Robust Subspace Tracking With Missing Entries: The Set-Theoretic Approach

In this paper, an Adaptive Projected Subgradient Method (APSM) based algorithm for robust subspace tracking is introduced. A properly chosen cost function is constructed at each time instance and the goal is to seek for points, which belong to the zero level set of this function; i.e., the set of points which score a zero loss. At each iteration, an outlier detection mechanism is employed, in order to conclude whether the current data vector contains outlier noise or not. In the sequel, a sparsity-promoting greedy algorithm is employed for the outlier vector estimation allowing the purification of the corrupted data from the outlier noise, prior to any further processing. Furthermore, the case where the observation vectors are partially observed is attacked via a prediction procedure, which estimates the values of the unobserved (missing) coefficients. A theoretical analysis is carried out and the simulation experiments, within the contexts of robust subspace estimation and robust matrix completion, demonstrate the enhanced performance of the proposed scheme compared to recently developed state of the art algorithms.