In this letter, a novel kernel adaptive algorithm, called kernel recursive generalized maximum correntropy algorithm (KRGMC), is derived in a kernel space and under the generalized maximum correntropy (GMC) criterion. The proposed kernel algorithm can effectively scale down the dynamic recursive weight coefficients influenced by the impulsive estimate error to avoid the significant performance degradation. The superior performance of the proposed algorithm is verified by numerical simulations about short-time series prediction in alpha-stable noise environment.

In this brief, a different kernel recursive maximum correntropy algorithm is derived using the weighted output information, called KRMC-W. To curb the network growth, we propose a new online sparsification strategy in a feature space, named vector projection (VP) method. Applying the VP to KRMC-W, two novel sparsified kernel adaptive filters, called soft projected KRMC-W (SP-KRMC-W) and hard projected KRMC-W (HP-KRMC-W), respectively, are developed to reduce the average computation complexity. Simulation results under the case of α-stable noise are conducted to demonstrate the efficiencies of the proposed algorithms.