论文标题
使用$ \ operatorName {l_2} $ Criterion稳健低升张量分解
Robust Low-rank Tensor Decomposition with the $\operatorname{L_2}$ Criterion
论文作者
论文摘要
科学和工程应用中张量数据或多路阵列的越来越多的患病率激发了对异常值强大的张量分解的需求。在本文中，我们基于$ \ operatatorName {l_2} $ criterion提出了强大的塔克分解估计器，称为tucker-$ \ permatatorName {l_2e} $。我们的数值实验表明，与现有替代方案相比，在更具挑战性的高级场景中，塔克 - $ \ peripatorname {l_2e} $在更具挑战性的高级方案中具有更强的恢复性能。可以以数据驱动的方式选择适当的塔克级，并进行交叉验证或保持验证。 Tucker-$ \ operatorname {l_2e} $的实际有效性已在fMRI张量Denoising，ParaFac分析荧光数据中的实际数据应用程序进行了验证，以及用于分类损坏图像的特征提取。
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.
