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Perturbations of the Tcur Decomposition for Tensor Valued Data in the Tucker Format

Author

Listed:
  • Maolin Che

    (Southwestern University of Finance and Economics
    Hong Kong Science Park)

  • Juefei Chen

    (Fudan University)

  • Yimin Wei

    (Fudan University)

Abstract

The tensor CUR decomposition in the Tucker format is a special case of Tucker decomposition with a low multilinear rank, where factor matrices are obtained by selecting some columns from the mode-n unfolding of the tensor. We perform a thorough investigation of what happens to the approximations in the presence of noise. We present two forms of the tensor CUR decomposition and deduce the errors of the approximation. We illustrate how the choice of columns from each mode-n unfolding reflects the quality of the tensor CUR approximation via some numerical examples.

Suggested Citation

  • Maolin Che & Juefei Chen & Yimin Wei, 2022. "Perturbations of the Tcur Decomposition for Tensor Valued Data in the Tucker Format," Journal of Optimization Theory and Applications, Springer, vol. 194(3), pages 852-877, September.
    • Handle: RePEc:spr:joptap:v:194:y:2022:i:3:d:10.1007_s10957-022-02051-w
    DOI: 10.1007/s10957-022-02051-w
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    References listed on IDEAS

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    1. J. Carroll & Jih-Jie Chang, 1970. "Analysis of individual differences in multidimensional scaling via an n-way generalization of “Eckart-Young” decomposition," Psychometrika, Springer;The Psychometric Society, vol. 35(3), pages 283-319, September.
    2. Ledyard Tucker, 1966. "Some mathematical notes on three-mode factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 31(3), pages 279-311, September.
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    Cited by:

    1. Minghui Ding & Yimin Wei & Pengpeng Xie, 2023. "A Randomized Singular Value Decomposition for Third-Order Oriented Tensors," Journal of Optimization Theory and Applications, Springer, vol. 197(1), pages 358-382, April.

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