Efficient Quasi-Geodesics on the Stiefel Manifold

Thomas Bendokat*, Ralf Zimmermann

*Kontaktforfatter for dette arbejde

Publikation: Kapitel i bog/rapport/konference-proceedingKonferencebidrag i proceedingsForskningpeer review

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Abstrakt

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.
OriginalsprogEngelsk
TitelGeometric Science of Information : 5th International Conference, GSI 2021, Paris, France, July 21–23, 2021, Proceedings
RedaktørerF. Nielsen, F. Barbaresco
ForlagSpringer
Publikationsdato14. jul. 2021
Sider763-771
ISBN (Trykt)978-3-030-80208-0
ISBN (Elektronisk)978-3-030-80209-7
DOI
StatusUdgivet - 14. jul. 2021
Begivenhed5th International Conference - Paris, Frankrig
Varighed: 21. jul. 202123. jul. 2021

Konference

Konference5th International Conference
Land/OmrådeFrankrig
ByParis
Periode21/07/202123/07/2021
NavnLecture Notes in Computer Science
Vol/bind12829
ISSN0302-9743

Bibliografisk note

1) Peer review<br/>2) arxiv version of accepted contribution to the proceedings of the <br/>5th conference on Geometric Science of Information in PARIS, Sorbonne University

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