Shiping Liu
Multi-way dual Cheeger constants and spectral bounds of graphs
Liu, Shiping
Authors
Abstract
We introduce a set of multi-way dual Cheeger constants and prove universal higher-order dual Cheeger inequalities for eigenvalues of normalized Laplace operators on weighted finite graphs. Our proof proposes a new spectral clustering phenomenon deduced from metrics on real projective spaces. We further extend those results to a general reversible Markov operator and find applications in characterizing its essential spectrum.
Citation
Liu, S. (2015). Multi-way dual Cheeger constants and spectral bounds of graphs. Advances in Mathematics, 268, 306-338. https://doi.org/10.1016/j.aim.2014.09.023
Journal Article Type | Article |
---|---|
Acceptance Date | Sep 29, 2014 |
Online Publication Date | Oct 10, 2014 |
Publication Date | Jan 2, 2015 |
Deposit Date | Aug 14, 2014 |
Publicly Available Date | Oct 13, 2014 |
Journal | Advances in Mathematics |
Print ISSN | 0001-8708 |
Publisher | Elsevier |
Peer Reviewed | Peer Reviewed |
Volume | 268 |
Pages | 306-338 |
DOI | https://doi.org/10.1016/j.aim.2014.09.023 |
Keywords | Cheeger constants, Higher-order dual Cheeger inequalities, Spectral clustering, Markov operators, Essential spectrum. |
Public URL | https://durham-repository.worktribe.com/output/1422296 |
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Publisher Licence URL
http://creativecommons.org/licenses/by/3.0/
Copyright Statement
© 2014 The Author. Published by Elsevier Inc. This is an
open access article under the CC BY license
(http://creativecommons.org/licenses/by/3.0/).
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