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.

翻译：在科学和工程应用中,高压数据或多道阵列日益普遍,这促使人们需要针对外星的强力反向分解。在本文中,我们根据$\operatorname{L_2}$的标准,提出一个强大的塔克分解估计器,称为Tucker-$\operatorname{L_2E}$。我们的数字实验表明,塔克-$\operatorname{L_2E}$,与现有替代品相比,在更具挑战性的高水平情景中,Tucker-$\operatorname{L_2E}$具有更强的恢复性能。我们还将塔克-$\operatorname{L_2E}$描述为过高的敏感度,并探索确定适当的塔克-美元标准的方法。Tucker-$\operatorname{L_2E}$的实际效力在FMRI Exnoisision、PARAFAC对荧光度数据的分析以及破损图像分类特征提取方面的实际数据应用得到验证。