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Fractional-order gradient descent with momentum for RBF neural network-based AIS trajectory restoration

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Abstract

In order to guarantee the integrity and accuracy of ship Automatic Identification System (AIS) data, and prevent maritime traffic accidents and make scientific decisions, a fractional-order gradient with momentum RBF neural network (FOGDM-RBF) is proposed. Fractional-order calculus is applied to gradient descent with momentum algorithm for training neural network. The convergence of the proposed algorithm is proved. The AIS data from Danish and Xiamen port are chosen to test the proposed algorithm. The results show FOGDM-RBF can repair the ship’s AIS trajectories with satisfying learning speed and interpolation accuracy. Comparisons show the proposed algorithm has lower training error than gradient descent, stochastic gradient descent and gradient descent with momentum. Compared with gradient descent, gradient descent with momentum, this algorithm has the advantages of better interpolation performance, higher accuracy, better generalization performance, and is not easy to fall into local optimum.

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Acknowledgements

The author thanks the reviewers for valuable comments that helped improve the clarity of presentation of this paper. The author is grateful to editors for valuable guidance and help.

Funding

The work is supported by the National Natural Science Foundation of China (51879119), Natural Science Foundation of Fujian Province (2018J05085), the high level research and cultivation fund of transportation engineering discipline in Jimei University (202003).

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Authors and Affiliations

  1. School of Navigation, Jimei University, Xiamen, 361021, Fujian, China

    Han Xue

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  1. Han Xue
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Correspondence to Han Xue.

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The author declares that they have no financial and personal relationships with other people or organizations that can inappropriately influence their work. There is no professional or other personal interest of any nature or kind in any product, service and company that could be construed as influencing the position presented in the manuscript.

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Communicated by A. Di Nola.

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Appendix: Matlab program of Caputo fractional differential

Appendix: Matlab program of Caputo fractional differential

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Xue, H. Fractional-order gradient descent with momentum for RBF neural network-based AIS trajectory restoration. Soft Comput 25, 869–882 (2021). https://doi.org/10.1007/s00500-020-05484-5

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