Personal tools
 

Stability of low-rank matrix recovery and its connections to Banach space geometry

— filed under:

J. Alejandro Chavez- Dominguez, University of Oklahoma

What
  • Colloquium
When Fri, Feb 24, 2017
from 11:00 AM to 11:50 AM
Add event to calendar vCal
iCal

Abstract: 

Compressed sensing deals with the problem of recovering a vector in a high-dimensional space from a lower-dimensional measurement, under the assumption that the vector is sparse (that is, it has relatively few non-zero coordinates). One of the best-known techniques to achieve such recovery is the $\ell_p$-norm minimization, and its properties are related to the geometry of the Banach spaces involved: theorems by Kashin-Temlyakov and Foucart-Pajor-Rauhut-Ullrich relate the stability of sparse vector recovery via $\ell_p$-minimization to the so-called Gelfand numbers of identity maps between finite-dimensional $\ell_p$-spaces.

In many practical situations the space of unknown vectors has in fact a matrix structure, a good example being the famous matrix completion problem (also known as the Netflix problem) where the unknown is a matrix and we are given a subset of its entries. In this case sparsity gets replaced by the more natural condition of having low rank, and the last few years have witnessed an explosion of work in this area. In this talk we present matrix analogues of the aforementioned results, relating the stability of low-rank matrix recovery via Schatten $p$-minimization to the Gelfand numbers of identity maps between finite-dimensional Schatten $p$-spaces.

« April 2017 »
April
SuMoTuWeThFrSa
1
2345678
9101112131415
16171819202122
23242526272829
30
Upcoming Events
Geometry/ Topology Seminar
Tue, May 02, 2017
The Causal Boundary Construction for Spacetimes, 11 Stacey Harris, SLU
Colloquium
Fri, May 05, 2017
Gilbreath Knots Jacqueline Jensen-Vallin, Lamar University
Annual Awards Ceremony
Fri, May 05, 2017
Let’s Get Knotty! Jacqueline Jensen-Vallin, Lamar University
Previous events…
Upcoming events…