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• W3176061093 abstract "Optimization problems on the generalized Stiefel manifold (and products of it) are prevalent across science and engineering. For example, in computational science they arise in the symmetric (generalized) eigenvalue problem, in nonlinear eigenvalue problems, and in electronic structures computations, to name a few problems. In statistics and machine learning, they arise, for example, in various dimensionality reduction techniques such as canonical correlation analysis. In deep learning, regularization and improved stability can be obtained by constraining some layers to have parameter matrices that belong to the Stiefel manifold. Solving problems on the generalized Stiefel manifold can be approached via the tools of Riemannian optimization. However, using the standard geometric components for the generalized Stiefel manifold has two possible shortcoming: computing some of the geometric components can be too expensive and converge can be rather slow in certain cases. Both shortcomings can be addressed using a technique called Riemannian preconditioning, which amounts to using geometric components derived using a precoditioner that defines a Riemannian metric on the constraint manifold. In this paper we develop the geometric components required to perform Riemannian optimization on the generalized Stiefel manifold equipped with a non-standard metric, and illustrate theoretically and numerically the use of those components and the effect of Riemannian preconditioning for solving optimization problems on the generalized Stiefel manifold." @default.
• W3176061093 created "2021-07-05" @default.
• W3176061093 creator A5072151198 @default.
• W3176061093 creator A5084643114 @default.
• W3176061093 date "2019-02-05" @default.
• W3176061093 modified "2023-09-27" @default.
• W3176061093 title "Preconditioned Riemannian Optimization on the Generalized Stiefel Manifold" @default.
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• W3176061093 hasPublicationYear "2019" @default.
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