Logarithmic Hyperbolic Cosine Adaptive Filter and Its Performance Analysis

Wang, Shiyuan; Wang, Wenyue; Xiong, Kui; Iu, Herbert Ho-Ching; Tse, Chi K.

doi:10.1109/tsmc.2019.2915663

Cited by 85 publications

(13 citation statements)

References 36 publications

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“…According to (12), the estimated output is given byf (u) = ( z ) T z(u) with z being the weight vector in the feature space. Thus, the proposed Nyström mapping based on k-means sampling can be applied in nonlinear adaptive filtering based on different cost functions, e.g., the correntropy [32], Cauchy kernel loss [33], and hyperbolic cosine loss [34], for online applications in the transformed feature space.…”

Section: Nyström Kernel Mappingmentioning

confidence: 99%

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The Nyström Kernel Conjugate Gradient Algorithm Based on $k$ -Means Sampling

Xiong

Wang

2020

IEEE Access

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The kernel conjugate gradient (KCG) algorithms have been proposed to improve the convergence rate and the filtering accuracy of kernel adaptive filters (KAFs) efficiently. However, sparsification is necessary in the KCG algorithms to curb the growth of network structure for online applications. To this end, a novel online kernel conjugate gradient algorithm under the mean square error criterion is proposed to approximate the kernel matrix in KAFs by combining k-means sampling into the Nyström method in a fixed-dimensional feature space, namely a Nyström kernel conjugate gradient algorithm based on k-means sampling (NysKCG-KM). The approximation accuracy of the kernel matrix as well as the filtering performance of NysKCG-KM are therefore guaranteed by k-means sampling. The proposed NysKCG-KM with no requirement of sparsification can achieve dramatically better filtering accuracy than the kernel least mean square with sparsification, and approach the filtering accuracy of the kernel recursive least squares with sparsification. Monte Carlo simulations using both the synthetic and real-world data validate the superiorities of the proposed NysKCG-KM.

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Section: Nyström Kernel Mappingmentioning

confidence: 99%

“…the proposed Nyström kernel mapping and the CG method can also be extended to the non-quadratic error based cost functions [32]- [34], e.g., correntropy, for combating non-Gaussian noises including large outliers efficiently.…”

Section: A Nyskcg-km Algorithmmentioning

confidence: 99%

The Nyström Kernel Conjugate Gradient Algorithm Based on $k$ -Means Sampling

Xiong

Wang

2020

IEEE Access

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“…K ERNEL adaptive filtering is a family of online kernel learning algorithms that has been widely studied in many fields such as nonlinear time series prediction [1], [2], [3], nonlinear channel equalization [4], [5] and system identification [6], [7]. The kernel least-mean-square (KLMS) algorithm has universal approximation ability and wellposedness property, where the basic idea is to transform the input data into a high-dimensional feature space using the reproducing kernel [8], [9], [10], [11], [12].…”

Section: Introductionmentioning

confidence: 99%

Accelerate Convergence of Polarized Random Fourier Feature-Based Kernel Adaptive Filtering With Variable Forgetting Factor and Step Size

Yang

Liu

et al. 2020

IEEE Access

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The random Fourier feature as an efficient kernel approximation method can effectively suppress the network growth of the traditional kernel-based adaptive filtering algorithm. Polarized random Fourier feature kernel least-mean-square(PRFFKLMS) remarkably improved the accuracy performance of random Fourier feature-based kernel least-mean-square algorithm and become the most representative random Fourier feature-based least-mean-square algorithm. In this paper, we studied the method that can improve the convergence speed of random Fourier feature-based least-mean-square algorithm. Based on the variable forgetting factor and variable step size strategy, three algorithm are proposed. The computational complexity of proposed algorithms are also given. The simulation results show that compared with PRFFKLMS algorithm, the convergence speed of the proposed algorithm is significantly improved. INDEX TERMS Random Fourier features; forgetting factor strategy; variable step size; kernel least-meansquare algorithm.

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“…In addition, the logarithmic error loss including the Cauchy loss is another type of effective non-quadratic loss for non-Gaussian noises [16]- [20]. It is worth noting that the logarithmic loss can provide better performance than C-Loss in specific environments [17], [18].…”

Section: Introductionmentioning

confidence: 99%

Multikernel Adaptive Filters Under the Minimum Cauchy Kernel Loss Criterion

2019

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The Cauchy loss has been successfully applied in robust learning algorithms in the presence of large outliers, but it may suffer from performance degradation in complex nonlinear tasks. To address this issue, by transforming the original data into the reproducing kernel Hilbert spaces (RKHS) with the kernel trick, a novel Cauchy kernel loss is developed in such a kernel space. Based on the minimum Cauchy kernel loss criterion, the multikernel minimum Cauchy kernel loss (MKMCKL) algorithm is proposed by mapping the input data into the multiple RKHS. The proposed MKMCKL algorithm can provide the performance improvement of the kernel adaptive filter (KAF) based on a single kernel, and also improve the stability of the multikernel adaptive filter based on the quadratic loss in impulsive noises, efficiently. To further curb the growth of network of MKMCKL, a novel sparsification method is presented to prune redundant data, thus reducing its computational and storage burdens. Simulations on different nonlinear applications illustrate the performance superiorities of the proposed algorithms in impulsive noises.

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Logarithmic Hyperbolic Cosine Adaptive Filter and Its Performance Analysis

Cited by 85 publications

References 36 publications

The Nyström Kernel Conjugate Gradient Algorithm Based on $k$ -Means Sampling

The Nyström Kernel Conjugate Gradient Algorithm Based on $k$ -Means Sampling

Accelerate Convergence of Polarized Random Fourier Feature-Based Kernel Adaptive Filtering With Variable Forgetting Factor and Step Size

Multikernel Adaptive Filters Under the Minimum Cauchy Kernel Loss Criterion

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