Rodolphe Sepulchre, June 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, Rangoli 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.