Provable Dynamic Robust PCA or Robust Subspace Tracking
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Dynamic robust PCA refers to the dynamic (time-varying) extension of the robust PCA (RPCA) problem. It assumes that the true (uncorrupted) data lies in a low-dimensional subspace that can change with time, albeit slowly. The goal is to track this changing subspace over time in the presence of sparse outliers. This work provides the first guarantee for dynamic RPCA that holds under weakened versions of standard RPCA assumptions and a few other simple assumptions. We analyze a novel algorithm based on the recently introduced Recursive Projected Compressive Sensing (ReProCS) framework. Our result is significant because (i) it removes the strong assumptions needed by the two previous complete guarantees for ReProCS-based algorithms; (ii) it shows that, it is possible to achieve significantly improved outlier tolerance by exploiting slow subspace change and a lower bound on most outlier magnitudes; and (iii) it proves that the proposed algorithm is online (after initialization), fast, and, has near-optimal storage complexity.
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