Provable Dynamic Robust PCA or Robust Subspace Tracking

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 standard RPCA assumptions, slow subspace change and two mild assumptions. We analyze a simple algorithm based on the 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 than all existing provable RPCA methods by exploiting slow subspace change and a lower bound on outlier magnitudes; and (iii) it proves that the proposed algorithm is online, fast, and memory-efficient.