The Power of Convex Relaxation: Near-Optimal Matrix Completion

This paper is concerned with the problem of recovering an unknown matrix from a small fraction of its entries. This is known as the matrix completion problem, and comes up in a great number of applications, including the famous Netflix Prize and other similar questions in collaborative filtering. In general, accurate recovery of a matrix from a small number of entries is impossible, but the knowledge that the unknown matrix has low rank radically changes this premise, making the search for solutions meaningful. This paper presents optimality results quantifying the minimum number of entries needed to recover a matrix of rank r exactly by any method whatsoever (the information theoretic limit). More…

• NS
  National Science Foundation

  Award: 0649473
• JD
  John D. and Catherine T. MacArthur Foundation
• OO
  Office of Naval Research

  Awards: N00014-08-1-0749, N00014