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   Liu, Lydia T.; Dobriban, Edgar; Singer, Amit (December 2018, The Annals of Applied Statistics)
2. Low-Precision Streaming PCA

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5. Robust PCA by Manifold Optimization

   Zhang, Teng; Yang, Yi (November 2018, Journal of machine learning research)

   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 lowrank 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 con rm the competitive performance of our method. 

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