Robust principal component analysis?

This article is about a curious phenomenon. Suppose we have a data matrix, which is the superposition of a low-rank component and a sparse component. Can we recover each component individually? We prove that under some suitable assumptions, it is possible to recover both the low-rank and the sparse components exactly by solving a very convenient convex program called Principal Component Pursuit ; among all feasible decompositions, simply minimize a weighted combination of the nuclear norm and of the ℓ 1 norm. This suggests the possibility of a principled approach to robust principal component analysis since our methodology and results assert that one can recover the principal components of a data matrix even…

• OO
  Office of Naval Research

  Award: N00014-09-1-0469N00014-08-1-0749N00014-09-1-0230
• DO
  Division of Information and Intelligent Systems

  Award: IIS 08-49292ECCS 07-01676
• DO
  Division of Electrical, Communications and Cyber Systems

  Award: IIS 08-49292ECCS 07-01676