  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. The
appropriate Tucker-rank can be selected in a data-driven manner with
cross-validation or hold-out validation. 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.
