Zhang Tao, Wang Shiyuan, Zhang Haonan, Xiong Kui, Wang Lin
College of Electronic and Information Engineering, Southwest University, Chongqing 400715, China.
Chongqing Key Laboratory of Nonlinear Circuits and Intelligent Information Processing, Chongqing 400715, China.
Entropy (Basel). 2019 Jun 13;21(6):588. doi: 10.3390/e21060588.
As a nonlinear similarity measure defined in the reproducing kernel Hilbert space (RKHS), the correntropic loss (C-Loss) has been widely applied in robust learning and signal processing. However, the highly non-convex nature of C-Loss results in performance degradation. To address this issue, a convex kernel risk-sensitive loss (KRL) is proposed to measure the similarity in RKHS, which is the risk-sensitive loss defined as the expectation of an exponential function of the squared estimation error. In this paper, a novel nonlinear similarity measure, namely kernel risk-sensitive mean -power error (KRP), is proposed by combining the mean -power error into the KRL, which is a generalization of the KRL measure. The KRP with p = 2 reduces to the KRL, and can outperform the KRL when an appropriate is configured in robust learning. Some properties of KRP are presented for discussion. To improve the robustness of the kernel recursive least squares algorithm (KRLS) and reduce its network size, two robust recursive kernel adaptive filters, namely recursive minimum kernel risk-sensitive mean -power error algorithm (RMKRP) and its quantized RMKRP (QRMKRP), are proposed in the RKHS under the minimum kernel risk-sensitive mean -power error (MKRP) criterion, respectively. Monte Carlo simulations are conducted to confirm the superiorities of the proposed RMKRP and its quantized version.
作为在再生核希尔伯特空间（RKHS）中定义的一种非线性相似性度量，熵损失（C-Loss）已在鲁棒学习和信号处理中得到广泛应用。然而，C-Loss的高度非凸性质导致性能下降。为了解决这个问题，提出了一种凸核风险敏感损失（KRL）来度量RKHS中的相似性，它是将风险敏感损失定义为平方估计误差的指数函数的期望。本文通过将平均功率误差与KRL相结合，提出了一种新的非线性相似性度量，即核风险敏感平均功率误差（KRP），它是KRL度量的一种推广。当p = 2时，KRP可简化为KRL，并且在鲁棒学习中配置适当的 时，其性能优于KRL。给出了KRP的一些性质以供讨论。为了提高核递归最小二乘算法（KRLS）的鲁棒性并减小其网络规模，在最小核风险敏感平均功率误差（MKRP）准则下，分别在RKHS中提出了两种鲁棒递归核自适应滤波器，即递归最小核风险敏感平均功率误差算法（RMKRP）及其量化版本QRMKRP。进行了蒙特卡罗模拟以证实所提出的RMKRP及其量化版本的优越性。
