The Kernel Recursive Generalized Cauchy Kernel Loss Algorithm

As a nonlinear measure similarity developed in a kernel space, the generalized correntropic loss (GC-Loss) has been successfully used for signal processing and machine learning in non-Gaussian situations thanks to its ability of extracting high-order statistical properties of data. However, a highly non-convex performance surface in GC-Loss leads to poor optimization performance. To address this issue, we propose a new similarity measure developed in the kernel space by combining a generalized Gaussian distributed kernel function into the Cauchy loss. By minimizing the proposed loss function and using the kernel method, a novel kernel recursive generalized Cauchy kernel loss (KRGCKL) algorithm in the reproducing kernel Hilbert space (RKHS) is proposed. Simulations on different examples under non-Gaussian noises show the superiorities of KRGCKL over other representative algorithms in terms of filtering accuracy and robustness to large outliers.