General Cauchy Conjugate Gradient Algorithms Based on Multiple Random Fourier Features

Zhang, Haonan; Yang, Bo; Wang, Lin; Wang, Shiyuan

doi:10.1109/tsp.2021.3065173

Cited by 18 publications

(6 citation statements)

References 48 publications

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“…en, ( 29) can be further determined by (36), as shown at the top of next page. By (36), thus the sufficient convergence condition on mean stability is given by…”

Section: Convergence Condition On Mean Stability Of the Kllad Algorithmmentioning

confidence: 99%

“…More recently, the logarithmic hyperbolic cosine-based adaptive filter (LHCAF) was proposed in [35] to address the issue of instability of its prototype algorithm, and the transient and steady-state analyses were also provided. Subsequently, the authors of [36] proposed the multiple random Fourier features Cauchy-loss conjugate gradient (MRFGCG) algorithm which has better performance than the classical KAF algorithms in terms of computational complexity and filtering accuracy. erefore, the cost functions adopting the frameworks of fractional order statistics of error or the distinct types of error measures are able to provide effective ways to reveal the robust performance against impulsive noises.…”

Section: Introductionmentioning

confidence: 99%

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Kernel Least Logarithmic Absolute Difference Algorithm

Wei

Shi

et al. 2022

Mathematical Problems in Engineering

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Kernel adaptive filtering (KAF) algorithms derived from the second moment of error criterion perform very well in nonlinear system identification under assumption of the Gaussian observation noise; however, they inevitably suffer from severe performance degradation in the presence of non-Gaussian impulsive noise and interference. To resolve this dilemma, we propose a novel robust kernel least logarithmic absolute difference (KLLAD) algorithm based on logarithmic error cost function in reproducing kernel Hilbert spaces, taking into account of the non-Gaussian impulsive noise. The KLLAD algorithm shows considerable improvement over the existing KAF algorithms without restraining impulsive interference in terms of robustness and convergence speed. Moreover, the convergence condition of KLLAD algorithm with Gaussian kernel and fixed dictionary is presented in the mean sense. The superior performance of KLLAD algorithm is confirmed by the simulation results.

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“…en, ( 29) can be further determined by (36), as shown at the top of next page. By (36), thus the sufficient convergence condition on mean stability is given by…”

Section: Convergence Condition On Mean Stability Of the Kllad Algorithmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Kernel Least Logarithmic Absolute Difference Algorithm

Wei

Shi

et al. 2022

Mathematical Problems in Engineering

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“…More importantly, due to its simplicity, the VRFF method can be readily applied to other RFF-based algorithms. Secondly, the adaptation steps (22) and (23) no longer guaranty that the {ω m,n } are driven by any Gaussian distribution N (0 D , ξ −2 I D ) as the algorithm progresses. This does not allow us to establish a correspondence between the {ω m,n } and the bandwidth ξ n of a Gaussian kernel.…”

Section: Adaptive Random Fourier Features Gklmsmentioning

confidence: 99%

“…The RFF principle was used with the kernel conjugate gradient algorithm [21]. The Cauchy-loss conjugate gradient method based on multiple RFF was proposed in [22] to improve robustness and reduce computational cost in the presence of non-Gaussian noises. Recently, several RFF kernel regression algorithms over graphs were proposed in [23], and their conditions for convergence in the mean and mean-square sense were also studied.…”

Section: Introductionmentioning

confidence: 99%

Random Fourier Features Multi-Kernel LMS Algorithm

Wei

Song

Chen

et al. 2020

2020 IEEE International Conference on Signal Processing, Communications and Computing (ICSPCC)

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We propose the adaptive random Fourier features Gaussian kernel LMS (ARFF-GKLMS). Like most kernel adaptive filters based on stochastic gradient descent, this algorithm uses a preset number of random Fourier features to save computation cost. However, as an extra flexibility, it can adapt the inherent kernel bandwidth in the random Fourier features in an online manner. This adaptation mechanism allows to alleviate the problem of selecting the kernel bandwidth beforehand for the benefit of an improved tracking in non-stationary circumstances. Simulation results confirm that the proposed algorithm achieves a performance improvement in terms of convergence rate, error at steady-state and tracking ability over other kernel adaptive filters with preset kernel bandwidth.

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“…Compared with the Nyström method, random Fourier features mapping is more appealing for non-stationary environments in online applications [21]. Therefore, the random Fourier features mapping is applied into MKAFs to generate the multiple random features (MRF) method [22,23].…”

Section: Introductionmentioning

confidence: 99%

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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General Cauchy Conjugate Gradient Algorithms Based on Multiple Random Fourier Features

Cited by 18 publications

References 48 publications

Kernel Least Logarithmic Absolute Difference Algorithm

Kernel Least Logarithmic Absolute Difference Algorithm

Random Fourier Features Multi-Kernel LMS Algorithm

Combined multiple random features least mean square algorithm for online applications

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