6 June 2012, h.14:30 - Sala 201 DEI/A
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The geometry of (thin) SVD revisited for large-scale computations
Rodolphe Sepulchre University of Liege, Belgium |
Abstract:
The talk will introduce a riemannian framework for large-scale computations over the set of low-rank matrices. The foundation is geometric and the motivation is algorithmic, with a bias towards efficient computations in large-scale problems. We will explore how classical matrix factorizations connect the riemannian geometry of the set of fixed-rank matrices to two well-studied manifolds: the Grassmann manifold of linear subspaces and the cone of positive definite matrices. The theory will be illustrated by two applications: an efficient framework for linear regression with low-rank priors and the choice of a suitable metric for Diffusion Tensor Imaging.