Robust PCA by Manifold Optimization

Abstract

Robust PCA is a widely used statistical procedure to recover a 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 (for two versions of retractions) based on manifold optimization. It is shown that, with a proper designed initialization, the proposed algorithms are guaranteed to converge to the underlying low-rank matrix linearly. Compared with a previous work based on the Burer-Monterio decomposition of low-rank matrices, the proposed algorithms reduce the dependence on the conditional number of the underlying low-rank matrix theoretically. Simulations and real data examples confirm the competitive performance of our method.

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Cited by in corpus (3)

• Robust Low-rank Matrix Completion via an Alternating Manifold Proximal Gradient Continuation Method
• On the Robustness of Cross-Concentrated Sampling for Matrix Completion
• Structured Sampling for Robust Euclidean Distance Geometry