Exact matrix completion via convex optimization

Abstract

Suppose that one observes an incomplete subset of entries selected from a low-rank matrix. When is it possible to complete the matrix and recover the entries that have not been seen? We demonstrate that in very general settings, one can perfectly recover all of the missing entries from most sufficiently large subsets by solving a convex programming problem that finds the matrix with the minimum nuclear norm agreeing with the observed entries. The techniques used in this analysis draw upon parallels in the field of compressed sensing, demonstrating that objects other than signals and images can be perfectly reconstructed from very limited information.

Document Details

Document Type
Pub Defense Publication
Publication Date
Jun 01, 2012
Source ID
10.1145/2184319.2184343

Entities

People

  • Benjamin Recht
  • Emmanuel Candès

Organizations

  • Division of Computing and Communication Foundations
  • Office of Naval Research
  • Stanford University
  • University of Wisconsin–Madison

Tags

Fields of Study

  • Computer science

Readers

  • Applied Combinatorial Optimization and Logic Circuit Design.
  • Image Processing and Computer Vision.
  • Operations Research