scholarly journals Performance evaluation of the maximum complex correntropy criterion with adaptive kernel width update

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Manoel B. L. Aquino ◽  
João P. F. Guimarães ◽  
Leandro L. S. Linhares ◽  
Aluísio I. R. Fontes ◽  
Allan M. Martins
Keyword(s):  
Free Parameter ◽  
Impulsive Noise ◽  
Gaussian Kernel ◽  
Kernel Width ◽  
Optimal Value ◽  
Gradient Solution ◽  
Adaptive Kernel ◽  
Gradient Based ◽  
Complex Valued ◽  
Steady State Performance

Abstract The complex correntropy is a recently defined similarity measure that extends the advantages of conventional correntropy to complex-valued data. As in the real-valued case, the maximum complex correntropy criterion (MCCC) employs a free parameter called kernel width, which affects the convergence rate, robustness, and steady-state performance of the method. However, determining the optimal value for such parameter is not always a trivial task. Within this context, several works have introduced adaptive kernel width algorithms to deal with this free parameter, but such solutions must be updated to manipulate complex-valued data. This work reviews and updates the most recent adaptive kernel width algorithms so that they become capable of dealing with complex-valued data using the complex correntropy. Besides that, a novel gradient-based solution is introduced to the Gaussian kernel and its respective convergence analysis. Simulations compare the performance of adaptive kernel width algorithms with different fixed kernel sizes in an impulsive noise environment. The results show that the iterative kernel adjustment improves the performance of the gradient solution for complex-valued data.

scholarly journals An adaptive kernel width convex combination method for maximum correntropy criterion

2021 ◽  
Vol 27 (1) ◽  
Author(s):  
Aluisio I. R. Fontes ◽  
Leandro L. S. Linhares ◽  
João P. F. Guimarães ◽  
Luiz F. Q. Silveira ◽  
Allan M. Martins
Keyword(s):  
Adaptive Filtering ◽  
Convergence Rates ◽  
Impulsive Noise ◽  
Convex Combination ◽  
Combination Method ◽  
Kernel Width ◽  
Optimal Value ◽  
Adaptive Kernel ◽  
Novel Method ◽  
Maximum Correntropy Criterion

AbstractRecently, the maximum correntropy criterion (MCC) has been successfully applied in numerous applications regarding nonGaussian data processing. MCC employs a free parameter called kernel width, which affects the convergence rate, robustness, and steady-state performance of the adaptive filtering. However, determining the optimal value for such parameter is not always a trivial task. Within this context, this paper proposes a novel method called adaptive convex combination maximum correntropy criterion (ACCMCC), which combines an adaptive kernel algorithm with convex combination techniques. ACCMCC takes advantage from a convex combination of two adaptive MCC-based filters, whose kernel widths are adjusted iteratively as a function of the minimum error value obtained in a predefined estimation window. Results obtained in impulsive noise environment have shown that the proposed approach achieves equivalent convergence rates but with increased accuracy and robustness when compared with other similar algorithms reported in literature.

scholarly journals Estimation of neuronal firing rate using Bayesian Adaptive Kernel Smoother (BAKS)

2017 ◽  
Author(s):  
Nur Ahmadi ◽  
Timothy G. Constandinou ◽  
Christos-Savvas Bouganis
Keyword(s):  
Firing Rate ◽  
Spike Train ◽  
Prior Distribution ◽  
Kernel Smoothing ◽  
Neuronal Firing ◽  
Gaussian Kernel ◽  
Single Trial ◽  
Adaptive Kernel ◽  
Neuronal Firing Rate ◽  
Spike Train Data

AbstractNeurons use sequences of action potentials (spikes) to convey information across neuronal networks. In neurophysiology experiments, information about external stimuli or behavioral tasks has been frequently characterized in term of neuronal firing rate. The firing rate is conventionally estimated by averaging spiking responses across multiple similar experiments (or trials). However, there exist a number of applications in neuroscience research that require firing rate to be estimated on a single trial basis. Estimating firing rate from a single trial is a challenging problem and current state-of-the-art methods do not perform well. To address this issue, we develop a new method for estimating firing rate based on kernel smoothing technique that considers the bandwidth as a random variable with prior distribution that is adaptively updated under a Bayesian framework. By carefully selecting the prior distribution together with Gaussian kernel function, an analytical expression can be achieved for the kernel bandwidth. We refer to the proposed method as Bayesian Adaptive Kernel Smoother (BAKS). We evaluate the performance of BAKS using synthetic spike train data generated by biologically plausible models: inhomogeneous Gamma (IG) and inhomogeneous inverse Gaussian (IIG). We also apply BAKS to real spike train data from non-human primate (NHP) motor and visual cortex. We benchmark the proposed method against the established and previously reported methods. These include: optimized kernel smoother (OKS), variable kernel smoother (VKS), local polynomial fit (Locfit), and Bayesian adaptive regression splines (BARS). Results using both synthetic and real data demonstrate that the proposed method achieves better performance compared to competing methods. This suggests that the proposed method could be useful for understanding the encoding mechanism of neurons in cognitive-related tasks. The proposed method could also potentially improve the performance of brain-machine interface (BMI) decoder that relies on estimated firing rate as the input.

scholarly journals Multi-Objective Grasshopper Optimization Based MPPT and VSC Control of Grid-Tied PV-Battery System

Electronics ◽  
2021 ◽  
Vol 10 (22) ◽  
pp. 2770
Author(s):  
Mukul Chankaya ◽  
Ikhlaq Hussain ◽  
Aijaz Ahmad ◽  
Hasmat Malik ◽  
Fausto Pedro García Márquez
Keyword(s):  
Maximum Power ◽  
Solar Irradiation ◽  
Gaussian Kernel ◽  
Mean Square ◽  
Maximum Power Point ◽  
Dynamic Conditions ◽  
Multi Objective ◽  
Kernel Width ◽  
Dc Bus ◽  
Power Point

This article presents the control of a three-phase three-wire (3P-3W) dual-stage grid-tied PV-battery storage system using a multi-objective grass-hopper optimization (MOGHO) algorithm. The voltage source converter (VSC) control of the presented system is implemented with adaptive kernel width sixth-order maximum correntropy criteria (AKWSOMCC) and maximum power point tracking (MPPT) control is accomplished using the variable step-size incremental conductance (VSS-InC) technique. The proposed VSC control offers lower mean square error and better accuracy, convergence rate and speed as compared to peer adaptive algorithms, i.e., least mean square (LMS), least mean fourth (LMF), maximum correntropy criteria (MCC), etc. The adaptive Gaussian kernel width is a function of the error signal, which changes to accommodate and filter Gaussian and non-Gaussian noise signals in each iteration. The VSS-InC based MPPT is provided with a MOGHO based modulation factor for better and faster tracking of the maximum power point during changing solar irradiation. Similarly, an optimized gain conventional PI controller regulates the DC bus to improve the power quality, and DC link stability during dynamic conditions. The optimized DC-link generates an accurate loss component of current, which further improves the VSC capability of fundamental load current component extraction. The VSC is designed to perform multi-functional operations, i.e., harmonics elimination, reactive power compensation, load balancing and power balancing at point of common coupling during diverse dynamic conditions. The MOSHO based VSS-InC, and DC bus performance is compared to particle swarm optimization (PSO) and genetic algorithm (GA). The proposed system operates satisfactorily as per IEEE519 standards in the MATLAB simulation environment.

scholarly journals Recursive Minimum Complex Kernel Risk-Sensitive Loss Algorithm

Entropy ◽  
2018 ◽  
Vol 20 (12) ◽  
pp. 902 ◽  
Author(s):  
Guobing Qian ◽  
Dan Luo ◽  
Shiyuan Wang
Keyword(s):  
Impulsive Noise ◽  
Recursive Least Squares ◽  
Complex Domain ◽  
Superior Performance ◽  
Mean Square ◽  
Kernel Space ◽  
Risk Sensitive ◽  
Simulation Results ◽  
Performance Surface ◽  
Complex Valued

The maximum complex correntropy criterion (MCCC) has been extended to complex domain for dealing with complex-valued data in the presence of impulsive noise. Compared with the correntropy based loss, a kernel risk-sensitive loss (KRSL) defined in kernel space has demonstrated a superior performance surface in the complex domain. However, there is no report regarding the recursive KRSL algorithm in the complex domain. Therefore, in this paper we propose a recursive complex KRSL algorithm called the recursive minimum complex kernel risk-sensitive loss (RMCKRSL). In addition, we analyze its stability and obtain the theoretical value of the excess mean square error (EMSE), which are both supported by simulations. Simulation results verify that the proposed RMCKRSL out-performs the MCCC, generalized MCCC (GMCCC), and traditional recursive least squares (RLS).

Gaussian kernel adaptive filters with adaptive kernel bandwidth

2020 ◽  
Vol 166 ◽  
pp. 107270 ◽  
Author(s):  
Ji Zhao ◽  
Hongbin Zhang ◽  
J. Andrew Zhang
Keyword(s):  
Adaptive Filters ◽  
Gaussian Kernel ◽  
Adaptive Kernel

Recurrent Neural Adaptive Control of Nonlinear Oscillatory Systems Using a Complex-valued Levenberg-Marquardt Learning Algorithm

2015 ◽  
Vol 13 (1-2) ◽  
pp. 10-24
Author(s):  
Ieroham Baruch ◽  
Edmundo P. Reynaud
Keyword(s):  
Adaptive Control ◽  
Learning Algorithm ◽  
Back Propagation ◽  
Neural Adaptive Control ◽  
Oscillatory Systems ◽  
Control Schemes ◽  
Levenberg Marquardt ◽  
Gradient Based ◽  
Adaptive Neural Controller ◽  
Complex Valued

Abstract In this work, a Recursive Levenberg-Marquardt learning algorithm in the complex domain is developed and applied in the training of two adaptive control schemes composed by Complex-Valued Recurrent Neural Networks. Furthermore, we apply the identification and both control schemes for a particular case of nonlinear, oscillatory mechanical plant to validate the performance of the adaptive neural controller and the learning algorithm. The comparative simulation results show the better performance of the newly proposed Complex-Valued Recursive Levenberg-Marquardt learning algorithm over the gradient-based recursive Back-propagation one.

Kernel online learning with adaptive kernel width

2016 ◽  
Vol 175 ◽  
pp. 233-242 ◽  
Author(s):  
Haijin Fan ◽  
Qing Song ◽  
Sumit B. Shrestha
Keyword(s):  
Online Learning ◽  
Kernel Width ◽  
Adaptive Kernel
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