In this paper, we extend the Discrete Empirical Interpolation Method (DEIM) to the third-order tensor case based on the t-product and use it to select important/significant lateral and horizontal slices/features. The proposed Tubal DEIM (TDEIM) is investigated both theoretically and numerically. In particular, the details of the error bounds of the proposed TDEIM method are derived. The experimental results show that the TDEIM can provide more accurate approximations than the existing methods. An application of the proposed method to the supervised classification task is also presented.

中文翻译：

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使用具有优化切片/特征选择的离散经验插值方法进行稳健的低输卵管等级张量恢复

在本文中，我们将离散经验插值法（DEIM）扩展到基于t积的三阶张量情况，并用它来选择重要/显着的横向和水平切片/特征。对所提出的管状 DEIM (TDEIM) 进行了理论和数值研究。特别是，推导了所提出的 TDEIM 方法的误差范围的详细信息。实验结果表明，TDEIM 可以提供比现有方法更准确的近似值。还提出了所提出的方法在监督分类任务中的应用。