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We study graph-based Laplacian semi-supervised learning at low labeling rates.
Gradient-based learning applied to document recognition
Y. LeCun, L. Bottou, Y. Bengio, and P. Haffner · 1998
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Random Geometric Graphs
M. Penrose · 2003
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Semi-supervised learning using Gaussian fields and harmonic functions
X. Zhu, Z. Ghahramani, and J. D. Lafferty · 2003
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Semi-supervised learning on riemannian manifolds
M. Belkin and P. Niyogi · 2004
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Semi-supervised learning by maximizing smoothness
D. Zhou, O. Bousquet, T. Lal, J. Weston, and B. Schölkopf · 2004
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Learning with local and global consistency
D. Zhou, O. Bousquet, T. N. Lal, J. Weston, and B. Schölkopf · 2004
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From graphs to manifolds – weak and strong pointwise consistency of graph Laplacians
M. Hein, J.-Y. Audibert, and U. von Luxburg · 2005
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Learning from labeled and unlabeled data on a directed graph
D. Zhou, J. Huang, and B. Schölkopf · 2005
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Regularization on discrete spaces
D. Zhou and B. Schölkopf · 2005
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Manifold regularization: A geometric framework for learning from labeled and unlabeled examples
M. Belkin, P. Niyogi, and V. Sindhwani · 2006
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Semi-supervised learning
O. Chapelle, B. Scholkopf, and A. Zien · 2006
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From graph to manifold Laplacian: The convergence rate
A. Singer · 2006
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A First Course in Sobolev Spaces
G. Leoni · 2009
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Statistical analysis of semi-supervised learning: The limit of infinite unlabelled data
B. Nadler, N. Srebro, and X. Zhou · 2009
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Random walk: a modern introduction
G. F. Lawler and V. Limic · 2010
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Concentration inequalities: A nonasymptotic theory of independence
S. Boucheron, G. Lugosi, and P. Massart · 2013
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Elliptic partial differential equations of second order
D. Gilbarg and N. S. Trudinger · 2015
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Asymptotic behavior of ℓ p \ell_{p} -based Laplacian regularization in semi-supervised learning
A. El Alaoui, X. Cheng, A. Ramdas, M. J. Wainwright, and M. I. Jordan · 2016
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Continuum limit of Total Variation on point clouds
N. García Trillos and D. Slepčev · 2016
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Consistency of Cheeger and ratio graph cuts
N. García Trillos, D. Slepčev, J. von Brecht, T. Laurent, and X. Bresson · 2016
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Optimal transport for manifold-valued images
J. H. Fitschen, F. Laus, and B. Schmitzer · 2017
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On the consistency of graph-based Bayesian learning and the scalability of sampling algorithms
A variational approach to the consistency of spectral clustering
N. García Trillos and D. Slepčev · 2018
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Error estimation of weighted nonlocal Laplacian on random point cloud
Z. Shi, B. Wang, and S. J. Osher · 2018
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Deep limits of residual neural networks
M. Thorpe and Y. van Gennip · 2018
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Consistency of Lipschitz learning with infinite unlabeled data and finite labeled data
J. Calder · 2019
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Improved spectral convergence rates for graph Laplacians on ε \varepsilon -graphs and k-NN graphs
J. Calder and N. García Trillos · 2019
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N. García Trillos, Z. Kaplan, T. Samakhoana, and D. Sanz-Alonso · 2017
Cited alongside, same era.
Estimating perimeter using graph cuts
N. García Trillos, D. Slepčev, and J. von Brecht · 2017
Cited alongside, same era.
Consistency of Dirichlet partitions
B. Osting and T. Reeb · 2017
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Weighted nonlocal Laplacian on interpolation from sparse data
Z. Shi, S. Osher, and W. Zhu · 2017
Cited alongside, same era.
A transportation L p L^{p} distance for signal analysis
M. Thorpe, S. Park, S. Kolouri, G. K. Rohde, and D. Slepčev · 2017
Cited alongside, same era.
The game theoretic p p -Laplacian and semi-supervised learning with few labels
J. Calder · 2018
Cited alongside, same era.
Large data limit for a phase transition model with the p p -Laplacian on point clouds
R. Cristoferi and M. Thorpe · 2018
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Properly-weighted graph Laplacian for semi-supervised learning
J. Calder and D. Slepčev · 2019
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Mumford-Shah functionals on graphs and their asymptotics
M. Caroccia, A. Chambolle, and D. Slepčev · 2019
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Algorithms for Lp-based semi-supervised learning on graphs
M. Flores, J. Calder, and G. Lerman · 2019
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Error estimates for 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
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A maximum principle argument for the uniform convergence of graph laplacian regressors
N. García Trillos and R. Murray · 2019
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Optimal Cheeger cuts and bisections of random geometric graphs
T. Müller and M. D. Penrose · 2019
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Analysis of p p -Laplacian regularization in semi-supervised learning
D. Slepčev and M. Thorpe · 2019
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Asymptotic analysis of the Ginzburg-Landau functional on point clouds
M. Thorpe and F. Theil · 2019
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Github Repository: GraphLearning
J. Calder · 2020
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A continuum limit for the PageRank algorithm
A. Yuan, J. Calder, and B. Osting · 2020
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