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dc.contributor.authorDavis, Erik
dc.contributor.authorSethuraman, Sunder
dc.date.accessioned2018-12-05T23:14:51Z
dc.date.available2018-12-05T23:14:51Z
dc.date.issued2018-08
dc.identifier.citationDavis, Erik; Sethuraman, Sunder. Consistency of modularity clustering on random geometric graphs. Ann. Appl. Probab. 28 (2018), no. 4, 2003--2062. doi:10.1214/17-AAP1313. https://projecteuclid.org/euclid.aoap/1533780266en_US
dc.identifier.issn1050-5164
dc.identifier.doi10.1214/17-AAP1313
dc.identifier.urihttp://hdl.handle.net/10150/631124
dc.description.abstractGiven a graph, the popular "modularity" clustering method specifies a partition of the vertex set as the solution of a certain optimization problem. In this paper, we discuss scaling limits of this method with respect to random geometric graphs constructed from i.i.d. points X-n = {X-1, X-2,..., X-n}, distributed according to a probability measure nu supported on a bounded domain D subset of R-d. Among other results, we show, via a Gamma convergence framework, a geometric form of consistency: When the number of clusters, or partitioning sets of X-n is a priori bounded above, the discrete optimal modularity clusterings converge in a specific sense to a continuum partition of the underlying domain D, characterized as the solution to a "soap bubble" or "Kelvin"-type shape optimization problem.en_US
dc.description.sponsorshipARO [W911NF-14-1-0179]en_US
dc.language.isoenen_US
dc.publisherINST MATHEMATICAL STATISTICSen_US
dc.relation.urlhttps://projecteuclid.org/euclid.aoap/1533780266en_US
dc.rights© Institute of Mathematical Statistics, 2018en_US
dc.subjectModularityen_US
dc.subjectcommunity detectionen_US
dc.subjectconsistencyen_US
dc.subjectrandom geometric graphen_US
dc.subjectGamma convergenceen_US
dc.subjectKelvin's problemen_US
dc.subjectscaling limiten_US
dc.subjectshape optimizationen_US
dc.subjectoptimal transporten_US
dc.subjecttotal variationen_US
dc.subjectperimeteren_US
dc.titleConsistency of modularity clustering on random geometric graphsen_US
dc.typeArticleen_US
dc.contributor.departmentUniv Arizona, Dept Mathen_US
dc.identifier.journalANNALS OF APPLIED PROBABILITYen_US
dc.description.collectioninformationThis item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at repository@u.library.arizona.edu.en_US
dc.eprint.versionFinal published versionen_US
dc.source.journaltitleThe Annals of Applied Probability
dc.source.volume28
dc.source.issue4
dc.source.beginpage2003
dc.source.endpage2062
refterms.dateFOA2018-12-05T23:14:52Z


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