The Nyström minimum kernel risk-sensitive loss algorithm with k-means sampling

Abstract The minimum kernel risk-sensitive loss (MKRSL) algorithm has been developed to improve the filtering accuracy and robustness of kernel least mean square (KLMS) in non-Gaussian noises. However, the linear growth of network size in MKRSL leads to a huge burden on time consumption and memory requirement. To curb this growth issue, a novel Nystr o ¨ m minimum kernel risk-sensitive loss with k-means sampling (NysMKRSL-KM) algorithm is proposed by using the Nystrom method combined with k-means sampling to approximate the kernel matrix of MKRSL in this paper. The proposed NysMKRSL-KM algorithm with low time and storage complexity achieves a comparable performance to kernel adaptive filters (KAFs). In addition, the energy conservation relation and the sufficient condition of NysMKRSL-KM are obtained for performing theoretical analysis and guaranteeing of the mean square convergence, respectively. The steady-state excess mean square errors (EMSEs) of NysMKRSL-KM for different noises are therefore derived for evaluating accuracy theoretically. Monte Carlo simulations are conducted to validate the theoretical analysis results and superiorities of the proposed NysMKRSL-KM algorithm.