Reference : Adaptive filtering for estimation of a low-rank positive semidefinite matrix
Scientific congresses and symposiums : Paper published in a book
Engineering, computing & technology : Electrical & electronics engineering
http://hdl.handle.net/2268/74860
Adaptive filtering for estimation of a low-rank positive semidefinite matrix
English
Bonnabel, Silvère mailto [Mines Paris-Tech > Robotics Group > > >]
Meyer, Gilles mailto [Université de Liège - ULg > Dép. d'électric., électron. et informat. (Inst.Montefiore) > Systèmes et modélisation >]
Sepulchre, Rodolphe mailto [Université de Liège - ULg > Dép. d'électric., électron. et informat. (Inst.Montefiore) > Systèmes et modélisation >]
Jul-2010
Proceedings of the 19th International Symposium on Mathematical Theory of Networks and Systems
Yes
Yes
International
19th International Symposium on Mathematical Theory of Networks and Systems (MTNS 2010)
5-9 july 2010
Budapest
Hongrie
[en] adaptive filtering ; low-rank ; least mean squares
[en] In this paper, we adopt a geometric viewpoint to tackle the problem of estimating a linear model whose parameter is a fixed-rank positive semidefinite matrix. We consider two gradient descent flows associated to two distinct Riemannian quotient geometries that underlie this set of matri- ces. The resulting algorithms are non-linear and can be viewed as a generalization of Least Mean Squares that instrically constrain the parameter within the manifold search space. Such algorithms designed for low-rank matrices find applications in high-dimensional distance learning problems for classification or clustering.
Fonds de la Recherche Scientifique (Communauté française de Belgique) - F.R.S.-FNRS
Researchers ; Professionals
http://hdl.handle.net/2268/74860

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