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In the classical literature of Statistics, a large amount of methods have been addressed for data analysis on Euclidean space. Over the past few decades, however, a growing interest has been devoted to non-Euclidean data analysis. In other words, newly collected data, extracted from a variety of new digital sensors, was unimaginable in the previous flat world of classical data analysis. Examples of such new data types include planar or 3D shapes, neuroimaging data (DTI, fMRI), and other types of medical images (CT, X-Rays). Due to the underlying geometry of the space where data lies, such complex data type can, however, not be analyzed in a Euclidean way. % In order to address this comprehensively, a new research field, so-called object-oriented data analysis (OODA) has emerged in Statistics. From the OODA point of view, data objects are represented as points on nonlinear metric spaces called object spaces. In various types of object spaces where data objects naturally lie are smooth manifolds. So the focus of this dissertation is on the development of statistical methods on manifolds.
A Dissertation submitted to the Department of Statistics in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
Bibliography Note
Includes bibliographical references.
Advisory Committee
Vic Patrangenaru, Professor Directing Dissertation; Petru Andrei, University Representative; Chao Huang, Committee Member; Andres Felipe Barrientos, Committee Member.
Publisher
Florida State University
Identifier
2020_Summer_Fall_Lee_fsu_0071E_16430
Lee, H. (2021). Extrinsic Analysis of Manifold Valued Data. Retrieved from https://purl.lib.fsu.edu/diginole/2020_Summer_Fall_Lee_fsu_0071E_16430