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The growing prevalence of tensor data, or multiway arrays, in science andengineering applications motivates the need for tensor decompositions that arerobust against outliers. In this paper, we present a robust Tuckerdecomposition estimator based on the $\operatorname{L_2}$ criterion, called theTucker-$\operatorname{L_2E}$. Our numerical experiments demonstrate thatTucker-$\operatorname{L_2E}$ has empirically stronger recovery performance inmore challenging high-rank scenarios compared with existing alternatives. Theappropriate Tucker-rank can be selected in a data-driven manner withcross-validation or hold-out validation. The practical effectiveness ofTucker-$\operatorname{L_2E}$ is validated on real data applications in fMRItensor denoising, PARAFAC analysis of fluorescence data, and feature extractionfor classification of corrupted images.

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