Generalized Correntropy for Robust Adaptive Filtering
Generalized Correntropy for Robust Adaptive Filtering
复制标题
鲁棒自适应滤波的广义熵
DOI：
10.1109/tsp.2016.2539127
复制
发表时间：
2016-07-01
影响因子：
5.4
通讯作者：
Principe, Jose C.
中科院分区：
文献类型：
--
作者：
Chen, Badong;Xing, Lei;Principe, Jose C.
相关熵作为核空间中一种鲁棒的非线性相似性度量，在机器学习和信号处理领域受到越来越多的关注。特别是，最大相关熵准则（MCC）最近已成功地应用于鲁棒回归和滤波。相关熵中的默认核函数是高斯核，当然，这并不总是最佳选择。本文提出了一种以广义高斯密度（GGD）函数为核函数的广义相关熵，并给出了它的一些重要性质。本文进一步提出了广义最大相关熵准则（GMCC），并将其应用于自适应滤波。一种自适应算法，称为GMCC算法，推导出，和稳定性问题和稳态性能进行了研究。我们表明，该算法是非常稳定的，可以实现零发散概率（POD）。仿真结果证实了理论预期，并证明了新算法的理想性能。
As a robust nonlinear similarity measure in kernel space, correntropy has received increasing attention in domains of machine learning and signal processing. In particular, the maximum correntropy criterion (MCC) has recently been successfully applied in robust regression and filtering. The default kernel function in correntropy is the Gaussian kernel, which is, of course, not always the best choice. In this paper, we propose a generalized correntropy that adopts the generalized Gaussian density (GGD) function as the kernel, and present some important properties. We further propose the generalized maximum correntropy criterion (GMCC) and apply it to adaptive filtering. An adaptive algorithm, called the GMCC algorithm, is derived, and the stability problem and steady-state performance are studied. We show that the proposed algorithm is very stable and can achieve zero probability of divergence (POD). Simulation results confirm the theoretical expectations and demonstrate the desirable performance of the new algorithm.