Maximum correntropy criterion-based kernel adaptive filters

Kernel adaptive filters (KAFs) are a family of powerful online kernel learning methods that can learn nonlinear and nonstationary systems efficiently. Most of the existing KAFs are obtained by minimizing the well-known mean square error (MSE). The MSE criterion is computationally simple and very easy to implement but may suffer from a lack of robustness to non-Gaussian noises. To deal with the non-Gaussian noises robustly, the optimization criteria must go beyond the second-order framework. Recently, the correntropy, a novel similarity measure that involves all even-order moments, has been shown to be very robust to the presence of heavy-tailed non-Gaussian noises. A generalized correntropy has been proposed in a recent study. Combining the KAFs with the maximum correntropy criterion (MCC) provides a unified and efficient approach to handle nonlinearity, nonstationarity and non-Gaussianity. The major goal of this chapter is to briefly characterize such an approach. The KAFs under the generalized MCC will be investigated, and some simulation results will be presented.