Fetching the paper…
Reading the bibliography…
In this paper we improve the spectral convergence rates for graph-based approximations of Laplace-Beltrami operators constructed from random data.
Riemannian geometry
M. P. do Carmo · 1992
Earlier work this paper cites.
Laplacian eigenmaps and spectral techniques for embedding and clustering
M. Belkin and P. Niyogi · 2002
Earlier work this paper cites.
On spectral clustering: Analysis and an algorithm
A. Y. Ng, M. I. Jordan, and Y. Weiss · 2002
Earlier work this paper cites.
Random geometric graphs
M. Penrose · 2003
Earlier work this paper cites.
Kernels and regularization on graphs
A. J. Smola and R. Kondor · 2003
Earlier work this paper cites.
Semi-supervised learning using Gaussian fields and harmonic functions
X. Zhu, Z. Ghahramani, and J. D. Lafferty · 2003
Earlier work this paper cites.
Semi-supervised learning: From Gaussian fields to Gaussian processes
X. Zhu, J. D. Lafferty, and Z. Ghahramani · 2003
Earlier work this paper cites.
Towards a theoretical foundation for Laplacian-based manifold methods
M. Belkin and P. Niyogi · 2005
Earlier work this paper cites.
Geometric diffusions as a tool for harmonic analysis and structure definition of data: Diffusion maps
R. R. Coifman, S. Lafon, A. B. Lee, M. Maggioni, B. Nadler, F. Warner, and S. W. Zucker · 2005
Earlier work this paper cites.
From graphs to manifolds–weak and strong pointwise consistency of graph Laplacians
M. Hein, J.-Y. Audibert, and U. Von Luxburg · 2005
Earlier work this paper cites.
Self-tuning spectral clustering
L. Zelnik-Manor and P. Perona · 2005
Earlier work this paper cites.
Learning on graph with Laplacian regularization
R. K. Ando and T. Zhang · 2006
Earlier work this paper cites.
Manifold regularization: A geometric framework for learning from labeled and unlabeled examples
M. Belkin, P. Niyogi, and V. Sindhwani · 2006
Earlier work this paper cites.
Semi-supervised learning
O. Chapelle, B. Scholkopf, and A. Zien · 2006
Earlier work this paper cites.
Empirical graph Laplacian approximation of Laplace-Beltrami operators: large sample results
E. Giné and V. Koltchinskii · 2006
Earlier work this paper cites.
From graph to manifold Laplacian: The convergence rate
A. Singer · 2006
Earlier work this paper cites.
Graph Laplacians and their convergence on random neighborhood graphs
M. Hein, J.-Y. Audibert, and U. v. Luxburg · 2007
Earlier work this paper cites.
Finite difference methods for ordinary and partial differential equations: steady-state and time-dependent problems
R. J. LeVeque · 2007
Earlier work this paper cites.
A tutorial on spectral clustering
U. von Luxburg · 2007
Earlier work this paper cites.
Consistency of spectral clustering
U. von Luxburg, M. Belkin, and O. Bousquet · 2008
Cited alongside, same era.
Optimal construction of k-nearest-neighbor graphs for identifying noisy clusters
M. Maier, M. Hein, and U. von Luxburg · 2009
Cited alongside, same era.
An analysis of the convergence of graph Laplacians
D. Ting, L. Huang, and M. Jordan · 2010
Cited alongside, same era.
Concentration inequalities: A nonasymptotic theory of independence
S. Boucheron, G. Lugosi, and P. Massart · 2013
Cited alongside, same era.
Nonparametric sparsity and regularization
L. Rosasco, S. Villa, S. Mosci, M. Santoro, and A. Verri · 2013
Cited alongside, same era.
A graph discretization of the Laplace-Beltrami operator
D. Burago, S. Ivanov, and Y. Kurylev · 2014
Cited alongside, same era.
J. Lei · 2018
Later among the works it cites.
Consistency of Lipschitz learning with infinite unlabeled data and finite labeled data
J. Calder · 2019
Closest in time.
Properly-weighted graph Laplacian for semi-supervised learning
J. Calder and D. Slepčev · 2019
Closest in time.
Mumford-shah functionals on graphs and their asymptotics
M. Caroccia, A. Chambolle, and D. Slepěv · 2019
Closest in time.
Large data and zero noise limits of graph-based semi-supervised learning algorithms
M. M. Dunlop, D. Slepčev, A. M. Stuart, and M. Thorpe · 2019
Closest in time.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Adaptive piecewise polynomial estimation via trend filtering
R. J. Tibshirani · 2014
Cited alongside, same era.
On the rate of convergence in Wasserstein distance of the empirical measure
N. Fournier and A. Guillin · 2015
Cited alongside, same era.
Elliptic partial differential equations of second order
D. Gilbarg and N. S. Trudinger · 2015
Cited alongside, same era.
Convergence of Laplacian spectra from random samples
Z. Shi · 2015
Cited alongside, same era.
Consistency of cheeger and ratio graph cuts
N. García Trillos, D. Slepčev, J. Von Brecht, T. Laurent, and X. Bresson · 2016
Cited alongside, same era.
Trend filtering on graphs
Y.-X. Wang, J. Sharpnack, A. J. Smola, and R. J. Tibshirani · 2016
Cited alongside, same era.
M. Flores, J. Calder, and G. Lerman · 2019
Closest in time.
Variational limits of k-nn graph-based functionals on data clouds
N. García Trillos · 2019
Closest in time.
Spectral convergence of the graph Laplacian on random geometric graphs towards the Laplace Beltrami operator
N. García Trillos, M. Gerlach, M. Hein, and D. Slepčev · 2019
Closest in time.
Geometric structure of graph Laplacian embeddings
N. García Trillos, F. Hoffmann, and B. Hosseini · 2019
Closest in time.
A maximum principle argument for the uniform convergence of graph Laplacian regressors
N. García Trillos and R. Murray · 2019
Closest in time.
Local regularization of noisy point clouds: Improved global geometric estimates and data analysis
N. García Trillos, D. Sanz-Alonso, and R. Yang · 2019
Closest in time.
Spectral analysis of weighted Laplacians arising in data clustering
F. Hoffmann, B. Hosseini, A. A. Oberai, and A. M. Stuart · 2019
Closest in time.
Consistency of semi-supervised learning algorithms on graphs: Probit and one-hot methods
F. Hoffmann, B. Hosseini, Z. Ren, and A. M. Stuart · 2019
Closest in time.
Optimal cheeger cuts and bisections of random geometric graphs
T. Müller and M. D. Penrose · 2019
Closest in time.
Analysis of p-Laplacian regularization in semisupervised learning
D. Slepcev and M. Thorpe · 2019
Closest in time.
Poisson Learning: Graph Based semi-supervised learning at very low label rates
J. Calder, B. Cook, M. Thorpe, and D. Slepčev · 2020
Closest in time.
Rates of convergence for Laplacian semi-supervised learning with low labelling rates
J. Calder, D. Slepčev, and M. Thorpe · 2020
Closest in time.
A continuum limit for the PageRank algorithm
A. Yuan, J. Calder, and B. Osting · 2020
Closest in time.