Set-membership adaptive kernel NLMS algorithms: Design and analysis

Flores, André R.; Lamare, Rodrigo C. de

doi:10.1016/j.sigpro.2018.07.007

Cited by 13 publications

(14 citation statements)

References 35 publications

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“…As for the recursive formulas of w i in K-SM-NLMS, it can be derived from the following constrained optimization problem [30], [34] when dictionary dimension at iteration i does not increase:…”

Section: Further Interpretations Of K-beacon and K-sm-nlmsmentioning

confidence: 99%

“…To date, however, most of the SMF algorithms have been developed using linear models, see, e.g., [24], [25], [27]- [32]. Kernel set-membership NLMS algorithms have been proposed in [33], [34]. One of the challenges of those algorithms is to control kernel expansion, i.e., the increase of dictionary dimension.…”

Section: Introductionmentioning

confidence: 99%

“…In [33], the approximate linear dependence (ALD) criterion was used for dictionary sparsification, which has a quadratic time complexity. In [34], no explicit sparsification rule was embedded except for the innovation check, which would likely yield excessively large dictionary. More detailed discussions on dictionary sparsification are given in Section II, as well as in Section V with simulation comparison.…”

Section: Introductionmentioning

confidence: 99%

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Nonlinear Adaptive Filtering With Kernel Set-Membership Approach

Chen

Werner

Kuh

et al. 2020

IEEE Trans. Signal Process.

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This paper develops nonlinear kernel adaptive filtering algorithms based on the set-membership filtering (SMF) framework. The set-membership-based filtering approach is distinct from the conventional adaptive filtering approaches in that it aims for the filtering error being bounded in magnitude, as opposed to seeking to minimize the time average or ensemble average of the squared errors. The proposed kernel SMF algorithms feature selective updates of their parameter estimates by making discerning use of the input data, and selective increase of the dimension in the kernel expansion. These result in less computational cost and faster tracking without compromising the mean-squared error performance. We show, through convergence analysis, that the sequences of parameter estimates of our proposed algorithms are convergent, and the filtering error is asymptotically upper bounded in magnitude. Simulations are performed which show clearly the advantages of the proposed algorithms in terms of lower computational complexity, reduced dictionary size, and steady-state meansquared errors comparable to existing algorithms.

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Section: Further Interpretations Of K-beacon and K-sm-nlmsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Nonlinear Adaptive Filtering With Kernel Set-Membership Approach

Chen

Werner

Kuh

et al. 2020

IEEE Trans. Signal Process.

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“…Esses métodos têm sido amplamente utilizados em conjunto com diferentes técnicas de processamento de sinais, como máquinas de vetores de suporte (support vector machines -SVM), análise de componentes principais (principal componente analysis -PCA), filtragem adaptativa, entre outras [1], [2]. Apesar dessas técnicas terem objetivos diferentes, todas elas mapeiam um vetor coluna u ∈ U ⊂ R M , sendo M a dimensão do espaço de entrada, em um espaço de alta dimensão H como ϕ(u), usando um kernel de Mercer [1]- [6].…”

Section: Introductionunclassified

“…O critério da novidade proporciona uma redução do custo computacional de métodos baseados em kernel. Mesmo assim, a utilização desses métodos em problemas que exigem soluções em tempo real, ainda está longe da realidade [5], [6]. O estudo de técnicas de esparsificação que proporcionem uma redução ainda maior no custo computacional sem causar uma degradação exagerada no desempenho desses métodosé algo de interesse.…”

Section: Introductionunclassified

Esparsificação de dicionário para métodos kernel baseada na ortogonalização de Gram-Schmidt

Bueno¹,

Silva²

2019

Anais De XXXVII Simpósio Brasileiro De Telecomunicações E Processamento De Sinais

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Resumo-Neste artigo, propõe-se uma técnica de esparsificação de dicionário para métodos baseados em núcleo (kernel). Ela se baseia no processo de ortogonalização de Gram-Schmidt, permitindo que os vetores do espaço de dimensão infinita induzido pelo kernel gaussiano sejam representados por vetores de dimensão finita. A técnica propostaé aplicada a um algoritmo do tipo LMS (least-mean-square). O algoritmo resultante apresenta vantagens em termos de custo computacional quando comparado com o algoritmo kernel LMS que utiliza o critério da novidade como técnica de esparsificação. Palavras-Chave-métodos baseados em kernel, filtragem adaptativa, processamento não linear de sinais Abstract-In this paper, we propose a technique for dictionary sparsification in kernel methods. It is based on the Gram-Schmidt orthogonalization process, which allows finite-dimensional vectors to represent vectors contained in the infinite-dimensional space induced by the Gaussian kernel. The proposed technique is applied to an LMS (least-mean-square)-type algorithm. The resulting algorithm presents a lower computational cost when compared to the kernel LMS implemented with the novelty criterion.

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