A quantized adaptive algorithm based on the q-Renyi kernel function

In this paper, we proposed a novel online kernel-adaptive learning algorithm under the reproducing kernel-Hilbert space (RKHS), which is called kernel q-Renyi (KqR) algorithm. The KqR algorithm is derived via constructing a q-Renyi kernel function as a cost function into kernel adaptive filtering algorithm (KAF). The vector-quantization (VQ) method is wildly used in the KAF algorithms, which is called quantized KAF. The quantized kernel q-Renyi (QKqR) algorithm is also proposed to significantly reduce computational cost via quantizing input space to curb the size of neural networks growth. The mean-square-convergence analysis of the QKqR algorithm is established, and the theoretical-value of the excess-mean-square-error (EMSE) are presented. The performance of the KqR and QKqR algorithms are investigated and demonstrated via tracking the Mackey-Glass (MG) time-series-prediction and the nonlinear channel equalization (NCE) under the non-Gaussian background interferences. (c) 2021 Elsevier Inc. All rights reserved.