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. 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.

翻译：本文基于t-乘积将离散经验插值法（DEIM）推广至三阶张量情形，并利用该方法选取重要的横向与纵向切片/特征。我们从理论与数值两方面对所提出的管状DEIM（TDEIM）方法进行了研究。实验结果表明，相较于现有方法，TDEIM能够提供更精确的近似。本文还展示了该方法在监督分类任务中的应用。