Robust principal component analysis?

  title={Robust principal component analysis?},
  author={Emmanuel J. Cand{\`e}s and Xiaodong Li and Yi Ma and John Wright},
  journal={J. ACM},
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… 

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