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Riemannian Optimization Methods for Averaging Symmetric Positive Definite Matrices

Title: Riemannian Optimization Methods for Averaging Symmetric Positive Definite Matrices.
Name(s): Yuan, Xinru, author
Gallivan, Kyle A., 1958-, professor co-directing dissertation
Absil, Pierre-Antoine, professor co-directing dissertation
Erlebacher, Gordon, 1957-, university representative
Ökten, Giray, committee member
Bauer, Martin, committee member
Florida State University, degree granting institution
College of Arts and Sciences, degree granting college
Department of Mathematics, degree granting department
Type of Resource: text
Genre: Text
Doctoral Thesis
Issuance: monographic
Date Issued: 2018
Publisher: Florida State University
Place of Publication: Tallahassee, Florida
Physical Form: computer
online resource
Extent: 1 online resource (164 pages)
Language(s): English
Abstract/Description: Symmetric positive definite (SPD) matrices have become fundamental computational objects in many areas. It is often of interest to average a collection of symmetric positive definite matrices. This dissertation investigates different averaging techniques for symmetric positive definite matrices. We use recent developments in Riemannian optimization to develop efficient and robust algorithms to handle this computational task. We provide methods to produce efficient numerical representations of geometric objects that are required for Riemannian optimization methods on the manifold of symmetric positive definite matrices. In addition, we offer theoretical and empirical suggestions on how to choose between various methods and parameters. In the end, we evaluate the performance of different averaging techniques in applications.
Identifier: 2018_Su_Yuan_fsu_0071E_14736 (IID)
Submitted Note: A Dissertation submitted to the Department of Mathematics in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
Degree Awarded: Summer Semester 2018.
Date of Defense: July 20, 2018.
Bibliography Note: Includes bibliographical references.
Advisory Committee: Kyle A. Gallivan, Professor Co-Directing Dissertation; Pierre-Antoine Absil, Professor Co-Directing Dissertation; Gordon Erlebacher, University Representative; Giray Okten, Committee Member; Martin Bauer, Committee Member.
Subject(s): Applied mathematics
Persistent Link to This Record:
Host Institution: FSU

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Yuan, X. (2018). Riemannian Optimization Methods for Averaging Symmetric Positive Definite Matrices. Retrieved from