Reference : Linear regression under fixed-rank constraints: a Riemannian approach
Scientific congresses and symposiums : Paper published in a book
Engineering, computing & technology : Computer science
http://hdl.handle.net/2268/90930
Linear regression under fixed-rank constraints: 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 >]
2011
Proceedings of the 28th International Conference on Machine Learning
Yes
28th International Conference on Machine Learning
Bellevue
USA
[en] linear regression ; fixed-rank matrices ; geometric optimization algorithms
[en] In this paper, we tackle the problem of learning a linear regression model whose parameter is a fixed-rank matrix. We study the Riemannian manifold geometry of the set of fixed-rank matrices and develop efficient line-search algorithms. The proposed algorithms have many applications, scale to high-dimensional problems, enjoy local convergence properties and confer a geometric basis to recent contributions on learning fixed-rank matrices. Numerical experiments on benchmarks suggest that the proposed algorithms compete with the state-of-the-art, and that manifold optimization offers a versatile framework for the design of rank-constrained machine learning algorithms.
Fonds de la Recherche Scientifique (Communauté française de Belgique) - F.R.S.-FNRS
Researchers ; Professionals
http://hdl.handle.net/2268/90930

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