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We study the game theoretic p-Laplacian for semi-supervised learning on graphs, and show that it is well-posed in the limit of finite labeled data and infinite unlabeled data.
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Probability inequalities for sums of bounded random variables
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Regularity for a more general class of quasilinear elliptic equations
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Boundary regularity for solutions of degenerate elliptic equations
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Convergence of approximation schemes for fully nonlinear second order equations
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User’s guide to viscosity solutions of second order partial differential equations
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Gradient-based learning applied to document recognition
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On the equivalence of viscosity solutions and weak solutions for a quasi-linear equation
Petri Juutinen, Peter Lindqvist, and Juan J Manfredi · 2001
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Semi-supervised learning using gaussian fields and harmonic functions
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Learning with local and global consistency
Dengyong Zhou, Olivier Bousquet, Thomas Navin Lal, Jason Weston, and Bernhard Schölkopf · 2004
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Ranking on data manifolds
Dengyong Zhou, Jason Weston, Arthur Gretton, Olivier Bousquet, and Bernhard Schölkopf · 2004
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Manifold-ranking based image retrieval
Jingrui He, Mingjing Li, Hong-Jiang Zhang, Hanghang Tong, and Changshui Zhang · 2004
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Distance-based classification with lipschitz functions
Ulrike von Luxburg and Olivier Bousquet · 2004
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A tour of the theory of absolutely minimizing functions
Gunnar Aronsson, Michael Crandall, and Petri Juutinen · 2004
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Nearly-linear time algorithms for graph partitioning, graph sparsification, and solving linear systems
Daniel A Spielman and Shang-Hua Teng · 2004
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Convex optimization
Stephen Boyd and Lieven Vandenberghe · 2004
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Learning from labeled and unlabeled data on a directed graph
Dengyong Zhou, Jiayuan Huang, and Bernhard Schölkopf · 2005
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Intrinsic dimensionality estimation of submanifolds in Rd
Matthias Hein and Jean-Yves Audibert · 2005
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Towards a theoretical foundation for Laplacian-based manifold methods
Mikhail Belkin and Partha Niyogi · 2005
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From graphs to manifolds–weak and strong pointwise consistency of graph Laplacians
Matthias Hein, Jean-Yves Audibert, and Ulrike Von Luxburg · 2005
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Semi-supervised learning
Olivier Chapelle, Bernhard Scholkopf, and Alexander Zien · 2006
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Generalized manifold-ranking-based image retrieval
Jingrui He, Mingjing Li, H-J Zhang, Hanghang Tong, and Changshui Zhang · 2006
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Determining intrinsic dimension and entropy of high-dimensional shape spaces
Jose A Costa and Alfred O Hero · 2006
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Efficient manifold ranking for image retrieval
Bin Xu, Jiajun Bu, Chun Chen, Deng Cai, Xiaofei He, Wei Liu, and Jiebo Luo · 2011
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Phase transition in the family of p-resistances
Morteza Alamgir and Ulrike V Luxburg · 2011
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Multi-manifold ranking: Using multiple features for better image retrieval
Yang Wang, Muhammad Aamir Cheema, Xuemin Lin, and Qing Zhang · 2013
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Saliency detection via graph-based manifold ranking
Chuan Yang, Lihe Zhang, Huchuan Lu, Xiang Ruan, and Ming-Hsuan Yang · 2013
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p-voltages: Laplacian regularization for semi-supervised learning on high-dimensional data
Nick Bridle and Xiaojin Zhu · 2013
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Finite difference methods for the infinity laplace and p-laplace equations
Adam M Oberman · 2013
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Uniform convergence of adaptive graph-based regularization
Matthias Hein · 2006
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Empirical graph laplacian approximation of Laplace–Beltrami operators: Large sample results
Evarist Giné, Vladimir Koltchinskii, et al · 2006
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From graph to manifold Laplacian: The convergence rate
Amit Singer · 2006
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Learning on graph with laplacian regularization
Rie Kubota Ando and Tong Zhang · 2007
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Graph Laplacians and their convergence on random neighborhood graphs
Matthias Hein, Jean-Yves Audibert, and Ulrike von Luxburg · 2007
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Semi-supervised learning with the graph Laplacian: The limit of infinite unlabelled data
Boaz Nadler, Nathan Srebro, and Xueyuan Zhou · 2009
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Concentration inequalities: A nonasymptotic theory of independence
Stéphane Boucheron, Gábor Lugosi, and Pascal Massart · 2013
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Game theoretical methods in pdes
Marta Lewicka and Juan J Manfredi · 2014
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Solving SDD linear systems in nearly m log 1/2 n time
Michael B Cohen, Rasmus Kyng, Gary L Miller, Jakub W Pachocki, Richard Peng, Anup B Rao, and Shen Chen Xu · 2014
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Algorithms for lipschitz learning on graphs
Rasmus Kyng, Anup Rao, Sushant Sachdeva, and Daniel A Spielman · 2015
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Nonlinear elliptic partial differential equations and p-harmonic functions on graphs
Juan J Manfredi, Adam M Oberman, and Alexander P Sviridov · 2015
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A PDE-based approach to non-dominated sorting
Jeff Calder, Selim Esedoḡlu, and Alfred O Hero III · 2015
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Asymptotic behavior of lp-based Laplacian regularization in semi-supervised learning
Ahmed El Alaoui, Xiang Cheng, Aaditya Ramdas, Martin J Wainwright, and Michael I Jordan · 2016
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Notes on the p-Laplace equation
Peter Lindqvist · 2017
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Consistency of Lipschitz learning with infinite unlabeled and finite labeled data
Jeff Calder · 2017
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Analysis of p p -laplacian regularization in semi-supervised learning
Dejan Slepčev and Matthew Thorpe · 2017
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Density estimation for statistics and data analysis
Bernard W Silverman · 2018
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