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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 selectimportant/ significant lateral and horizontal slices/features. The proposedTubal DEIM (TDEIM) is investigated both theoretically and numerically. Theexperimental results show that the TDEIM can provide more accurateapproximations than the existing methods. An application of the proposed methodto the supervised classification task is also presented.

Robust Low-Tubal-rank tensor recovery Using Discrete Empirical Interpolation Method with Optimized Slice/Feature Selection