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UID:5001@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20171124T100000
DTEND;TZID=Europe/Paris:20171124T110000
DTSTAMP:20171109T090000Z
URL:https://www.i2m.univ-amu.fr/events/covariance-matrices-and-covariance-
operators-in-machine-learning-and-pattern-recognition-a-geometrical-framew
ork/
SUMMARY:Covariance matrices and covariance operators in machine learning an
d pattern recognition: A geometrical framework -
DESCRIPTION:Symmetric positive definite (SPD) matrices\, in particular cova
riance matrices\, play important roles in many areas of mathematics and s
tatistics\, with numerous applications in various different fields\, incl
uding machine learning\, brain imaging\, and computer vision. The set of S
PD matrices is not a subspace of Euclidean space and consequently algorith
ms utilizing only the Euclidean metric tend to be suboptimal in practice.
A lot of recent research has therefore focused on exploiting the intrinsi
c geometrical structures of SPD matrices\, in particular the view of this
set as a Riemannian manifold. In this talk\, we will present a survey of
some of the recent developments in the generalization of finite-dimensiona
l covariance matrices to infinite-dimensional covariance operators via ke
rnel methods\, along with the corresponding geometrical structures. This d
irection exploits the power of kernel methods from machine learning in th
e framework of Riemannian geometry\, both mathematically and algorithmica
lly. The theoretical formulation will be illustrated with applications in
computer vision\, which demonstrate both the power of kernel covariance o
perators as well as of the algorithms based on their intrinsic geometry.ht
tp://www.iit.it/people/minh-haquang
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