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Tensor Factorization-Based Method for Tensor Completion with Spatio-temporal Characterization

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Abstract

In this paper, we propose a novel tensor factorization-based method for the third-order tensor completion problem with spatio-temporal characterization. For this aim, we consider tensor fibered rank, which extends tubal rank, to improve the flexibility and accuracy of data characterization. Based on this rank, we apply a factorization-based method to complete the third-order low-rank tensors with spatio-temporal characteristics, which are intrinsic features of image, video and internet traffic tensor data. The model not only makes good use of the low-rank structure of tensors, but also takes into account the spatio-temporal characteristics of the data. Finally, we report numerical results on completing image, video and internet traffic data. The results demonstrate that our method outperforms some existing methods.

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Data Availability

Codes supporting the numerical results are freely available in the GitHub repository, https://github.com/quanyumath/STTF.

Notes

  1. http://trace.eas.asu.edu/yuv/.

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Acknowledgements

Xinzhen Zhang was partially supported by NSFC (11871369). Zheng-Hai Huang was partially supported by NSFC (12171357).

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Authors and Affiliations

  1. School of Mathematics, Hunan University, Changsha, 410082, Hunan, China

    Quan Yu

  2. School of Mathematics, Tianjin University, Tianjin, 300354, China

    Xinzhen Zhang & Zheng-Hai Huang

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  1. Quan Yu
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Correspondence to Xinzhen Zhang.

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Communicated by Hedy Attouch.

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Yu, Q., Zhang, X. & Huang, ZH. Tensor Factorization-Based Method for Tensor Completion with Spatio-temporal Characterization. J Optim Theory Appl 199, 337–362 (2023). https://doi.org/10.1007/s10957-023-02287-0

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