Kernel Risk-Sensitive Mean p-Power Error Algorithms for Robust Learning
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 conv...
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| 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 p = 2 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. |
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| AbstractList | 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 p = 2 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. 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 p = 2 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.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 p = 2 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. |
| Author | Wang, Shiyuan Zhang, Haonan Wang, Lin Xiong, Kui Zhang, Tao |
| AuthorAffiliation | 2 Chongqing Key Laboratory of Nonlinear Circuits and Intelligent Information Processing, Chongqing 400715, China 1 College of Electronic and Information Engineering, Southwest University, Chongqing 400715, China |
| AuthorAffiliation_xml | – name: 1 College of Electronic and Information Engineering, Southwest University, Chongqing 400715, China – name: 2 Chongqing Key Laboratory of Nonlinear Circuits and Intelligent Information Processing, Chongqing 400715, China |
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| Cites_doi | 10.1109/SPAWC.2012.6292933 10.1109/TSP.2007.896065 10.1109/49.339922 10.1007/978-1-4419-1570-2 10.1109/TPAMI.2010.220 10.1002/9780470608593 10.1109/TSP.2005.849213 10.1109/TSP.2004.830991 10.1109/TNNLS.2011.2178446 10.1016/j.sigpro.2015.04.024 10.1016/j.engappai.2016.11.010 10.1109/TSP.2017.2669903 10.1109/TSP.2015.2453133 10.1109/TSP.2007.907881 10.3390/e19070365 10.1109/TCYB.2017.2727278 10.1162/neco.1991.3.2.213 10.1016/j.neunet.2013.11.011 10.1109/9.989082 10.1109/TSP.2008.2009895 10.1109/LSP.2014.2319308 10.1109/TSP.2004.830985 10.1109/TNET.2012.2187923 10.1109/TNNLS.2013.2258936 10.1007/978-3-642-30574-0_41 10.1109/TIP.2010.2103949 10.1016/j.dsp.2015.09.015 10.1016/j.dsp.2017.01.010 10.1109/TSP.2006.872524 |
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| SubjectTerms | Accuracy Adaptive filters Algorithms Approximation correntropic Exponential functions Hilbert space kernel adaptive filters kernel risk-sensitive mean p-power error Kernels Machine learning Performance degradation quantized Random variables recursive Risk Robustness Signal processing Similarity Similarity measures |
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