Nyström kernel algorithm based on least logarithmic hyperbolic cosine loss

Abstract

Kernel adaptive filters (KAFs) have sparked substantial attraction for online non-linear learning applications. It is noted that the effectiveness of KAFs is highly reliant on a rational learning criterion. Concerning this, the logarithmic hyperbolic cosine (lncosh) criterion with better robustness and convergence has drawn attention in recent studies. However, existing lncosh loss-based KAFs use the stochastic gradient descent (SGD) for optimization, which lack a trade-off between the convergence speed and accuracy. But recursion-based KAFs can provide more effective filtering performance. Therefore, a Nyström method-based robust sparse kernel recursive least lncosh loss algorithm is derived in this article. Experiments via measures and synthetic data against the non-Gaussian noise confirm the superiority with regard to the robustness, accuracy performance, and computational cost.

Keywords

• Kernel adaptive filter (KAF)
• logarithmic hyperbolic cosine (lncosh) loss
• Nyström method
• Recursive