IEEE Trans Cybern. 2018 Jul;48(7):2101-2113. doi: 10.1109/TCYB.2017.2727278. Epub 2017 Jul 25.
Correntropy is a second order statistical measure in kernel space, which has been successfully applied in robust learning and signal processing. In this paper, we define a nonsecond order statistical measure in kernel space, called the kernel mean- power error (KMPE), including the correntropic loss (C-Loss) as a special case. Some basic properties of KMPE are presented. In particular, we apply the KMPE to extreme learning machine (ELM) and principal component analysis (PCA), and develop two robust learning algorithms, namely ELM-KMPE and PCA-KMPE. Experimental results on synthetic and benchmark data show that the developed algorithms can achieve better performance when compared with some existing methods.
协方差是核空间中的二阶统计量，已成功应用于鲁棒学习和信号处理。本文定义了核空间中的一种非二阶统计量，称为核均方误差（KMPE），包括协方差损失（C-Loss）作为特例。给出了 KMPE 的一些基本性质。特别地，我们将 KMPE 应用于极限学习机（ELM）和主成分分析（PCA），并开发了两种鲁棒学习算法，即 ELM-KMPE 和 PCA-KMPE。在合成数据和基准数据上的实验结果表明，与一些现有方法相比，所提出的算法具有更好的性能。
