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Semi-supervised and unsupervised machine learning methods often rely on graphs to model data, prompting research on how theoretical properties of operators on graphs are leveraged in learning problems.
User’s guide to viscosity solutions of second order partial differential equations
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On spectral clustering: Analysis and an algorithm
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Measure based regularization
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Manifold-ranking based image retrieval
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Diffusion maps and geometric harmonics
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Deeper inside PageRank
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Ranking on data manifolds
D. Zhou, J. Weston, A. Gretton, O. Bousquet, and B. Schölkopf · 2004
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Towards a theoretical foundation for Laplacian-based manifold methods
M. Belkin and P. Niyogi · 2005
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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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Semi-supervised learning on directed graphs
D. Zhou, T. Hofmann, and B. Schölkopf · 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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Diffusion maps
R. R. Coifman and S. Lafon · 2006
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Generalized manifold-ranking-based image retrieval
J. He, M. Li, H.-J. Zhang, H. Tong, and C. Zhang · 2006
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From graph to manifold Laplacian: The convergence rate
A. Singer · 2006
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Learning on graph with Laplacian regularization
R. K. Ando and T. Zhang · 2007
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Convergence of Laplacian eigenmaps
M. Belkin and P. Niyogi · 2007
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Graph Laplacians and their convergence on random neighborhood graphs
M. Hein, J.-Y. Audibert, and U. v. Luxburg · 2007
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Consistency of spectral clustering
U. Von Luxburg, M. Belkin, and O. Bousquet · 2008
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Partial Differential Equations
A minimal surface criterion for graph partitioning
D. Zosso and B. Osting · 2016
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Consistency of Dirichlet partitions
B. Osting and T. H. Reeb · 2017
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Fashion-mnist: a novel image dataset for benchmarking machine learning algorithms
H. Xiao, K. Rasul, and R. Vollgraf · 2017
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The game theoretic p-Laplacian and semi-supervised learning with few labels
J. Calder · 2018
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Lecture notes on viscosity solutions
J. Calder · 2018
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The limit shape of convex hull peeling
J. Calder and C. K. Smart · 2018
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L. Evans · 2010
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An analysis of the convergence of graph Laplacians
D. Ting, L. Huang, and M. Jordan · 2010
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Efficient manifold ranking for image retrieval
B. Xu, J. Bu, C. Chen, D. Cai, X. He, W. Liu, and J. Luo · 2011
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An iterated graph Laplacian approach for ranking on manifolds
X. Zhou, M. Belkin, and N. Srebro · 2011
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Diffuse interface models on graphs for classification of high dimensional data
A. L. Bertozzi and A. Flenner · 2012
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Multi-manifold ranking: Using multiple features for better image retrieval
Y. Wang, M. A. Cheema, X. Lin, and Q. Zhang · 2013
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Algorithms for lp-based semi-supervised learning on graphs
M. Flores, J. Calder, and G. Lerman · 2018
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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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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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Properly-weighted graph Laplacian for semi-supervised learning
J. Calder and D. Slepčev · 2019
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Diffusion based Gaussian process regression via heat kernel reconstruction
D. B. Dunson, H.-T. Wu, and N. Wu · 2019
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Variational limits of k-nn graph-based functionals on data clouds
N. García Trillos · 2019
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Spectral analysis of weighted Laplacians arising in data clustering
F. Hoffmann, B. Hosseini, A. A. Oberai, and A. M. Stuart · 2019
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Recovering hidden components in multimodal data with composite diffusion operators
T. Shnitzer, M. Ben-Chen, L. Guibas, R. Talmon, and H.-T. Wu · 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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Rates of convergence for Laplacian semi-supervised learning with low labeling rates
J. Calder, D. Slepčev, and M. Thorpe · 2020
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Error estimates for spectral convergence of the graph laplacian on random geometric graphs toward the laplace–beltrami operator
N. García Trillos, M. Gerlach, M. Hein, and D. Slepčev · 2020
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A maximum principle argument for the uniform convergence of graph laplacian regressors
N. García Trillos and R. W. Murray · 2020
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