The statistical detection of clusters in networks

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dc.contributor Melnykov, Volodymyr
dc.contributor Perry, Marcus B.
dc.contributor Melouk, Sharif H.
dc.contributor Bachrach, Daniel G.
dc.contributor.advisor Perry, Marcus B. Ballard, Marcus Alan
dc.contributor.other University of Alabama Tuscaloosa 2018-12-14T18:12:24Z 2018-12-14T18:12:24Z 2018
dc.identifier.other u0015_0000001_0003136
dc.identifier.other Ballard_alatus_0004D_13496
dc.description Electronic Thesis or Dissertation en_US
dc.description.abstract A 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.extent 109 p.
dc.format.medium electronic
dc.format.mimetype application/pdf
dc.language English
dc.language.iso en_US
dc.publisher University of Alabama Libraries
dc.relation.ispartof The University of Alabama Electronic Theses and Dissertations
dc.relation.ispartof The University of Alabama Libraries Digital Collections
dc.relation.hasversion born digital
dc.rights All rights reserved by the author unless otherwise indicated. en_US
dc.subject Statistics
dc.subject Operations research
dc.subject Applied mathematics
dc.title The statistical detection of clusters in networks en_US
dc.type thesis
dc.type text University of Alabama. Department of Information Systems, Statistics, and Management Science Applied Statistics The University of Alabama doctoral Ph.D.

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