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Robust low tubal rank tensor recovery using discrete empirical interpolation method with optimized slice/feature selection

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Abstract

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.

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Data Availability

The data used in the numerical experiments are available at http://trace.eas.asu.edu/yuv/ and http://yann.lecun.com/exdb/mnist/.

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Acknowledgements

The authors express their sincere gratitude to the editors and two reviewers for their insightful comments, which have greatly elevated the paper’s quality.

Funding

This work was partially funded by the Ministry of Education and Science (grant 075.10.2021.068). Cesar F. Caiafa work was partially supported by grants PICT 2020-SERIEA-00457 and PIP 112202101 00284CO (Argentina).

Author information

Authors and Affiliations

  1. Center for Artificial Intelligence Technology, Skolkovo Institute of Science and Technology, Moscow, Russia

    Salman Ahmadi-Asl & Anh-Huy Phan

  2. Innopolis University, Innopolis, Russia

    Salman Ahmadi-Asl

  3. Instituto Argentino de Radioastronomia—CCT La Plata, CONICET/CIC-PBA/UNLP, Villa Elisa, 1894, Argentina

    Cesar F. Caiafa

  4. Systems Research Institute of Polish Academy of Science, Warsaw, Poland

    Andrzej Cichocki

Authors
  1. Salman Ahmadi-Asl
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  2. Anh-Huy Phan
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  3. Cesar F. Caiafa
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  4. Andrzej Cichocki
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Correspondence to Salman Ahmadi-Asl.

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Communicated by: Raymond H. Chan

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Ahmadi-Asl, S., Phan, AH., Caiafa, C.F. et al. Robust low tubal rank tensor recovery using discrete empirical interpolation method with optimized slice/feature selection. Adv Comput Math 50, 23 (2024). https://doi.org/10.1007/s10444-024-10117-8

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Keywords

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