Reference : Linear regression under fixed-rank constraints: a Riemannian approach

	Document type :	Scientific congresses and symposiums : Paper published in a book
	Discipline(s) :	Engineering, computing & technology : Computer science
	To cite this reference:	http://hdl.handle.net/2268/90930

Title :	Linear regression under fixed-rank constraints: a Riemannian approach
Language :	English
Author, co-author :	Meyer, Gilles [Université de Liège - ULg > Dép. d'électric., électron. et informat. (Inst.Montefiore) > Systèmes et modélisation >]
	Bonnabel, Silvère [Mines ParisTech > Robotics Center > > >]
	Sepulchre, Rodolphe [Université de Liège - ULg > Dép. d'électric., électron. et informat. (Inst.Montefiore) > Systèmes et modélisation >]
Publication date :	2011
Main document title :	Proceedings of the 28th International Conference on Machine Learning
Event name :	28th International Conference on Machine Learning
Event place (city) :	Bellevue
Event country :	USA
Keywords :	[en] linear regression ; fixed-rank matrices ; geometric optimization algorithms
Abstract :	[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.
Funders :	Fonds de la Recherche Scientifique (Communauté française de Belgique) - F.R.S.-FNRS
Target :	Researchers ; Professionals
Permalink :	http://hdl.handle.net/2268/90930

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