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Tensor neural network models for tensor singular value decompositions

Author

Listed:
  • Xuezhong Wang

    (Hexi University)

  • Maolin Che

    (Southwestern University of Finance and Economics)

  • Yimin Wei

    (Fudan University)

Abstract

Tensor decompositions have become increasingly prevalent in recent years. Traditionally, tensors are represented or decomposed as a sum of rank-one outer products using either the CANDECOMP/PARAFAC, the Tucker model, or some variations thereof. The motivation of these decompositions is to find an approximate representation for a given tensor. The main propose of this paper is to develop two neural network models for finding an approximation based on t-product for a given third-order tensor. Theoretical analysis shows that each of the neural network models ensures the convergence performance. The computer simulation results further substantiate that the models can find effectively the left and right singular tensor subspace.

Suggested Citation

  • Xuezhong Wang & Maolin Che & Yimin Wei, 2020. "Tensor neural network models for tensor singular value decompositions," Computational Optimization and Applications, Springer, vol. 75(3), pages 753-777, April.
    • Handle: RePEc:spr:coopap:v:75:y:2020:i:3:d:10.1007_s10589-020-00167-1
    DOI: 10.1007/s10589-020-00167-1
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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.
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    Cited by:

    1. Feiyang Han & Yimin Wei & Pengpeng Xie, 2024. "Regularized and Structured Tensor Total Least Squares Methods with Applications," Journal of Optimization Theory and Applications, Springer, vol. 202(3), pages 1101-1136, September.
    2. Huang, Baohua, 2024. "Conjugate gradient-type method for the tensor linear system via the T-product and its application in the calculation of Moore-Penrose inverse," Applied Mathematics and Computation, Elsevier, vol. 472(C).
    3. Xuezhong Wang & Ping Wei & Yimin Wei, 2023. "A Fixed Point Iterative Method for Third-order Tensor Linear Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 197(1), pages 334-357, April.

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