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 tensortrain (TT) format, called ROBOT. 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.
- Our MATLAB code requires the Tensor Toolbox which is already attached to this repository.
- MATLAB 2019a
- Run demo_xyz.m for synthetic data
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Effect of the noise level
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Effect of the time-varying factor
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Effect of the missing data
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Effect of sparse outliers
This code is free and open source for research purposes. If you use this code, please acknowledge the following paper.
[1] L.T. Thanh, K. Abed-Meraim, N.L. Trung, A. Hafiance. "Robust Tensor Tracking With Missing Data Under Tensor-Train Formats". Proc. 30th EUSIPCO, 2022. [PDF].