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The Cauchy loss has been successfully applied in robust learning algorithms in the presence of large outliers, but it may suffer from performance degradation in complex nonlinear tasks. To address this issue, by transforming the original data into the reproducing kernel Hilbert spaces (RKHS) with the kernel trick, a novel Cauchy kernel loss is developed in such a kernel space. Based on the minimum Cauchy kernel loss criterion, the multikernel minimum Cauchy kernel loss (MKMCKL) algorithm is proposed by mapping the input data into the multiple RKHS. The proposed MKMCKL algorithm can provide the performance improvement of the kernel adaptive filter (KAF) based on a single kernel, and also improve the stability of the multikernel adaptive filter based on the quadratic loss in impulsive noises, efficiently. To further curb the growth of network of MKMCKL, a novel sparsification method is presented to prune redundant data, thus reducing its computational and storage burdens. Simulations on different nonlinear applications illustrate the performance superiorities of the proposed algorithms in impulsive noises.

Multikernel Adaptive Filters Under the Minimum Cauchy Kernel Loss Criterion