The statistical detection of clusters in networks

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dc.contributorMelnykov, Volodymyr
dc.contributorPerry, Marcus B.
dc.contributorMelouk, Sharif H.
dc.contributorBachrach, Daniel G.
dc.contributor.advisorPerry, Marcus B.
dc.contributor.authorBallard, Marcus Alan
dc.contributor.otherUniversity of Alabama Tuscaloosa
dc.date.accessioned2018-12-14T18:12:24Z
dc.date.available2018-12-14T18:12:24Z
dc.date.issued2018
dc.descriptionElectronic Thesis or Dissertationen_US
dc.description.abstractA network consists of vertices and edges that connect the vertices. A network is clustered by assigning each of the N vertices to one of k groups, usually in order to optimize a given objective function. This dissertation proposes statistical likelihood as an objective function for network clustering for both undirected networks, in which edges have no direction, and directed networks, in which edges have direction. Clustering networks by optimizing an objective function is computationally expensive and quickly becomes prohibitive as the number of vertices in a network grows large. To address this, theorems are developed to increase the efficiency of likelihood parameter estimation during the optimization and a significant decrease in time-to-solution is demonstrated. When the clustering performance of likelihood is rigorously compared to competitor objective function modularity using Monte Carlo simulation, likelihood is frequently found to be superior. A novel statistical significance test for clusters identified when using likelihood as an objective function is also derived and both clustering using the likelihood objective function and subsequent significance testing are demonstrated on real-world networks, both undirected and directed.en_US
dc.format.extent109 p.
dc.format.mediumelectronic
dc.format.mimetypeapplication/pdf
dc.identifier.otheru0015_0000001_0003136
dc.identifier.otherBallard_alatus_0004D_13496
dc.identifier.urihttp://ir.ua.edu/handle/123456789/5268
dc.languageEnglish
dc.language.isoen_US
dc.publisherUniversity of Alabama Libraries
dc.relation.hasversionborn digital
dc.relation.ispartofThe University of Alabama Electronic Theses and Dissertations
dc.relation.ispartofThe University of Alabama Libraries Digital Collections
dc.rightsAll rights reserved by the author unless otherwise indicated.en_US
dc.subjectStatistics
dc.subjectOperations research
dc.subjectApplied mathematics
dc.titleThe statistical detection of clusters in networksen_US
dc.typethesis
dc.typetext
etdms.degree.departmentUniversity of Alabama. Department of Information Systems, Statistics, and Management Science
etdms.degree.disciplineApplied Statistics
etdms.degree.grantorThe University of Alabama
etdms.degree.leveldoctoral
etdms.degree.namePh.D.

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