Article

An analysis of the convergence of graph Laplacians

Authors:

Michael I. JordanAuthors Info & Claims

ICML'10: Proceedings of the 27th International Conference on International Conference on Machine Learning

Pages 1079 - 1086

Published: 21 June 2010 Publication History

Abstract

Existing approaches to analyzing the asymptotics of graph Laplacians typically assume a well-behaved kernel function with smoothness assumptions. We remove the smoothness assumption and generalize the analysis of graph Laplacians to include previously unstudied graphs including kNN graphs. We also introduce a kernel-free framework to analyze graph constructions with shrinking neighborhoods in general and apply it to analyze locally linear embedding (LLE). We also describe how, for a given limit operator, desirable properties such as a convergent spectrum and sparseness can be achieved by choosing the appropriate graph construction.

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Cited By

Taseska Mvan Waterschoot THabets ETalmon R(2020)Nonlinear Filtering With Variable Bandwidth Exponential KernelsIEEE Transactions on Signal Processing10.1109/TSP.2019.295919068(314-326)Online publication date: 1-Jan-2020
https://dl.acm.org/doi/10.1109/TSP.2019.2959190
Chen YMeila MWallach HLarochelle HBeygelzimer Ad'Alché-Buc FFox E(2019)Selecting the independent coordinates of manifolds with large aspect ratiosProceedings of the 33rd International Conference on Neural Information Processing Systems10.5555/3454287.3454385(1088-1097)Online publication date: 8-Dec-2019
https://dl.acm.org/doi/10.5555/3454287.3454385
Perrault-Joncas DMeilǎ MMcQueen J(2017)Improved graph laplacian via geometric consistencyProceedings of the 31st International Conference on Neural Information Processing Systems10.5555/3294996.3295199(4460-4469)Online publication date: 4-Dec-2017
https://dl.acm.org/doi/10.5555/3294996.3295199
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Published In

cover image Guide Proceedings

ICML'10: Proceedings of the 27th International Conference on International Conference on Machine Learning

June 2010

1262 pages

ISBN:9781605589077

Sponsors

NSF: National Science Foundation
Xerox
Microsoft Research: Microsoft Research
Yahoo!
IBM: IBM

Publisher

Omnipress

Madison, WI, United States

Publication History

Published: 21 June 2010

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Cited By

Taseska Mvan Waterschoot THabets ETalmon R(2020)Nonlinear Filtering With Variable Bandwidth Exponential KernelsIEEE Transactions on Signal Processing10.1109/TSP.2019.295919068(314-326)Online publication date: 1-Jan-2020
https://dl.acm.org/doi/10.1109/TSP.2019.2959190
Chen YMeila MWallach HLarochelle HBeygelzimer Ad'Alché-Buc FFox E(2019)Selecting the independent coordinates of manifolds with large aspect ratiosProceedings of the 33rd International Conference on Neural Information Processing Systems10.5555/3454287.3454385(1088-1097)Online publication date: 8-Dec-2019
https://dl.acm.org/doi/10.5555/3454287.3454385
Perrault-Joncas DMeilǎ MMcQueen J(2017)Improved graph laplacian via geometric consistencyProceedings of the 31st International Conference on Neural Information Processing Systems10.5555/3294996.3295199(4460-4469)Online publication date: 4-Dec-2017
https://dl.acm.org/doi/10.5555/3294996.3295199
McQueen JMeila MPerrault-Joncas D(2016)Nearly isometric embedding by relaxationProceedings of the 30th International Conference on Neural Information Processing Systems10.5555/3157382.3157393(2639-2647)Online publication date: 5-Dec-2016
https://dl.acm.org/doi/10.5555/3157382.3157393
Hashimoto TSun YJaakkola T(2015)From random walks to distances on unweighted graphsProceedings of the 29th International Conference on Neural Information Processing Systems - Volume 210.5555/2969442.2969622(3429-3437)Online publication date: 7-Dec-2015
https://dl.acm.org/doi/10.5555/2969442.2969622

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