Consistency of Modularity Clustering on Random Geometric Graphs
| dc.contributor.advisor | Sethuraman, Sunder | en |
| dc.contributor.author | Davis, Erik | |
| dc.creator | Davis, Erik | en |
| dc.date.accessioned | 2016-09-26T20:26:36Z | |
| dc.date.available | 2016-09-26T20:26:36Z | |
| dc.date.issued | 2016 | |
| dc.identifier.uri | http://hdl.handle.net/10150/620720 | |
| dc.description.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. | |
| dc.language.iso | en_US | en |
| dc.publisher | The University of Arizona. | en |
| dc.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. | en |
| dc.subject | Mathematics | en |
| dc.title | Consistency of Modularity Clustering on Random Geometric Graphs | en_US |
| dc.type | text | en |
| dc.type | Electronic Dissertation | en |
| thesis.degree.grantor | University of Arizona | en |
| thesis.degree.level | doctoral | en |
| dc.contributor.committeemember | Sethuraman, Sunder | en |
| dc.contributor.committeemember | Kennedy, Tom | en |
| dc.contributor.committeemember | Friedlander, Leonid | en |
| dc.contributor.committeemember | Venkataramani, Shankar | en |
| thesis.degree.discipline | Graduate College | en |
| thesis.degree.discipline | Mathematics | en |
| thesis.degree.name | Ph.D. | en |
| refterms.dateFOA | 2018-06-14T15:36:31Z | |
| html.description.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. |
