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The Low-Rank Approximation of Fourth-Order Partial-Symmetric and Conjugate Partial-Symmetric Tensor

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Abstract

We present an orthogonal matrix outer product decomposition for the fourth-order conjugate partial-symmetric (CPS) tensor and show that the greedy successive rank-one approximation (SROA) algorithm can recover this decomposition exactly. Based on this matrix decomposition, the CP rank of CPS tensor can be bounded by the matrix rank, which can be applied to low-rank tensor completion. Additionally, we give the rank-one equivalence property for the CPS tensor based on the SVD of matrix, which can be applied to the rank-one approximation for CPS tensors.

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Author information

Authors and Affiliations

  1. School of Mathematics and Statistics, Kashi University, Kashi, 844008, Xinjiang, China

    Amina Sabir

  2. School of Mathematical Sciences and LPMC, Nankai University, Tianjin, 300071, China

    Amina Sabir, Peng-Fei Huang & Qing-Zhi Yang

Authors
  1. Amina Sabir
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  2. Peng-Fei Huang
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  3. Qing-Zhi Yang
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Contributions

Amina Sabir, Peng-Fei Huang and Qing-Zhi Yang designed the algorithms, performed the numerial experiments, drafted the manuscript, read and approved the final manuscript.

Corresponding author

Correspondence to Peng-Fei Huang.

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The authors declare that they have no conflict of interest.

Additional information

This work was funded by the National Natural Science Foundation of China (Nos. 11671217 and 12071234) and Key Program of Natural Science Foundation of Tianjin, China (No. 21JCZDJC00220).

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Sabir, A., Huang, PF. & Yang, QZ. The Low-Rank Approximation of Fourth-Order Partial-Symmetric and Conjugate Partial-Symmetric Tensor. J. Oper. Res. Soc. China 11, 735–758 (2023). https://doi.org/10.1007/s40305-022-00425-5

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  • DOI: https://doi.org/10.1007/s40305-022-00425-5

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