Efficient Quasi-Geodesics on the Stiefel Manifold

Thomas Bendokat*, Ralf Zimmermann

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingArticle in proceedingsResearchpeer-review

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Abstract

Solving the so-called geodesic endpoint problem, i.e., finding a geodesic that connects two given points on a manifold, is at the basis of virtually all data processing operations, including averaging, clustering, interpolation and optimization. On the Stiefel manifold of orthonormal frames, this problem is computationally involved. A remedy is to use quasi-geodesics as a replacement for the Riemannian geodesics. Quasi-geodesics feature constant speed and covariant acceleration with constant (but possibly non-zero) norm. For a well-known type of quasi-geodesics, we derive a new representation that is suited for large-scale computations. Moreover, we introduce a new kind of quasi-geodesics that turns out to be much closer to the Riemannian geodesics.
Original languageEnglish
Title of host publicationGeometric Science of Information : 5th International Conference, GSI 2021, Paris, France, July 21–23, 2021, Proceedings
EditorsFrank Nielsen, Frédéric Barbaresco
PublisherSpringer
Publication date14. Jul 2021
Pages763-771
ISBN (Print)978-3-030-80208-0
ISBN (Electronic)978-3-030-80209-7
DOIs
Publication statusPublished - 14. Jul 2021
Event5th International Conference - Paris, France
Duration: 21. Jul 202123. Jul 2021

Conference

Conference5th International Conference
Country/TerritoryFrance
CityParis
Period21/07/202123/07/2021
SeriesLecture Notes in Computer Science
Volume12829
ISSN0302-9743

Keywords

  • Stiefel Manifold
  • Geodesic
  • Quasi-geodesic
  • Geodesic Endpoint Problem
  • Stiefel manifold
  • Geodesic endpoint problem

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