The purpose of kernel adaptive filtering (KAF) is to map input samples into reproducing kernel Hilbert spaces and use the stochastic gradient approximation to address learning problems. However, the growth of the weig...
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The purpose of kernel adaptive filtering (KAF) is to map input samples into reproducing kernel Hilbert spaces and use the stochastic gradient approximation to address learning problems. However, the growth of the weighted networks for KAF based on existing kernel functions leads to high computational complexity. This paper introduces a reduced Gaussian kernel that is a finite-order Taylor expansion of a decomposed Gaussian kernel. The corresponding reduced Gaussian kernel least-mean-square (RGklms) algorithm is derived. The proposed algorithm avoids the sustained growth of the weighted network in a nonstationary environment via an implicit feature map. To verify the performance of the proposed algorithm, extensive simulations are conducted based on scenarios involving time-series prediction and nonlinear channel equalization, thereby proving that the RGklms algorithm is a universal approximator under suitable conditions. The simulation results also demonstrate that the RGklms algorithm can exhibit a comparable steady-state mean-square-error performance with a much lower computational complexity compared with other algorithms.
With highly correlated input signal, the kernel least-mean-square algorithm(klms) always possess a low convergence rate. To overcome this problem the input signal should be decorrelated before adaptive filtering. A de...
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ISBN:
(纸本)9781509013456
With highly correlated input signal, the kernel least-mean-square algorithm(klms) always possess a low convergence rate. To overcome this problem the input signal should be decorrelated before adaptive filtering. A decorrelated kernel least-mean-square algorithm(Dklms) is proposed, which is the combination of klms and decorrelation. Using the characteristics of Gaussian kernel, the correlation coefficient is simplified, and the normalized variable step size is obtained and simplified. The iteration process of Dklms algorithm is presented. The computer simulation results show that Dklms has a smaller steady-state error and a faster convergence rate than klms, and outperforms DLMS.
This paper presents an online nonparametric methodology based on the Kernel Least Mean Square (klms) algorithm and the surprise criterion, which is based on an information theoretic framework. Surprise quantifies the ...
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ISBN:
(纸本)9781424496365
This paper presents an online nonparametric methodology based on the Kernel Least Mean Square (klms) algorithm and the surprise criterion, which is based on an information theoretic framework. Surprise quantifies the amount of information a datum contains given a known system state, and can be estimated online using Gaussian Process Theory. Based on this concept, we use the klms algorithm together with surprise criterion to detect regime change in nonstationary time series. We test the methodology on a synthesized chaotic time series to illustrate this criterion. The results show that surprise criterion is better than the conventional segmentation based on the error criterion.
With highly correlated input signal, the kernel least-mean-square algorithm(klms) always possess a low convergence rate. To overcome this problem the input signal should be decorrelated before adaptive filtering. A de...
详细信息
With highly correlated input signal, the kernel least-mean-square algorithm(klms) always possess a low convergence rate. To overcome this problem the input signal should be decorrelated before adaptive filtering. A decorrelated kernel least-mean-square algorithm(Dklms) is proposed, which is the combination of klms and decorrelation. Using the characteristics of Gaussian kernel, the correlation coefficient is simplified, and the normalized variable step size is obtained and simplified. The iteration process of Dklms algorithm is presented. The computer simulation results show that Dklms has a smaller steady-state error and a faster convergence rate than klms, and outperforms DLMS.
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