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UID:2021@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20171124T100000
DTEND;TZID=Europe/Paris:20171124T110000
DTSTAMP:20171109T090000Z
URL:https://www.i2m.univ-amu.fr/evenements/covariance-matrices-and-covaria
 nce-operators-in-machine-learning-and-pattern-recognition-a-geometrical-fr
 amework/
SUMMARY: (...): Covariance matrices and covariance operators in machine lea
 rning and pattern recognition: A geometrical framework
DESCRIPTION:: Symmetric positive definite (SPD) matrices\, in particular co
 variance matrices\, play important roles in many areas of mathematics and 
  statistics\, with numerous applications in various different fields\,  in
 cluding machine learning\, brain imaging\, and computer vision. The set of
  SPD matrices is not a subspace of Euclidean space and consequently algori
 thms utilizing only  the Euclidean metric tend to be suboptimal in practic
 e. A lot of recent research has therefore focused on exploiting the intrin
 sic geometrical structures of SPD matrices\, in particular the view of thi
 s set  as a Riemannian manifold. In this talk\, we will present a survey o
 f some of the recent developments in the generalization of finite-dimensio
 nal covariance matrices to  infinite-dimensional covariance operators via 
 kernel methods\, along with the corresponding geometrical structures. This
  direction exploits the power of  kernel methods from machine learning in 
 the framework of  Riemannian geometry\, both mathematically and algorithmi
 cally. The theoretical formulation will be illustrated with applications i
 n computer vision\, which demonstrate both the power of  kernel covariance
  operators as well as of the algorithms based on their intrinsic geometry.
 http://www.iit.it/people/minh-haquang
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