Outlier-Robust Tensor PCA

Low-rank tensor analysis is important for various real applications in computer vision. However, existing methods focus on recovering a low-rank tensor contaminated by Gaussian or gross sparse noise and hence cannot effectively handle outliers that are common in practical tensor data. To solve this issue, we propose an outlier-robust tensor principle component analysis (OR-TPCA) method for simultaneous low-rank tensor recovery and outlier detection. For intrinsically low-rank tensor observations with arbitrary outlier corruption, OR-TPCA is the first method that has provable performance guarantee for exactly recovering the tensor subspace and detecting outliers under mild conditions. Since tensor data are naturally high-dimensional and multi-way, we further develop a fast randomized algorithm that requires small sampling size yet can substantially accelerate OR-TPCA without performance drop. Experimental results on four tasks: outlier detection, clustering, semi-supervised and supervised learning, clearly demonstrate the advantages of our method.