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As a novel similarity measure that is defined as the expectation of a kernel function between two random variables, correntropy has been successfully applied in robust machine learning and signal processing to combat large outliers. The kernel function in correntropy is usually a zero-mean Gaussian kernel. In a recent work, the concept of mixture correntropy (MC) was proposed to improve the learning performance, where the kernel function is a mixture Gaussian kernel, namely, a linear combination of several zero-mean Gaussian kernels with different widths. In both correntropy and MC, the center of the kernel function is, however, always located at zero. In the present work, to further improve the learning performance, we propose the concept of multikernel correntropy (MKC), in which each component of the mixture Gaussian kernel can be centered at a different location. The properties of the MKC are investigated and an efficient approach is proposed to determine the free parameters in MKC. Experimental results show that the learning algorithms under the maximum MKC criterion (MMKCC) can outperform those under the original maximum correntropy criterion (MCC) and the maximum MC criterion (MMCC). [ABSTRACT FROM AUTHOR]

In recent years, correntropy has been successfully applied to robust adaptive filtering to eliminate adverse effects of impulsive noises or outliers. Correntropy is generally defined as the expectation of a Gaussian kernel between two random variables. This definition is reasonable when the error between the two random variables is symmetrically distributed around zero. For the case of asymmetric error distribution, the symmetric Gaussian kernel is however inappropriate and cannot adapt to the error distribution well. To address this problem, in this brief we propose a new variant of correntropy, named asymmetric correntropy, which uses an asymmetric Gaussian model as the kernel function. In addition, a robust adaptive filtering algorithm based on asymmetric correntropy is developed and its steady-state convergence performance is analyzed. Simulations are provided to confirm the theoretical results and good performance of the proposed algorithm. [ABSTRACT FROM AUTHOR]

In recent years, the sparse system identification (SSI) has received increasing attention, and various sparsity-aware adaptive algorithms based on the minimum mean square error (MMSE) criterion have been developed, which are optimal under the assumption of Gaussian distributions. However, the Gaussian assumption does not always hold in real-world environments. The maximum correntropy criterion (MCC) is used to replace the MMSE criterion to suppress the heavy-tailed non-Gaussian noises. For some more complex non-Gaussian noises such as those from multimodal distributions, the minimum error entropy (MEE) criterion can outperform MCC although it is computationally somewhat more expensive. To improve the performance of SSI in non-Gaussian noises, in this brief we develop a class of sparsity-aware MEE algorithms with the fixed point iteration (MEE-FP) by incorporating the zero-attracting ($\ell _{1}$ -norm), reweighted zero-attracting (reweighted $\ell _{1}$ -norm) and correntropy induced metric (CIM) penalty terms into the cost function. The corresponding algorithms are termed as ZA-MEE-FP, RZA-MEE-FP, and CIM-MEE-FP, which can achieve better performance than the original MEE-FP algorithm and the MCC based sparsity-aware algorithms. Simulation results confirm the excellent performance of the new algorithms. [ABSTRACT FROM AUTHOR]