Abstract
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 p-power error (KRP), is proposed by combining the mean p-power error into the KRL, which is a generalization of the KRL measure. The KRP with reduces to the KRL, and can outperform the KRL when an appropriate p 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 p-power error algorithm (RMKRP) and its quantized RMKRP (QRMKRP), are proposed in the RKHS under the minimum kernel risk-sensitive mean p-power error (MKRP) criterion, respectively. Monte Carlo simulations are conducted to confirm the superiorities of the proposed RMKRP and its quantized version.
Highlights
Online kernel-based learning is to extend the kernel methods to online settings where the data arrives sequentially, which has been widely applied in signal processing thanks to its excellent performance in addressing nonlinear issues [1]
To inherit the advantages of both kernel risk-sensitive loss (KRL) and MPE for robustness improvement, we propose the risk-sensitive mean p-power error (RP) defined as the expectation of an exponential function of the pth absolute moment of the estimation error, and its kernel RP (KRP)
Note that the steady-state mean square error (MSE) of kernel least mean square (KLMS), quantized kernel least mean square algorithm (QKLMS), kernel recursive least squares algorithm (KRLS), and quantized kernel recursive least squares algorithm (QKRLS) are not shown in Table 1 since they cannot converge in such impulsive noise environment
Summary
Online kernel-based learning is to extend the kernel methods to online settings where the data arrives sequentially, which has been widely applied in signal processing thanks to its excellent performance in addressing nonlinear issues [1]. For Gaussian noises, the second-order similarity measures of errors are generally used as a cost function of KAFs to achieve desirable filtering accuracy. The non-second order similarity measures can be divided into three categories, i.e., the mean p-power error (MPE) criterion [15], information theoretic learning (ITL) [14], and risk-sensitive loss (RL) based criteria [16,17]. To inherit the advantages of both KRL and MPE for robustness improvement, we propose the risk-sensitive mean p-power error (RP) defined as the expectation of an exponential function of the pth absolute moment of the estimation error, and its kernel RP (KRP). The proposed KRP criterion is used to derive a novel recursive minimum kernel risk-sensitive mean p-power error (RMKRP) algorithm for desirable filtering performance by combining the weighted output information.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
