Robust Tensor Tracking With Missing Data Under Tensor-Train Format

Robust tensor tracking or robust adaptive tensor decomposition of streaming tensors is crucial when observations are corrupted by sparse outliers and missing data. In this paper, we introduce a novel tensor tracking algorithm for factorizing incomplete streaming tensors with sparse outliers under tensor-train (TT) format. The proposed algorithm consists of two main stages: online outlier rejection and tracking of TT-cores. In the former stage, outliers affecting the data streams are efficiently detected by an ADMM solver. In the latter stage, we propose an effective recursive least-squares solver to incrementally update TT-cores at each time t. Several numerical experiments on both simulated and real data are presented to verify the effectiveness of the proposed algorithm.