Application of Hidden Markov Model in Finite Mixture Modeling of High-Dimensional Data

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dc.contributorMa, Wenchao
dc.contributorMelnykov, Volodymyr
dc.contributorMelnykov, Yana
dc.contributorPerry, Marcus
dc.contributorSarkar, Shuchismita
dc.contributor.advisorZhu, Xuwen
dc.contributor.authorAsilkalkan, Abdullah
dc.date.accessioned2023-11-30T15:21:25Z
dc.date.available2028-08-10
dc.date.issued2023
dc.descriptionElectronic Thesis or Dissertationen_US
dc.description.abstractFinite mixture models (FMMs) are widely used in practice and are famous for modeling heterogeneous data in a convenient and effective way. Owing to their flexibility, finitemixtures have since been applied to a wide range of problems in diverse fields, includingimage analysis, medicine, agriculture, and many others. FMMs are particularly useful formodel-based clustering, where each group is assumed to be represented by one of the mixturecomponents. Although finite mixtures can adopt various functional forms, Gaussian densities are one of the most widely used representations. Specifically, multivariate Gaussiandensities based on vector-valued data have received considerable research attention owingto their wide utilization range. However, as datasets with higher dimensions are becomingincreasingly prevalent due to rapid improvements in computational power and data storagecapabilities, well-known issues such as overparameterization may emerge in the FMM framework, which leads to underestimation of the correct mixture order. This issue has motivatedthe current dissertation, as a part of which the FMM framework that can be applied todata with higher dimensions is proposed. The organization of this dissertation is as follows.In the first chapter, a hidden Markov model (HMM) for matrix-variate time series data isdeveloped, followed by a finite mixture of HMMs aimed at tensor-variate time series data inthe second chapter. Finally, in the third chapter, we develop an extension of matrix-variatetime series modeling with HMMs observed over multiple time points that will be completedlater and applied to the US institutions enrollment data in the context of a hypothesis testingproblem.en_US
dc.format.mediumelectronic
dc.format.mimetypeapplication/pdf
dc.identifier.otherhttp://purl.lib.ua.edu/188241
dc.identifier.otheru0015_0000001_0004760
dc.identifier.otherASILKALKAN_alatus_0004D_15291
dc.identifier.urihttps://ir.ua.edu/handle/123456789/12747
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.titleApplication of Hidden Markov Model in Finite Mixture Modeling of High-Dimensional Dataen_us
dc.typethesis
dc.typetext
etdms.degree.departmentUniversity of Alabama. Department of Information Systems, Statistics, and Management Science
etdms.degree.disciplineStatistics
etdms.degree.grantorThe University of Alabama
etdms.degree.leveldoctoral
etdms.degree.namePh.D.

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