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Transformed Low Tubal-Rank Approximations of Third Order Tensors via Frequent Directions

Ling Chen et al.

Pacific Journal of Optimization2026https://doi.org/10.61208/pjo-2026-008article
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0.50

What the paper says

(Communicated by Zheng-Hai Huang) Tensor low rank approximation is an important tool in tensor data analysis and processing. In the sense of tensor-tensor product (T-product) derived from general invertible transformation, the best low tubal-rank approximation of third order tensors can be obtained through truncated tensor singular value decomposition (T-SVD). In this paper, we first present two deterministic frequent directions type algorithms for near optimal low tubal-rank approximations of third order tensors. Moreover, we propose a randomized frequent directions algorithm for near optimal low tubal-rank approximations of third order tensors. Corresponding relative error bounds for the presented algorithms are derived. The related numerical examples on third order tensors of color image, grayscale video and synthetic data with larger scale illustrate the favorable performance of the presented methods compared to some existing methods.

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https://doi.org/https://doi.org/10.61208/pjo-2026-008

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@article{ling2026,
  title        = {{Transformed Low Tubal-Rank Approximations of Third Order Tensors via Frequent Directions}},
  author       = {Ling Chen et al.},
  journal      = {Pacific Journal of Optimization},
  year         = {2026},
  doi          = {https://doi.org/https://doi.org/10.61208/pjo-2026-008},
}

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0.50

Balanced mode · F 0.40 / M 0.15 / V 0.05 / R 0.40

F · citation impact0.50 × 0.4 = 0.20
M · momentum0.50 × 0.15 = 0.07
V · venue signal0.50 × 0.05 = 0.03
R · text relevance †0.50 × 0.4 = 0.20

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