Federated Over-Air Subspace Tracking from Incomplete and Corrupted Data

Abstract: In this work we study the problem of Subspace Tracking with missing data (ST-miss) and outliers (Robust ST-miss). We propose a novel algorithm, and provide a guarantee for both these problems. Unlike past work on this topic, the current work does not impose the piecewise constant subspace change assumption. Additionally, the proposed algorithm is much simpler (uses fewer parameters) than our previous work. Secondly, we extend our approach and its analysis to provably solving these problems when the data is federated and when the over-air data communication modality is used for information exchange between the $K$ peer nodes and the center. We validate our theoretical claims with extensive numerical experiments.