Efficient Quasi-Geodesics on the Stiefel Manifold

Thomas Bendokat; Ralf Zimmermann

doi:10.1007/978-3-030-80209-7_82

Efficient Quasi-Geodesics on the Stiefel Manifold

Thomas Bendokat^*, Ralf Zimmermann

^*Kontaktforfatter

Institut for Matematik og Datalogi

Publikation: Kapitel i bog/rapport/konference-proceeding › Konferencebidrag i proceedings › Forskning › peer 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.

Originalsprog	Engelsk
Titel	Geometric Science of Information : 5th International Conference, GSI 2021, Paris, France, July 21–23, 2021, Proceedings
Redaktører	Frank Nielsen, Frédéric Barbaresco
Forlag	Springer
Publikationsdato	14. jul. 2021
Sider	763-771
ISBN (Trykt)	978-3-030-80208-0
ISBN (Elektronisk)	978-3-030-80209-7
DOI	https://doi.org/10.1007/978-3-030-80209-7_82
Status	Udgivet - 14. jul. 2021
Begivenhed	5th International Conference - Paris, Frankrig Varighed: 21. jul. 2021 → 23. jul. 2021

Konference

Konference	5th International Conference
Land/Område	Frankrig
By	Paris
Periode	21/07/2021 → 23/07/2021

Navn	Lecture Notes in Computer Science
Vol/bind	12829
ISSN	0302-9743

Bibliografisk note

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

Dokumenter og links

10.1007/978-3-030-80209-7_82

Open Access VersionIndsendt manuskript, 172 KB

SDU link

Tjek adgangen til materialet i Syddansk Universitetsbiblioteks søgemaskine

1 Ph.d.-afhandling

The Classical and Symplectic Stiefel and Grassmann Manifolds: Geometry and Applications
Bendokat, T., 30. nov. 2021, Syddansk Universitet. Det Naturvidenskabelige Fakultet. 145 s.
Publikation: Afhandling › Ph.d.-afhandling

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Citationsformater

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title = "Efficient Quasi-Geodesics on the Stiefel Manifold",

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.",

keywords = "Stiefel Manifold, Geodesic, Quasi-geodesic, Geodesic Endpoint Problem, Stiefel manifold, Geodesic endpoint problem",

author = "Thomas Bendokat and Ralf Zimmermann",

note = "1) Peer review 2) arxiv version of accepted contribution to the proceedings of the 5th conference on Geometric Science of Information in PARIS, Sorbonne University; 5th International Conference, GSI 2021 ; Conference date: 21-07-2021 Through 23-07-2021",

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doi = "10.1007/978-3-030-80209-7_82",

language = "English",

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series = "Lecture Notes in Computer Science",

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editor = "Frank Nielsen and Fr{\'e}d{\'e}ric Barbaresco",

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Bendokat, T & Zimmermann, R 2021, Efficient Quasi-Geodesics on the Stiefel Manifold. i F Nielsen & F Barbaresco (red), Geometric Science of Information: 5th International Conference, GSI 2021, Paris, France, July 21–23, 2021, Proceedings. Springer, Lecture Notes in Computer Science, bind 12829, s. 763-771, 5th International Conference, Paris, Frankrig, 21/07/2021. https://doi.org/10.1007/978-3-030-80209-7_82

Efficient Quasi-Geodesics on the Stiefel Manifold. / Bendokat, Thomas; Zimmermann, Ralf.
Geometric Science of Information: 5th International Conference, GSI 2021, Paris, France, July 21–23, 2021, Proceedings. red. / Frank Nielsen; Frédéric Barbaresco. Springer, 2021. s. 763-771 (Lecture Notes in Computer Science, Bind 12829).

Publikation: Kapitel i bog/rapport/konference-proceeding › Konferencebidrag i proceedings › Forskning › peer review

TY - GEN

T1 - Efficient Quasi-Geodesics on the Stiefel Manifold

AU - Bendokat, Thomas

AU - Zimmermann, Ralf

N1 - 1) Peer review 2) arxiv version of accepted contribution to the proceedings of the 5th conference on Geometric Science of Information in PARIS, Sorbonne University

PY - 2021/7/14

Y1 - 2021/7/14

N2 - 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.

AB - 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.

KW - Stiefel Manifold

KW - Geodesic

KW - Quasi-geodesic

KW - Geodesic Endpoint Problem

KW - Stiefel manifold

KW - Geodesic endpoint problem

U2 - 10.1007/978-3-030-80209-7_82

DO - 10.1007/978-3-030-80209-7_82

M3 - Article in proceedings

SN - 978-3-030-80208-0

T3 - Lecture Notes in Computer Science

SP - 763

EP - 771

BT - Geometric Science of Information

A2 - Nielsen, Frank

A2 - Barbaresco, Frédéric

PB - Springer

T2 - 5th International Conference

Y2 - 21 July 2021 through 23 July 2021

ER -

Efficient Quasi-Geodesics on the Stiefel Manifold

Abstract

Konference

Bibliografisk note

Dokumenter og links

SDU link

Fingeraftryk

Relaterede publikationer

The Classical and Symplectic Stiefel and Grassmann Manifolds: Geometry and Applications

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