Solution of Constrained Clustering Problems through Homotopy Tracking

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dc.contributor.authorEasterling, David R.en
dc.contributor.committeechairWatson, Layne T.en
dc.contributor.committeememberRamakrishnan, Narenen
dc.contributor.committeememberCao, Yangen
dc.contributor.committeememberBorggaard, Jeffrey T.en
dc.contributor.committeememberCameron, Kirk W.en
dc.contributor.committeememberThacker, William Ivanhoeen
dc.contributor.departmentComputer Scienceen
dc.date.accessioned2015-01-16T09:00:32Zen
dc.date.available2015-01-16T09:00:32Zen
dc.date.issued2015-01-15en
dc.description.abstractModern machine learning methods are dependent on active optimization research to improve the set of methods available for the efficient and effective extraction of information from large datasets. This, in turn, requires an intense and rigorous study of optimization methods and their possible applications to crucial machine learning applications in order to advance the potential benefits of the field. This thesis provides a study of several modern optimization techniques and supplies a mathematical inquiry into the effectiveness of homotopy methods to attack a fundamental machine learning problem, effective clustering under constraints. The first part of this thesis provides an empirical survey of several popular optimization algorithms, along with one approach that is cutting-edge. These algorithms are tested against deeply challenging real-world problems with vast numbers of local minima, and compares and contrasts the benefits of each when confronted with problems of different natures. The second part of this thesis proposes a new homotopy map for use with constrained clustering problems. This thesis explores the connections between the map and the problem, providing several theorems to justify the use of the map and making use of modern homotopy tracking software to compare an optimization that employs the map with several modern approaches to solving the same problem.en
dc.description.degreePh. D.en
dc.format.mediumETDen
dc.identifier.othervt_gsexam:3901en
dc.identifier.urihttp://hdl.handle.net/10919/51189en
dc.publisherVirginia Techen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectMultiobjective optimizationen
dc.subjectstochastic optimizationen
dc.subjectdeterministic op- timizationen
dc.subjectbiomechanicsen
dc.subjectquadratic optimizationen
dc.subjectDIRECTen
dc.subjectQNSTOPen
dc.subjectKNITROen
dc.subjectSPANen
dc.subjectsimulated annealingen
dc.subjecthomotopyen
dc.subjectconstrained clusteringen
dc.titleSolution of Constrained Clustering Problems through Homotopy Trackingen
dc.typeDissertationen
thesis.degree.disciplineComputer Science and Applicationsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.leveldoctoralen
thesis.degree.namePh. D.en

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