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Spectral clustering based on the graph p-Laplacian

Authors:

Thomas Bühler,

Matthias HeinAuthors Info & Claims

ICML '09: Proceedings of the 26th Annual International Conference on Machine Learning

Pages 81 - 88

https://doi.org/10.1145/1553374.1553385

Published: 14 June 2009 Publication History

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Abstract

We present a generalized version of spectral clustering using the graph p-Laplacian, a nonlinear generalization of the standard graph Laplacian. We show that the second eigenvector of the graph p-Laplacian interpolates between a relaxation of the normalized and the Cheeger cut. Moreover, we prove that in the limit as p → 1 the cut found by thresholding the second eigenvector of the graph p-Laplacian converges to the optimal Cheeger cut. Furthermore, we provide an efficient numerical scheme to compute the second eigenvector of the graph p-Laplacian. The experiments show that the clustering found by p-spectral clustering is at least as good as normal spectral clustering, but often leads to significantly better results.

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Li XDai WLi SLi CZou JXiong H(2024)3-D Point Cloud Attribute Compression With -Laplacian Embedding Graph Dictionary LearningIEEE Transactions on Pattern Analysis and Machine Intelligence10.1109/TPAMI.2023.332837746:2(975-993)Online publication date: Feb-2024
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Chen JWang YZhang D(2024)HGT: Transformer Architecture for Arbitrary Hypergraphs Based on P-Laplacian2024 International Joint Conference on Neural Networks (IJCNN)10.1109/IJCNN60899.2024.10650472(1-9)Online publication date: 30-Jun-2024
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Published In

ICML '09: Proceedings of the 26th Annual International Conference on Machine Learning

June 2009

1331 pages

ISBN:9781605585161

DOI:10.1145/1553374

General Chair:
Andrea Danyluk
Williams College
,
Program Chairs:
Léon Bottou
NEC Laboratories America
,
Michael Littman
Rutgers University

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Association for Computing Machinery

New York, NY, United States

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Published: 14 June 2009

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Sponsor:

Microsoft Research

ICML '09: The 26th Annual International Conference on Machine Learning held in conjunction with the 2007 International Conference on Inductive Logic Programming

June 14 - 18, 2009

Quebec, Montreal, Canada

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Overall Acceptance Rate 140 of 548 submissions, 26%

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Li XDai WLi SLi CZou JXiong H(2024)3-D Point Cloud Attribute Compression With -Laplacian Embedding Graph Dictionary LearningIEEE Transactions on Pattern Analysis and Machine Intelligence10.1109/TPAMI.2023.332837746:2(975-993)Online publication date: Feb-2024
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Chen JWang YZhang D(2024)HGT: Transformer Architecture for Arbitrary Hypergraphs Based on P-Laplacian2024 International Joint Conference on Neural Networks (IJCNN)10.1109/IJCNN60899.2024.10650472(1-9)Online publication date: 30-Jun-2024
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Saito SHerbster MKrause ABrunskill ECho KEngelhardt BSabato SScarlett J(2023)Multi-class graph clustering via approximated effective p-resistanceProceedings of the 40th International Conference on Machine Learning10.5555/3618408.3619641(29697-29733)Online publication date: 23-Jul-2023
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Zhu YSegarra S(2023)Hypergraphs with edge-dependent vertex weights: p-Laplacians and spectral clusteringFrontiers in Big Data10.3389/fdata.2023.10201736Online publication date: 21-Feb-2023
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El Bouchairi IFadili JHafiene YElmoataz A(2023)Nonlocal Continuum Limits of p-Laplacian Problems on Graphs10.1017/9781009327862Online publication date: 13-Apr-2023
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