The Exact Solution to Rank-1 L1-Norm TUCKER2 Decomposition

This letter studies the rank-1 L1-norm-based TUCKER2 (L1-TUCKER2) decomposition of 3-way tensors. First, we prove that the problem is formally NP-hard. Then, we derive the first two algorithms in the literature for its exact solution. Our algorithms are accompanied by formal complexity analysis. Finally, we conduct numerical studies to compare the performance of exact L1-TUCKER2 (proposed) with standard HOSVD, HOOI, GLRAM, PCA, L1-PCA, and TPCA-L1. In our numerical studies, L1-TUCKER2 outperforms (e.g., in tensor approximation) all the aforementioned counterparts when the processed data are outlier corrupted.