Robust Tensor Tracking With Missing Data Under Tensor-Train Format

Abstract

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.