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.
翻译:随着张量数据或多维数组在科学和工程应用中的日益普及,促使我们需要针对异常值具有鲁棒性的张量分解。本文提出了一种基于 $\operatorname{L_2}$ 准则的鲁棒 Tucker 分解估计器,称为 Tucker-$\operatorname{L_2E}$。我们的数值实验表明,与现有的替代方案相比,在更具挑战性的高秩场景下,Tucker-$\operatorname{L_2E}$ 具有更强的恢复性能。适当的 Tucker 秩可以通过交叉验证或保留验证以数据驱动的方式选择。Tucker-$\operatorname{L_2E}$ 的实际有效性在 fMRI 张量降噪、荧光数据的 PARAFAC 分析以及带有的损坏图像分类的特征提取方面得到了验证。