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Kernel Generalized Half-Quadratic Correntropy Conjugate Gradient Algorithm for Online Prediction of Chaotic Time Series

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Abstract

Kernel adaptive filter armed with information theoretic learning has gained popularity in the domain of time series online prediction. In particular, the generalized correntropy criterion (GCC), as a nonlinear similarity measure, is robust to non-Gaussian noise or outliers in time series. However, due to the nonconvex nature of GCC, optimal parameter estimation may be difficult. Therefore, this paper deliberately combines it with half-quadratic (HQ) optimization to generate the generalized HQ correntropy (GHC) criterion, which provides reliable calculations for convex optimization. After that, a novel adaptive algorithm called kernel generalized half-quadratic correntropy conjugate gradient (KGHCG) algorithm is designed by integrating GHC and the conjugate gradient method. The proposed approach effectively enhances the robustness of non-Gaussian noise and greatly improves the convergence speed and filtering accuracy, and its sparse version KGHCG-VP limits the dimension of the kernel matrix through vector projection, which successfully handles the bottleneck of high computational complexity. In addition, we also discuss the convergence properties, computational complexity and memory requirements in terms of theoretical analysis. Finally, online prediction simulation results with the benchmark Mackey–Glass chaotic time series and real-world datasets show that KGHCG and KGHCG-VP have better convergence and prediction performance.

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Data Availability

he datasets used to support the findings of this study are available from the corresponding author on reasonable request.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (62173063).

Funding

This work was supported by the National Natural Science Foundation of China (62173063).

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Authors and Affiliations

  1. Faculty of Electronic Information and Electrical Engineering, Dalian University of Technology, Dalian, 116024, China

    Huijuan Xia

  2. College of Intelligent Systems Science and Engineering, Harbin Engineering University, Harbin, 150001, China

    Weijie Ren

  3. Key Laboratory of Intelligent Control and Optimization for Industrial Equipment of Ministry of Education, Dalian University of Technology, Dalian, 116024, China

    Min Han

  4. Professional Technology Innovation Center of Distributed Control for Industrial Equipment of Liaoning Province, Dalian University of Technology, Dalian, 116024, China

    Min Han

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  1. Huijuan Xia
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  2. Weijie Ren
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Correspondence to Min Han.

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Xia, H., Ren, W. & Han, M. Kernel Generalized Half-Quadratic Correntropy Conjugate Gradient Algorithm for Online Prediction of Chaotic Time Series. Circuits Syst Signal Process 42, 2698–2722 (2023). https://doi.org/10.1007/s00034-022-02258-2

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