Difference between revisions of "Rodolphe Sepulchre, June 2013"

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(Abstract)
Line 32: Line 32:
 
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
  • 9:45-10:45: Necmiye, Mumu, Eric, Ivan
  • 10:45-11:45: Enoch, Marcella, Anandh, Dan
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.