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http://hdl.handle.net/11375/28448
Title: | Hyperbolic Distributions and Transformations for Clustering Incomplete Data with Extensions to Matrix Variate Normality |
Authors: | Pocuca, Nikola |
Advisor: | McNicholas, Paul |
Department: | Mathematics and Statistics |
Keywords: | Model-based clustering |
Publication Date: | 2023 |
Abstract: | Under realistic scenarios, data are often incomplete, asymmetric, or of high-dimensionality. More intricate data structures often render standard approaches infeasible due to methodological or computational limitations. This monograph consists of four contributions each solving a specific problem within model-based clustering. An R package is developed consisting of a three-phase imputation method for both elliptical and hyperbolic parsimonious models. A novel stochastic technique is employed to speed up computations for hyperbolic distributions demonstrating superior performance overall. A hyperbolic transformation model is conceived for clustering asymmetrical data within a heterogeneous context. Finally, for high-dimensionality, a framework is developed for assessing matrix variate normality within three-way datasets. All things considered, this work constitutes a powerful set of tools to deal with the ever-growing complexity of big data |
URI: | http://hdl.handle.net/11375/28448 |
Appears in Collections: | Open Access Dissertations and Theses |
Files in This Item:
File | Description | Size | Format | |
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NikolaPocucaThesisPhD.pdf | 6.77 MB | Adobe PDF | View/Open |
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