Kernel adaptive filtering with maximum correntropy criterion

Abstract

Abstract-Kernel adaptive filters have drawn increasing attention due to their advantages such as universal nonlinear approximation with universal kernels, linearity and convexity in Reproducing Kernel Hilbert Space (RKHS). Among them, the kernel least mean square (KLMS) algorithm deserves particular attention because of its simplicity and sequential learning approach. Similar to most conventional adaptive filtering algorithms, the KLMS adopts the mean square error (MSE) as the adaptation cost. However, the mere second-order statistics is often not suitable for nonlinear and non-Gaussian situations. Therefore, various non-MSE criteria, which involve higherorder statistics, have received an increasing interest. Recently, the correntropy, as an alternative of MSE, has been successfully used in nonlinear and non-Gaussian signal processing and machine learning domains. This fact motivates us in this paper to develop a new kernel adaptive algorithm, called the kernel maximum correntropy (KMC), which combines the advantages of the KLMS and maximum correntropy criterion (MCC). We also study its convergence and self-regularization properties by using the energy conservation relation. The superior performance of the new algorithm has been demonstrated by simulation experiments in the noisy frequency doubling problem.

Correntropy kernel temporal differences for reinforcement learning brain machine interfaces

“…Using the ideas of both kernel least mean square (KLMS) [10] and maximum correntropy criterion [8], kernel maximum correntropy (KMC) is introduced in supervised learning [9]. To maximize the error correntropy, we can use stochastic gradient ascent on the new cost function in the feature space.…”

“…Maximum correntropy criterion (MCC) has been applied to obtain robust methods for adaptive systems in supervised learning [8], [9]. Using MCC, a system can be adapted in such a way that a similarity measure between desired and predicted signals is maximized.…”

“…Using MCC, a system can be adapted in such a way that a similarity measure between desired and predicted signals is maximized. In particular, kernel maximum correntropy (KMC), which is a blend between kernel least mean square (KLMS) [10] and MCC, was proposed in [9]. The basic idea of KMC is that input data is transferred to an RKHS using a nonlinear mapping function, and MCC is applied as a cost function to minimize the error.…”

A Quantized Kernel Learning Algorithm Using a Minimum Kernel Risk-Sensitive Loss Criterion and Bilateral Gradient Technique

“…In addition, the corresponding maximum correntropy criterion (MCC) has been used as a cost function to derive various robust nonlinear adaptive filtering algorithms, such as the kernel maximum correntropy (KMC) algorithm [36] and the kernel recursive maximum correntropy (KRMC) algorithm [27], and they show better performance than those classical second-order schemes, e.g., KLMS and KRLS. However, correntropic loss (C-Loss) is a non-convex function, and may converge slowly, especially when the initial value is far away from the optimal value.…”

Robust Hammerstein Adaptive Filtering under Maximum Correntropy Criterion

“…The MCC aims at maximizing the similarity (measured by correntropy) between the model output and the desired response such that the adaptive model is as close as possible to the unknown system. It has been shown that, the MCC in terms of the stability and accuracy, is very robust with respect to impulsive noises [33][34][35][36][37][38][39]. Compared with the traditional Hammerstein adaptive filtering algorithms based on the MSE criterion, the new algorithm can achieve better performance especially in the presence of impulsive non-Gaussian noises.…”