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    Area of Science:

    • Machine Learning
    • Time Series Analysis
    • Computational Science

    Background:

    • Kernel Recursive Least Squares (KRLS) is a kernel method for time series online prediction.
    • KRLS offers low computational complexity and recursive updates.
    • Challenges include increased computational complexity with data size and difficulty adapting to time-varying environments.

    Purpose of the Study:

    • To present an improved KRLS algorithm for multivariate chaotic time series online prediction.
    • To enhance computational efficiency and adaptivity in time-varying conditions.

    Main Methods:

    • The improved KRLS algorithm combines approximate linear dependency, dynamic adjustment, and coherence criterion with quantization.
    • This approach addresses the limitations of standard KRLS in handling large datasets and dynamic environments.

    Main Results:

    • The proposed algorithm demonstrates improved computational efficiency during online prediction.
    • It allows for adaptive weight adjustments in time-varying environments.
    • Effectiveness is validated on Lorenz, El Nino-Southern Oscillation, sunspots, and Yellow River runoff chaotic time series.

    Conclusions:

    • The improved KRLS algorithm effectively addresses computational complexity and adaptivity issues in chaotic time series prediction.
    • It offers a robust solution for real-world applications requiring online, adaptive forecasting.