Multiple Nyström Kernel Adaptive Filter under Minimum Generalized Cauchy Loss Criterion

The multikernel adaptive filters (MKAFs) have been successfully applied to resolve the issue of kernel parameter selection in traditional single kernel adaptive filters. However, owing to the linear growing network structures, conventional MKAFs commonly suffer a lot from large computational and memory burdens. To solve this problem, a multiple Nyström approximation is proposed to curb the computational complexity of MKAFs in this brief. More concretely, the multiple Nyström method is incorporated into the kernel generalized Cauchy conjugate gradient algorithm, generating a novel multiple Nyström kernel generalized Cauchy conjugate gradient algorithm (MNKGCCG). It is noted that the MNKGCCG can achieve the desirable filtering performance with low computational cost in the fixed-dimensional feature space. Experimental results on Mackey-Glass time series and sunspots time series predictions in non-Gaussian noise environments demonstrate the superiorities of the proposed MNKGCCG algorithm in terms of filtering accuracy and robustness.