Manifold Learning, Topological Data Analysis, and Their Applications to Medical ImagingdissertationsMeng, KuncreatorEloyan, AniAdvisorGatsonis, ConstantineReaderHarrison, MatthewReaderCrawford, LorinReaderBrown University. Department of Biostatisticssponsor2022, None p.born digitalThesis (Ph. D.)--Brown University, 2022thesesThis dissertation aims to develop several statistical methods for learning the manifold and topology structures of data, provide the corresponding theoretical foundations, and apply the proposed methods to medical imaging. Specifically, this dissertation is concerned with manifold learning, brain networks, and topological data analysis.Applied mathematicsBiostatisticsEnglishRPB20220706