Kernel Least Mean Square Based on the Nyström Method

Wang, Shiyuan; Wang, Wenyue; Dang, Lujuan; Jiang, Yunxiang

doi:10.1007/s00034-018-1006-2

Cited by 18 publications

(9 citation statements)

References 30 publications

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“…As we know, a KAF cannot converge when the value of step-size is greater than η + , where η + is the upper bound of step-size and its default value is 1 here. Therefore, if εη 1 (k) > η + , the value of step-sizes in Equation (15) will not be updated, but the weight transfer operation is still executed by SHEN ET AL.…”

Section: Combined Weight Transfer Strategymentioning

confidence: 99%

“…Although the sparsification methods [4,13] can effectively alleviate the network growth problem, the network size cannot be fixed in advance and the computational complexity still increases over time. Unlike the sparsification methods, the Nyström method [14][15][16] uses a subset of samples to obtain a low rank matrix approximation to the kernel matrix in a fixed dimensional space. However, the selection of samples used for approximation is crucial to the accuracy of the Nyström method.…”

Section: Introductionmentioning

confidence: 99%

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Combined multiple random features least mean square algorithm for online applications

Shen

Feng

Huang

et al. 2022

IET Signal Processing

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The multikernel least mean square (MKLMS) algorithm is a classical algorithm of multikernel adaptive filters due to its simplicity. However, the linear growth network structure is a main challenge of MKLMS. To address this issue, a novel multiple random features least mean square (MRFLMS) algorithm is proposed by approximating multiple Gaussian kernels with the multiple random features method. In addition, a combined weight transfer strategy is adopted in MRFLMS to develop another combined multiple random features least mean square (CMRFLMS) algorithm to alleviate the influence of step‐size on filtering performance and convergence rate. CMRFLMS with a fixed dimensional network structure can provide comparable performance and faster convergence rate than MKLMS. Simulations on prediction of synthetic and real non‐linear system identification illustrate the superiorities of the proposed CMRFLMS algorithm from the aspects of filtering accuracy, convergence rate, and tracking performance.

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Section: Combined Weight Transfer Strategymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Combined multiple random features least mean square algorithm for online applications

Shen

Feng

Huang

et al. 2022

IET Signal Processing

Self Cite

View full text Add to dashboard Cite

show abstract

“…In a traditional method of system identification, the reason for applying gradient-based algorithms for estimating parameters in a model is because it minimizes the mean square error (MSE) for both model and system [3]. For instance, an iterative algorithm based on a gradient descent algorithm was employed to identify the Hammerstein model [4].…”

Section: Introductionmentioning

confidence: 99%

Metaheuristics algorithms to identify nonlinear Hammerstein model: a decade survey

2022

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Metaheuristics have been acknowledged as an effective solution for many difficult issues related to optimization. The metaheuristics, especially swarm’s intelligence and evolutionary computing algorithms, have gained popularity within a short time over the past two decades. Various metaheuristics algorithms are being introduced on an annual basis and applications that are more new are gradually being discovered. This paper presents a survey for the years 2011-2021 on multiple metaheuristics algorithms, particularly swarm and evolutionary algorithms, to identify a nonlinear block-oriented model called the Hammerstein model, mainly because such model has garnered much interest amidst researchers to identify nonlinear systems. Besides introducing a complete survey on the various population-based algorithms to identify the Hammerstein model, this paper also investigated some empirically verified actual process plants results. As such, this article serves as a guideline on the fundamentals of identifying nonlinear block-oriented models for new practitioners, apart from presenting a comprehensive summary of cutting-edge trends within the context of this topic area.

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“…Nevertheless, the batch form of these algorithms usually requires a large amount of memory and computational complexity [27]. Kernel adaptive filters (KAFs) for online kernel processing have been studied extensively [9][10][11][12]14,15,[17][18][19][20]26,31,[33][34][35]37,38], including the kernel least mean square (KLMS) [17], kernel affine projection (KAP) [18,26], kernel conjugate gradient (KCG) [38] and kernel recursive least squares (KRLS) [14].…”

Section: Introductionmentioning

confidence: 99%

The Generalized Complex Kernel Affine Projection Algorithms

Wang

Zhang

et al. 2021

Circuits Syst Signal Process

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The complex kernel adaptive filter (CKAF) has been widely applied to the complex-valued nonlinear problem in signal processing and machine learning. However, most of the CKAF applications involve the complex kernel least mean square (CKLMS) algorithms, which work in a pure complex or complexified reproducing kernel Hilbert space (RKHS). In this paper, we propose the generalized complex kernel affine projection (GCKAP) algorithms in the widely linear complex-valued RKHS (WL-RKHS). The proposed algorithms have two main notable features. One is that they provide a complete solution for both circular and non-circular complex nonlinear problems and show many performance improvements over the CKAP algorithms. The other is that the GCKAP algorithms inherit the simplicity of the CKLMS algorithm while reducing its gradient noise and boosting its convergence. The second-order statistical characteristics of WL-RKHS have also been developed. An augmented Gram matrix consists of a standard Gram matrix and a pseudo-Gram matrix. This decomposition provides more underlying information when the real and imaginary parts of the signal are correlated and learning is independent. In addition, some online sparsification criteria are compared comprehensively in the GCKAP algorithms, including the novelty criterion, the coherence criterion, and the angle criterion. Finally, two nonlinear channel equalization experiments with non-circular complex inputs are presented to illustrate the performance improvements of the proposed algorithms.

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Kernel Least Mean Square Based on the Nyström Method

Cited by 18 publications

References 30 publications

Combined multiple random features least mean square algorithm for online applications

Combined multiple random features least mean square algorithm for online applications

Metaheuristics algorithms to identify nonlinear Hammerstein model: a decade survey

The Generalized Complex Kernel Affine Projection Algorithms

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