Robust PCA by Manifold Optimization

Robust PCA is a widely used statistical procedure to recover an underlying low-rank matrix with grossly corrupted observations. This work considers the problem of robust PCA as a nonconvex optimization problem on the manifold of low-rank matrices and proposes two algorithms based on manifold optimization. It is shown that, with a properly designed initialization, the proposed algorithms are guaranteed to converge to the underlying low-rank matrix linearly. Compared with a previous work based on the factorization of low-rank matrices Yi et al. (2016), the proposed algorithms reduce the dependence on the condition number of the underlying low-rank matrix theoretically. Simulations and real data examples confirm the competitive performance of our method. [abs] [ pdf ][ bib ] &copy JMLR 2018. ( edit, beta )

Authors

• Teng Zhang Institute of Computing Technology, Chinese Academy of Sciences University of Chinese Academy of Sciences Beijing Key Laboratory of Mobile Computing and Pervasive Device
• Yi Yang

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