Closed-form geodesics and optimization for Riemannian logarithms of Stiefel and flag manifolds

DOI10.1007/s10957-022-02012-3zbMath1500.53056arXiv2103.13327OpenAlexW4293226819WikidataQ115382529 ScholiaQ115382529MaRDI QIDQ2671438

Du Dinh Nguyen

Publication date: 3 June 2022

Published in: Journal of Optimization Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2103.13327

zbMATH Keywords

flag manifoldcomputer visionStiefel manifoldgeodesicFréchet derivativeRiemannian center of masslogarithm map

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) Learning and adaptive systems in artificial intelligence (68T05) Grassmannians, Schubert varieties, flag manifolds (14M15) Special Riemannian manifolds (Einstein, Sasakian, etc.) (53C25) Geodesics in global differential geometry (53C22) Variational problems in applications to the theory of geodesics (problems in one independent variable) (58E10) Machine vision and scene understanding (68T45) Real-valued functions on manifolds (58C05) Relations of manifolds and cell complexes with engineering (57Z20) Relations of manifolds and cell complexes with computer and data science (57Z25)

Related Items

Operator-valued formulas for Riemannian gradient and Hessian and families of tractable metrics in Riemannian optimization ⋮ Rethinking the Riemannian logarithm on flag manifolds as an orthogonal alignment problem ⋮ StiefelLog

Uses Software

• SciPy
• minFunc
• Python
• GitHub
• geomstats

Cites Work

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