  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.
