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A Barzilai–Borwein Gradient Algorithm for Spatio-Temporal Internet Traffic Data Completion via Tensor Triple Decomposition

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Abstract

With the coming of high-speed network and 5G era, internet traffic data is crucial for various network tasks such as traffic engineering, capacity planning and anomaly detection. To explore the natural spatio-temporal structure of network flow, we use the novel triple decomposition of tensors to establish an optimization model with the spatio-temporal regularization for completing the internet traffic data. A Barzilai–Borwein gradient algorithm is designed for solving the spatio-temporal internet traffic tensor completion problem. We prove the convergence of this algorithm and analyze its convergence rate with the tool of the Kurdyka-Łojasiewicz property. Numerical experiments on Abilene and GÉANT datasets report that the proposed tensor completion method is effective.

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Data availability

The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.

Notes

  1. The Abilene Observatory Data Collections. “http://abilene.internet2.edu/observatory/datacollections.html”.

  2. “https://www.mathworks.com/matlabcentral/fileexchange/26395-matrix-completion-via-thresholding”.

  3. “https://www.math.ucla.edu/~wotaoyin/papers/bcu/”.

  4. “https://www.math.ucla.edu/~wotaoyin/papers/tmac_tensor_recovery.html”.

  5. “https://github.com/jamiezeminzhang/Tensor_Completion_and_Tensor_RPCA”.

  6. “https://github.com/lijunsun/bgcp_imputation”.

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Acknowledgements

The authors are grateful to the associate editor and anonymous referees for helping us to improve the original manuscript.

Author information

Authors and Affiliations

  1. School of Mathematical Sciences, South China Normal University, Guangzhou, China

    Yannan Chen

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

    Xinzhen Zhang

  3. Future Network Theory Lab, 2012 Labs Huawei Technologies Investment Co., Ltd., Shatin, New Territory, Hong Kong, China

    Liqun Qi

  4. Department of Mathematics, School of Science, Hangzhou Dianzi University, Hangzhou, 310018, China

    Liqun Qi

  5. Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, China

    Liqun Qi

  6. Huawei Theory Research Lab, Kowloon, Hong Kong, China

    Yanwei Xu

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  1. Yannan Chen
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Correspondence to Liqun Qi.

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Yannan Chen author was supported by the National Natural Science Foundation of China (11771405 and 12071159) and the Guangdong Basic and Applied Basic Research Foundation (2020A1515010489).

Xinzhen Zhang author’s work was supported by NSFC (Grant No. 11871369)

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Chen, Y., Zhang, X., Qi, L. et al. A Barzilai–Borwein Gradient Algorithm for Spatio-Temporal Internet Traffic Data Completion via Tensor Triple Decomposition. J Sci Comput 88, 65 (2021). https://doi.org/10.1007/s10915-021-01574-0

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  • DOI: https://doi.org/10.1007/s10915-021-01574-0

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