Efficient Quasi-Geodesics on the Stiefel Manifold

Thomas Bendokat; Ralf Zimmermann

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

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arXiv · 2105.07017

Efficient Quasi-Geodesics on the Stiefel Manifold

Thomas Bendokat·Ralf Zimmermann

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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.

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BibTeX RIS

Thomas Bendokat, Ralf Zimmermann. 2021-05-14. Efficient Quasi-Geodesics on the Stiefel Manifold. https://doi.org/10.1007/978-3-030-80209-7_82

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