Tucker-$\operatorname{L_2E}$: Robust Low-rank Tensor Decomposition with the $\operatorname{L_2}$ Criterion

The growing prevalence of tensor data, or multiway arrays, in science and engineering applications motivates the need for tensor decompositions that are robust against outliers. In this paper, we present a robust Tucker decomposition estimator based on the $\operatorname{L_2}$ criterion called the Tucker-$\operatorname{L_2E}$. Our numerical experiments demonstrate that Tucker-$\operatorname{L_2E}$ has empirically stronger recovery performance in more challenging high-rank scenarios compared with existing alternatives. We also characterize Tucker-$\operatorname{L_2E}$'s insensitivity to rank overestimation and explore approaches for identifying the appropriate Tucker-rank. The practical effectiveness of Tucker-$\operatorname{L_2E}$ is validated on real data applications in fMRI tensor denoising, PARAFAC analysis of fluorescence data, and feature extraction for classification of corrupted images.