Meyer, G and Bonnabel, S and Sepulchre, R (2011) Linear regression under fixed-rank constraints: A Riemannian approach. In: UNSPECIFIED pp. 545-552..Full text not available from this repository.
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. Copyright 2011 by the author(s)/owner(s).
|Item Type:||Conference or Workshop Item (UNSPECIFIED)|
|Divisions:||Div F > Control|
|Depositing User:||Cron Job|
|Date Deposited:||07 Mar 2014 11:25|
|Last Modified:||08 Dec 2014 02:18|