Reference : Regression on fixed-rank positive semidefinite matrices: a Riemannian approach
Scientific journals : Article
Engineering, computing & technology : Computer science
http://hdl.handle.net/2268/83992
Regression on fixed-rank positive semidefinite matrices: a Riemannian approach
English
Meyer, Gilles mailto [Université de Liège - ULg > Dép. d'électric., électron. et informat. (Inst.Montefiore) > Systèmes et modélisation >]
Bonnabel, Silvère mailto [Mines ParisTech > Robotics center > > >]
Sepulchre, Rodolphe mailto [Université de Liège - ULg > Dép. d'électric., électron. et informat. (Inst.Montefiore) > Systèmes et modélisation >]
3-Mar-2011
Journal of Machine Learning Research
Microtome Publishing
12
Feb
593−625
Yes (verified by ORBi)
International
1532-4435
1533-7928
Brookline
MA
[en] linear regression ; positive semidefinite matrices ; low-rank approximation ; Riemannian geometry ; gradient-based learning
[en] The paper addresses the problem of learning a regression model parameterized by a fixed-rank positive semidefinite matrix. The focus is on the nonlinear nature of the search space and on scalability to high-dimensional problems. The mathematical developments rely on the theory of gradient descent algorithms adapted to the Riemannian geometry that underlies the set of fixed-rank positive semidefinite matrices. In contrast with previous contributions in the literature, no restrictions are imposed on the range space of the learned matrix. The resulting algorithms maintain a linear complexity in the problem size and enjoy important invariance properties. We apply the proposed algorithms to the problem of learning a distance function parameterized by a positive semidefinite matrix. Good performance is observed on classical benchmarks.
Fonds de la Recherche Scientifique (Communauté française de Belgique) - F.R.S.-FNRS
Researchers ; Professionals
http://hdl.handle.net/2268/83992

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