Persistent Link:
http://hdl.handle.net/10150/620720
Title:
Consistency of Modularity Clustering on Random Geometric Graphs
Author:
Davis, Erik
Issue Date:
2016
Publisher:
The University of Arizona.
Rights:
Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
Abstract:
We consider a large class of random geometric graphs constructed from independent, identically distributed observations of an underlying probability measure on a bounded domain. The popular `modularity' clustering method specifies a partition of a graph as the solution of an optimization problem. In this dissertation we derive scaling limits of the modularity clustering on random geometric graphs. Among other results, we show a geometric form of consistency: When the number of clusters is a priori bounded above, the discrete optimal partitions converge in a certain sense to a continuum partition of the underlying domain, characterized as the solution of a type of Kelvin's shape optimization problem.
Type:
text; Electronic Dissertation
Keywords:
Mathematics
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Graduate College; Mathematics
Degree Grantor:
University of Arizona
Advisor:
Sethuraman, Sunder

Full metadata record

DC FieldValue Language
dc.language.isoen_USen
dc.titleConsistency of Modularity Clustering on Random Geometric Graphsen_US
dc.creatorDavis, Eriken
dc.contributor.authorDavis, Eriken
dc.date.issued2016-
dc.publisherThe University of Arizona.en
dc.rightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.en
dc.description.abstractWe consider a large class of random geometric graphs constructed from independent, identically distributed observations of an underlying probability measure on a bounded domain. The popular `modularity' clustering method specifies a partition of a graph as the solution of an optimization problem. In this dissertation we derive scaling limits of the modularity clustering on random geometric graphs. Among other results, we show a geometric form of consistency: When the number of clusters is a priori bounded above, the discrete optimal partitions converge in a certain sense to a continuum partition of the underlying domain, characterized as the solution of a type of Kelvin's shape optimization problem.en
dc.typetexten
dc.typeElectronic Dissertationen
dc.subjectMathematicsen
thesis.degree.namePh.D.en
thesis.degree.leveldoctoralen
thesis.degree.disciplineGraduate Collegeen
thesis.degree.disciplineMathematicsen
thesis.degree.grantorUniversity of Arizonaen
dc.contributor.advisorSethuraman, Sunderen
dc.contributor.committeememberSethuraman, Sunderen
dc.contributor.committeememberKennedy, Tomen
dc.contributor.committeememberFriedlander, Leoniden
dc.contributor.committeememberVenkataramani, Shankaren
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