tim Hurst
Carola-Bibiane Schönlieb
Matthew Thorpe
K. Zygalakis
3DPC
20
2
0
23 Sep 2019
Spectral Analysis Of Weighted Laplacians Arising In Data Clustering
Spectral Analysis Of Weighted Laplacians Arising In Data Clustering
Franca Hoffmann
Bamdad Hosseini
Assad A. Oberai
Andrew M. Stuart
11
23
0
13 Sep 2019
Volume Doubling Condition and a Local Poincaré Inequality on
  Unweighted Random Geometric Graphs
Volume Doubling Condition and a Local Poincaré Inequality on Unweighted Random Geometric Graphs
F. Göbel
Gilles Blanchard
14
0
0
06 Jul 2019
Mumford-Shah functionals on graphs and their asymptotics
Mumford-Shah functionals on graphs and their asymptotics
M. Caroccia
A. Chambolle
D. Slepčev
22
21
0
22 Jun 2019
Consistency of semi-supervised learning algorithms on graphs: Probit and
  one-hot methods
Consistency of semi-supervised learning algorithms on graphs: Probit and one-hot methods
Franca Hoffmann
Bamdad Hosseini
Zhi Ren
Andrew M. Stuart
14
23
0
18 Jun 2019
Learning by Active Nonlinear Diffusion
Learning by Active Nonlinear Diffusion
Mauro Maggioni
James M. Murphy
11
19
0
30 May 2019
Diffusion $K$-means clustering on manifolds: provable exact recovery via
  semidefinite relaxations
Diffusion KKK-means clustering on manifolds: provable exact recovery via semidefinite relaxations
Xiaohui Chen
Yun Yang
24
16
0
11 Mar 2019
Geometric structure of graph Laplacian embeddings
Geometric structure of graph Laplacian embeddings
Nicolas García Trillos
Franca Hoffmann
Bamdad Hosseini
33
23
0
30 Jan 2019
A maximum principle argument for the uniform convergence of graph
  Laplacian regressors
A maximum principle argument for the uniform convergence of graph Laplacian regressors
Nicolas García Trillos
Ryan W. Murray
8
20
0
29 Jan 2019
When Locally Linear Embedding Hits Boundary
When Locally Linear Embedding Hits Boundary
Hau‐Tieng Wu
Nan Wu
14
11
0
11 Nov 2018
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