Stable Principal Component Pursuit

In this paper, we study the problem of recovering a low-rank matrix (the principal components) from a highdimensional data matrix despite both small entry-wise noise and gross sparse errors. Recently, it has been shown that a convex program, named Principal Component Pursuit (PCP), can recover the low-rank matrix when the data matrix is corrupted by gross sparse errors. We further prove that the solution to a related convex program (a relaxed PCP) gives an estimate of the low-rank matrix that is simultaneously stable to small entrywise noise and robust to gross sparse errors. More precisely, our result shows that the proposed convex program recovers the low-rank matrix even though a positive fraction of its entries are arbitrarily corrupted, with an error bound proportional to the noise level. We present simulation results to support our result and demonstrate that the new convex program accurately recovers the principal components (the low-rank matrix) under quite broad conditions. To...

• Type: Journal
• Year: 2010
• Where: CORR
• Authors: Zihan Zhou, Xiaodong Li, John Wright, Emmanuel J. Candès, Yi Ma
• Keywords: CORR 2010, Education, Low-rank Matrix, Principal Component, Sparse Errors