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A sparse optimization approach for simultaneous orthogonal tensor diagonalization

Author

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  • Li, Xinying
  • Chang, Chao
  • Li, Jianze
  • Yang, Yuning

Abstract

This paper presents a sparse optimization method for the simultaneous orthogonal tensor diagonalization. The model treats off-diagonal elements of tensors as entities requiring sparsity, guided by an ℓ1 norm regularizer to optimize the diagonalization process. A gradient-based alternating multi-block Jacobi-AMB algorithm is developed to address the optimization problem on the product of orthogonal groups. We establish the global convergence based on the Kurdyka-Łojasiewicz property. Numerical experiments demonstrate that the Jacobi-AMB performs well in efficiency; under certain circumstances, its stability and effectiveness also perform well.

Suggested Citation

  • Li, Xinying & Chang, Chao & Li, Jianze & Yang, Yuning, 2025. "A sparse optimization approach for simultaneous orthogonal tensor diagonalization," Applied Mathematics and Computation, Elsevier, vol. 490(C).
    • Handle: RePEc:eee:apmaco:v:490:y:2025:i:c:s0096300324006647
    DOI: 10.1016/j.amc.2024.129203
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    References listed on IDEAS

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    1. Genevera I. Allen & Logan Grosenick & Jonathan Taylor, 2014. "A Generalized Least-Square Matrix Decomposition," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(505), pages 145-159, March.
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