A quotient geometry on the manifold of fixed-rank positive-semidefinite matrices

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• Estelle Massart (NPL-postdoc, University of Oxford)
• Wednesday 11 March 2020, 12:00-13:00
• Physics West 103.

If you have a question about this talk, please contact Sergey Sergeev.

Riemannian optimization aims to design optimization algorithms for constrained problems, where the constraints enforce the variables to belong to a Riemannian manifold. Classical examples of Riemannian manifolds include, e.g., the set of orthogonal matrices, the set of subspaces of a given dimension (called the Grassman manifold), and the set of fixed-rank matrices.

After a quick introduction to Riemannian optimization, and more specifically Riemannian gradient descent (RGD), we will present the tools needed to run RGD on the manifold of fixed-rank positive-semidefinite matrices, seen as a quotient of the set of full-rank rectangular matrices by the orthogonal group. We will also present recent results about related geometrical tools on that manifold. This manifold is particularly relevant when dealing with low-rank approximations of large positive-(semi)definite matrices.

This talk is part of the Optimisation and Numerical Analysis Seminars series.

This talk is included in these lists:

• Physics West 103
• School of Mathematics Events

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