Robust Subspace Tracking with Missing Data and Outliers: Novel Algorithm with Convergence Guarantee

In this article, we propose a novel algorithm, namely PETRELS-ADMM, to deal with subspace tracking in the presence of outliers and missing data. The proposed approach consists of two main stages: outlier rejection and subspace estimation. In the first stage, alternating direction method of multipliers (ADMM) is effectively exploited to detect outliers affecting the observed data. In the second stage, we propose an improved version of the parallel estimation and tracking by recursive least squares (PETRELS) algorithm to update the underlying subspace in the missing data context. We then present a theoretical convergence analysis of PETRELS-ADMM which shows that it generates a sequence of subspace solutions converging to the optimum of its batch counterpart. The effectiveness of the proposed algorithm, as compared to state-of-the-art algorithms, is illustrated on both simulated and real data.