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

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.

Automated summary

This study combines information theoretic learning with kernel adaptive filter to propose the generalized HQ correntropy (GHC) criterion by integrating the generalized correntropy criterion (GCC) and half-quadratic (HQ) optimization. A novel adaptive algorithm called kernel generalized half-quadratic correntropy conjugate gradient (KGHCG) algorithm is designed, which effectively enhances the robustness against non-Gaussian noise and greatly improves the convergence speed and filtering accuracy.