  Recently, tensor low-rank representation (TLRR) has become a popular tool for
tensor data recovery and clustering, due to its empirical success and
theoretical guarantees. However, existing TLRR methods consider Gaussian or
gross sparse noise, inevitably leading to performance degradation when the
tensor data are contaminated by outliers or sample-specific corruptions. This
paper develops an outlier-robust tensor low-rank representation (OR-TLRR)
method that provides outlier detection and tensor data clustering
simultaneously based on the t-SVD framework. For tensor observations with
arbitrary outlier corruptions, OR-TLRR has provable performance guarantee for
exactly recovering the row space of clean data and detecting outliers under
mild conditions. Moreover, an extension of OR-TLRR is proposed to handle the
case when parts of the data are missing. Finally, extensive experimental
results on synthetic and real data demonstrate the effectiveness of the
proposed algorithms. We release our code at
https://github.com/twugithub/2024-AISTATS-ORTLRR.
