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CATEGORIES:Optimisation and Numerical Analysis Seminars
SUMMARY:A quotient geometry on the manifold of fixed-rank
positive-semidefinite matrices - Estelle Massart (
NPL-postdoc\, University of Oxford)
DTSTART:20200311T120000Z
DTEND:20200311T130000Z
UID:TALK4171AT
URL:/talk/index/4171
DESCRIPTION:Riemannian optimization aims to design optimizatio
n algorithms for constrained problems\, where the
constraints enforce the variables to belong to a R
iemannian manifold. Classical examples of Riemanni
an manifolds include\, e.g.\, the set of orthogona
l matrices\, the set of subspaces of a given dimen
sion (called the Grassman manifold)\, and the set
of fixed-rank matrices.\n\nAfter a quick introduct
ion to Riemannian optimization\, and more specific
ally Riemannian gradient descent (RGD)\, we will p
resent the tools needed to run RGD on the manifold
of fixed-rank positive-semidefinite matrices\, se
en as a quotient of the set of full-rank rectangul
ar matrices by the orthogonal group. We will also
present recent results about related geometrical t
ools on that manifold. This manifold is particular
ly relevant when dealing with low-rank approximati
ons of large positive-(semi)definite matrices.\n
LOCATION:Physics West 103
CONTACT:Sergey Sergeev
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