Online Gradient Descent for Kernel-Based Maximum Correntropy Criterion

Wang, Baobin; Hu, Ting

doi:10.3390/e21070644

Cited by 3 publications

(1 citation statement)

References 21 publications

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“…In view of the abnormal and invalid values of the equivalent diameters of floc particles during the coagulation process, maximum correntropy criterion (MCC) [17][18][19] will be introduced in this article, and an optimal method will be proposed to calculate the mean equivalent diameter of floc particles based on MCC.…”

Section: Complexitymentioning

confidence: 99%

Optimal Calculation Method of Mean Equivalent Diameter of Floc Particles Based on MCC

2022

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In the process of water treatment, coagulation is an important process to remove minerals and organic particles from raw water, which has typical time delay and nonlinearity. The effect of coagulation directly affects the turbidity of the effluent. According to the good correlation between the mean equivalent diameter of floc particles and the turbidity of effluent water, the image processing method is used to preprocess the floc image, the parameters of floc particles are quantitatively analyzed, and the mean equivalent diameter of floc particles is obtained, which is used as one of the bases for the control of coagulant dosage. However, no matter whether the coagulation process in actual situations interferes with the outside world or not, the equivalent diameters of floc particles after coagulation may have abnormal and invalid values, which may lead to a problem that there is a large difference between the mean equivalent diameter of floc particles calculated by a least square method and the mean valid equivalent diameter of floc particles. In response to this problem, this article proposes an optimal calculation method of the mean equivalent diameter of floc particles based on the maximum correntropy criterion (MCC) to reduce the negative impact of the abnormal and invalid equivalent diameters of floc particles on the mean equivalent diameter and provide an important reference data for the precise dosing control of coagulants. Finally, the feasibility of the theoretical results is verified by several numerical experiments.

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Section: Complexitymentioning

confidence: 99%

Optimal Calculation Method of Mean Equivalent Diameter of Floc Particles Based on MCC

2022

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Tikhonov regularization for Gaussian empirical gain maximization in RKHS is consistent

Feng,

2025

Applied and Computational Harmonic Analysis

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Stochastic Gradient Descent for Kernel-Based Maximum Correntropy Criterion

Li,

Wang,

Peng

et al. 2024

Entropy

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Maximum correntropy criterion (MCC) has been an important method in machine learning and signal processing communities since it was successfully applied in various non-Gaussian noise scenarios. In comparison with the classical least squares method (LS), which takes only the second-order moment of models into consideration and belongs to the convex optimization problem, MCC captures the high-order information of models that play crucial roles in robust learning, which is usually accompanied by solving the non-convexity optimization problems. As we know, the theoretical research on convex optimizations has made significant achievements, while theoretical understandings of non-convex optimization are still far from mature. Motivated by the popularity of the stochastic gradient descent (SGD) for solving nonconvex problems, this paper considers SGD applied to the kernel version of MCC, which has been shown to be robust to outliers and non-Gaussian data in nonlinear structure models. As the existing theoretical results for the SGD algorithm applied to the kernel MCC are not well established, we present the rigorous analysis for the convergence behaviors and provide explicit convergence rates under some standard conditions. Our work can fill the gap between optimization process and convergence during the iterations: the iterates need to converge to the global minimizer while the obtained estimator cannot ensure the global optimality in the learning process.

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Online Gradient Descent for Kernel-Based Maximum Correntropy Criterion

Cited by 3 publications

References 21 publications

Optimal Calculation Method of Mean Equivalent Diameter of Floc Particles Based on MCC

Optimal Calculation Method of Mean Equivalent Diameter of Floc Particles Based on MCC

Tikhonov regularization for Gaussian empirical gain maximization in RKHS is consistent

Stochastic Gradient Descent for Kernel-Based Maximum Correntropy Criterion

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