Rodolphe Sepulchre, June 2013: Difference between revisions
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fixed-rank matrices to two well-studied manifolds: the Grassmann manifold of linear subspaces and the cone | 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 on various applications, including | of positive definite matrices. The theory will be illustrated on various applications, including | ||
low-rank Kalman filtering, linear regression with low-rank priors, matrix completion, and the choice of a suitable | low-rank Kalman filtering, linear regression with low-rank priors, matrix completion, and the choice of a suitable metric for Diffusion Tensor Imaging. | ||
Revision as of 00:47, 30 May 2013
Rodolphe Sepulchre will visit Caltech on 3 June 2013 (Mon).
Agenda
| 9:30a | Richard Murray, 109 Steele Lab |
| 9:45a | Meet with Richard's NCS group, 110 Steele
|
| 11:45 | Seminar setup |
| 12:00p | Seminar, 213 ANB |
| 1:00p | Lunch with Venkat, CMS faculty |
| 2:15p | Venkat Chandrasekaran, 300 Annenberg |
| 3:00p | Open |
| 3:45p | Open |
| 4:30p | Andrea Censi) |
| 5:15p | Done |
Abstract
The geometry of (thin) SVD revisited for large-scale computations
Rodolphe Sepulchre
University of Liege, Belgium
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 on various applications, including low-rank Kalman filtering, linear regression with low-rank priors, matrix completion, and the choice of a suitable metric for Diffusion Tensor Imaging.
