Generalized Maximum Correntropy Criterion Research Articles

Generalized kernel maximum correntropy criterion with variable center: Formulation and performance analysis

Recently, the kernel adaptive filtering algorithm with the generalized maximum correntropy criterion (GMCC) has gained attention due to its excellent nonlinear system modeling ability and robustness to non-Gaussian noise. However, since the default center of the GMCC is located at zero, it hampers its performance in the non-zero mean noise environment. To overcome the problem, this paper proposes a kernel adaptive filtering algorithm based on the GMCC with variable center (GMCC-VC) called generalized kernel maximum correntropy criterion with variable center (GKMCC-VC). In addition, the online vector quantization (VQ) method is introduced to the GKMCC-VC algorithm for suppressing the increasing network size. The probability of divergence, the mean-square steady-state behavior, and the convergence condition of the GKMCC-VC algorithm are also obtained under some assumptions. The potential relationship between the GMCC-VC and the generalized minimum error entropy (GMEE) criteria is discussed in the paper. Finally, the simulation results verify the superiority of the proposed algorithm in modeling nonlinear systems and the correctness of the theoretical model.

Jointly Distributed Filtering Based on Generalized Maximum Correntropy Criterion: Memory-Based Event-Triggered Cases

This article addresses jointly distributed entropy filtering issues based on the generalized maximum correntropy criterion (GMCC) for discrete-time stochastic parameter systems with fault and non-Gaussian noise effects. By taking current and historical triggered information, a memory-based event-triggered scheme with a time-varying threshold is put forward to govern the network communication. According to the constructed jointly distributed entropy filter with a two-step form, the upper bounds of the filtering error covariance matrices are derived and an ideal filter gain is obtained to maximize GMCC. Furthermore, an accessible gain is received via fixed-point iterative rules and the corresponding convergence is disclosed in theory. Finally, an application of the proposed distributed filter in ballistic object tracking is provided to show its effectiveness under non-Gaussian environments.

Robust multi-task distributed estimation based on generalized maximum correntropy criterion

False data injection (FDI) attacks are common in the distributed estimation of multi-task network environments, so an attack detection strategy is designed by combining the generalized maximum correntropy criterion. Based on this, we propose a diffusion least-mean-square algorithm based on the generalized maximum correntropy criterion (GMCC-DLMS) for multi-task networks. The algorithm achieves gratifying estimation results. Even more, compared to the related work, it has better robustness when the number of attacked nodes increases. Moreover, the assumption about the number of attacked nodes is relaxed, which is applicable to multi-task environments. In addition, the performance of the proposed GMCC-DLMS algorithm is analyzed in the mean and mean-square senses. Finally, simulation experiments confirm the performance and effectiveness against FDI attacks of the algorithm.

A Variable Parameter LMS Algorithm Based on Generalized Maximum Correntropy Criterion for Graph Signal Processing

The least mean square (LMS) algorithm of the graph signal processing (GSP) based on the mean square error criterion has a poor reconstruction effect when the graph sampling signal is disturbed by impulse noise. To solve this problem, the generalized maximum correntropy criterion (GMCC) is introduced, which is robust to impulse noise in adaptive filtering. Therefore, this paper proposes the GSP LMS algorithm based on the GMCC (GSP LMSGMCC) by using the graph Fourier transform, which has a good effect when the graph sampling signal is disturbed by impulse noise. In addition, the GSP LMSGMCC algorithm based on the fixed parameter including step size and kernel width must make a compromise between convergence speed and steady-state error. To prevent this, the fixed parameters of the proposed GSP LMSGMCC algorithm are optimized, respectively. To facilitate understanding and analysis, the steady-state performance of the proposed GSP LMSGMCC algorithm is studied. Finally, the computer simulations are carried out to verify the superiority of the proposed algorithm when the signals on the graph are static graph signals and streaming graph signals respectively.

Generalized Modified Blake–Zisserman Robust Sparse Adaptive Filters

In the past years, the generalized maximum correntropy criterion (GMCC) has been widely used in adaptive filters to provide robust behavior under non-Gaussian/impulsive noise environments. However, GMCC-based adaptive filters are affected by high steady-state misalignment. In order to enhance the robustness under non-Gaussian noise environments and reduce steady-state misalignment, a generalized modified Blake–Zisserman (GMBZ) robust loss function is introduced in this correspondence. Furthermore, a GMBZ adaptive filter (GMBZ-AF) has been developed that provides improved convergence performance over other existing algorithms. The proposed learning scheme has a computational complexity very similar to that of the GMCC-based adaptive filtering method. In order to further exploit the sparse nature of the system for identifying sparse systems and simultaneously provide robust convergence, two new robust sparse adaptive filters: 1) zero attracting GMBZ-AF (ZA-GMBZ-AF) and 2) reweighted ZA-GMBZ-AF (RZA-GMBZ-AF) have also been proposed. To further enhance the filter convergence performance, a new robust and sparsity-aware loss function called generalized modified dual Blake–Zisserman (GMDBZ) is also introduced in this correspondence and the corresponding GMDBZ adaptive filter (GMDBZ-AF) has been developed.

Newton Recursion Based Random Data-Reusing Generalized Maximum Correntropy Criterion Adaptive Filtering Algorithm.

For system identification under impulsive-noise environments, the gradient-based generalized maximum correntropy criterion (GB-GMCC) algorithm can achieve a desirable filtering performance. However, the gradient method only uses the information of the first-order derivative, and the corresponding stagnation point of the method can be a maximum point, a minimum point or a saddle point, and thus the gradient method may not always be a good selection. Furthermore, GB-GMCC merely uses the current input signal to update the weight vector; facing the highly correlated input signal, the convergence rate of GB-GMCC will be dramatically damaged. To overcome these problems, based on the Newton recursion method and the data-reusing method, this paper proposes a robust adaptive filtering algorithm, which is called the Newton recursion-based data-reusing GMCC (NR-DR-GMCC). On the one hand, based on the Newton recursion method, NR-DR-GMCC can use the information of the second-order derivative to update the weight vector. On the other hand, by using the data-reusing method, our proposal uses the information of the latest M input vectors to improve the convergence performance of GB-GMCC. In addition, to further enhance the filtering performance of NR-DR-GMCC, a random strategy can be used to extract more information from the past M input vectors, and thus we obtain an enhanced NR-DR-GMCC algorithm, which is called the Newton recursion-based random data-reusing GMCC (NR-RDR-GMCC) algorithm. Compared with existing algorithms, simulation results under system identification and acoustic echo cancellation are conducted and validate that NR-RDR-GMCC can provide a better filtering performance in terms of filtering accuracy and convergence rate.

Robust state of charge estimation for Li-ion batteries based on cubature kalman filter with generalized maximum correntropy criterion

Kalman filters (KFs) are widely used for state-of-charge (SOC) estimation of Li-ion batteries due to their excellent dynamic tracking capability. Especially the cubature KF (CKF), with the computational efficiency and nonlinear processing ability, is an outstanding candidate for SOC estimation. However, the actual working conditions are complex and changeable, and the measurement data is usually accompanied by non-Gaussian noise (outliers). Therefore, the performance of the original CKF with minimum mean square error (MMSE) criterion may be degraded seriously in these cases. In order to enhance the robustness of CKF, the MMSE in the CKF framework is substituted by the generalized maximum correntropy criterion (GMCC), and thus a robust CKF with GMCC (GMCC-CKF) is developed by fixed point iteration approach in this work. Furthermore, a SOC estimation model via the GMCC-CKF is proposed to improve estimation accuracy under non-Gaussian noise environments. The simulation results show that, compared with the traditional KFs, the proposed GMCC-CKF can accurately estimate the SOC of lithium batteries under different temperatures and operating conditions considering non-Gaussian noise interference. The results of mean absolute error (MAE) and root mean square error (RMSE) are less than 1%, which verifies the excellent performance of GMCC-CKF.

A novel electricity consumption forecasting model based on kernel extreme learning machine-with generalized maximum correntropy criterion

Electricity consumption forecasting (ECF) plays a crucial role in the new open electricity market nowadays, and in order to pass the ECF test, the ECF error is required to be less than 5%. However, for historical electricity consumption (EC) data and the error distribution of ECF is usually nonlinear and non-Gaussian distributed, and some random events and data collection errors have a great impact on the forecasting accuracy. Therefore, the traditional forecasting methods designed based on mean squared error (MSE) have the problem of unstable forecasting results and difficult to improve the accuracy. To solve this problem, this paper first uses the Generalized Maximum Correntropy Criterion to optimize the Kernel Extreme Learning Machine, and proposes a new forecasting model of KELM-GMCC. Finally, the historical EC and corresponding temperature data of a commercial customer in China in 2018 and 2019 are used to test and guide the electricity prediction in 2020 and 2021. The model proposed in this paper has a mean absolute percentage error of 1.46% in forecasting daily EC using annual data. The results show that the proposed model is robust and has high forecasting accuracy compared with existing models such as Back Propagation (BP), Support Vector Regression (SVR), and Extreme Learning Machine (ELM).

Noise-Immune Extreme Ensemble Learning for Early Diagnosis of Neuropsychiatric Systemic Lupus Erythematosus.

Early diagnosis is currently the most effective way of saving the life of patients with neuropsychiatric systemic lupus erythematosus (NPSLE). However, it is rather difficult to detect this terrible disease at the early stage, due to the subtle and elusive symptomatic signals. Recent studies show that the 1H-MRS (proton magnetic resonance spectroscopy) imaging technique can capture more information reflecting the early appearance of this disease than conventional magnetic resonance imaging techniques. 1H-MRS data, however, also presents more noises that can bring serious diagnosis bias. We hence proposed a noise-immune extreme ensemble learning technique for effectively leveraging 1H-MRS data for advancing the early diagnosis of NPSLE. Our main results are that 1) by developing generalized maximum correntropy criterion in the kernel extreme learning setting, many types of non-Gaussian noises can be distinguished, and 2) weighted recursive feature elimination, using maximal information coefficient to weight feature's importance, helps to further alleviate the bad impact of noises on the diagnosis performance. The proposed method is assessed on a publicly available dataset with 97.5% accuracy, 95.8% sensitivity and 99.9% specificity, which well demonstrates its efficacy.

Generalized Maximum Correntropy Kalman Filter for Target Tracking in TianGong-2 Space Laboratory

Target tracking plays an important role in the construction, operation, and maintenance of the space station by the robot, which puts forward high requirements on the accuracy of target tracking. However, the special space environment may cause complex non-Gaussian noise in target tracking data. And the performance of traditional Kalman Filter will deteriorate seriously when the error signals are non-Gaussian, which may lead to mission failure. In the paper, a novel Kalman Filter algorithm with Generalized Maximum Correntropy Criterion (GMCKF) is proposed to improve the tracking accuracy with non-Gaussian noise. The GMCKF algorithm, which replaces the default Gaussian kernel with the generalized Gaussian density function as kernel, can adapt to multi-type non-Gaussian noises and evaluate the noise accurately. A parameter automatic selection algorithm is proposed to determine the shape parameter of GMCKF algorithm, which helps the GMCKF algorithm achieve better performance for complex non-Gaussian noise. The performance of the proposed algorithm has been evaluated by simulations and the ground experiments. Then, the algorithm has been applied in the maintenance experiments in TianGong-2 space laboratory of China. The results validated the feasibility of the proposed method with the target tracking precision improved significantly in complex non-Gaussian environment.

Diffusion Generalized MCC with a Variable Center Algorithm for Robust Distributed Estimation

Classical adaptive filtering algorithms with a diffusion strategy under the mean square error (MSE) criterion can face difficulties in distributed estimation (DE) over networks in a complex noise environment, such as non-zero mean non-Gaussian noise, with the object of ensuring a robust performance. In order to overcome such limitations, this paper proposes a novel robust diffusion adaptive filtering algorithm, which is developed by using a variable center generalized maximum Correntropy criterion (GMCC-VC). Generalized Correntropy with a variable center is first defined by introducing a non-zero center to the original generalized Correntropy, which can be used as robust cost function, called GMCC-VC, for adaptive filtering algorithms. In order to improve the robustness of the traditional MSE-based DE algorithms, the GMCC-VC is used in a diffusion adaptive filter to design a novel robust DE method with the adapt-then-combine strategy. This can achieve outstanding steady-state performance under non-Gaussian noise environments because the GMCC-VC can match the distribution of the noise with that of non-zero mean non-Gaussian noise. The simulation results for distributed estimation under non-zero mean non-Gaussian noise cases demonstrate that the proposed diffusion GMCC-VC approach produces a more robustness and stable performance than some other comparable DE methods.

Noise immune state of charge estimation of li-ion battery via the extreme learning machine with mixture generalized maximum correntropy criterion

The state of charge (SOC) plays a crucial role in battery management system, which directly reflects the usage of the battery. Recently the extreme learning machine (ELM) model as a data-driven method has been utilized to estimate SOC due to its simple single hidden layer structure and fast learning performance. The battery management system, however, may usually work in complex working conditions, which means that the non-Gaussian complex noise (or outliers) interference problem may exist in some measurement data for model training. So the performance of the classical ELM with mean square error (MSE) criterion may be degraded under this case. This work considers Non-Gaussian noise interference issue, the MSE in ELM is substituted by mixture generalized maximum correntropy criterion (MGMCC), and a novel robust ELM model is developed to improve the SOC estimation capability which mainly relies on the stable and robust nonlinear similarity characteristics of the MGMCC. A data set from a Panasonic 18,650 battery cell is used to verify the robustness of the proposed model, the experiment results demonstrate that it can achieve better estimation performance in terms of different evaluation metrics compared with the traditional methods.

Mean square cross error: performance analysis and applications in non-Gaussian signal processing

Most of the cost functions of adaptive filtering algorithms include the square error, which depends on the current error signal. When the additive noise is impulsive, we can expect that the square error will be very large. By contrast, the cross error, which is the correlation of the error signal and its delay, may be very small. Based on this fact, we propose a new cost function called the mean square cross error for adaptive filters, and provide the mean value and mean square performance analysis in detail. Furthermore, we present a two-stage method to estimate the closed-form solutions for the proposed method, and generalize the two-stage method to estimate the closed-form solution of the information theoretic learning methods, including least mean fourth, maximum correntropy criterion, generalized maximum correntropy criterion, and minimum kernel risk-sensitive loss. The simulations of the adaptive solutions and closed-form solution show the effectivity of the new method.

Exponential Hyperbolic Cosine Robust Adaptive Filters for Audio Signal Processing

In recent years, correntropy-based algorithms which include maximum correntropy criterion (MCC), generalized MCC (GMCC), kernel MCC (KMCC) and hyperbolic cosine function-based algorithms such as hyperbolic cosine adaptive filter (HCAF), logarithmic HCAF (LHCAF), least lncosh (Llncosh) have been widely utilized in adaptive filtering due to their robustness towards non-Gaussian/impulsive background noises. However, the performance of such algorithms suffers from high steady-state misalignment. To minimize the steady-state misalignment along with having comparable computational complexity, an exponential hyperbolic cosine function (EHCF) based new robust norm is introduced and a corresponding EHCF based adaptive filter called exponential hyperbolic cosine adaptive filter (EHCAF) is developed in this letter. Further, computational complexity and bound on learning rate for stability of the proposed algorithm is also studied. A set of simulation studies has been carried out for system identification scenario to assess the performance of the proposed algorithm. Further, EHCAF algorithm has been extended and the filtered-x EHCAF (Fx-EHCAF) algorithm is proposed for robust room equalization.

Sparsity Constrained Recursive Generalized Maximum Correntropy Criterion With Variable Center Algorithm

This brief developed a novel sparsity constrained recursive adaptive filtering algorithm via the generalized correntropy criterion with variable center (GMCC-VC) for sparse system parameters estimation. In order to improve the performance of the adaptive filtering algorithm with GMCC under the non-Gaussian and non-zero mean noise environments, the GMCC is extended by adding a center which can be located at any position in the generalized Gaussian kernel function. Specifically, we proposed a novel adaptive online update method to optimize the kernel method and center. In addition, we mainly derived a recursive GMCC-VC algorithm based on the GMCC with the sparse constraint to exploit sparsity. Numerical simulation results are given to show that the proposed algorithm is efficient for sparse system parameter estimation problems in non-Gaussian and non-mean noise environments.

Newtonian-Type Adaptive Filtering Based on the Maximum Correntropy Criterion.

This paper provides a novel Newtonian-type optimization method for robust adaptive filtering inspired by information theory learning. With the traditional minimum mean square error (MMSE) criterion replaced by criteria like the maximum correntropy criterion (MCC) or generalized maximum correntropy criterion (GMCC), adaptive filters assign less emphasis on the outlier data, thus become more robust against impulsive noises. The optimization methods adopted in current MCC-based LMS-type and RLS-type adaptive filters are gradient descent method and fixed point iteration, respectively. However, in this paper, a Newtonian-type method is introduced as a novel method for enhancing the existing body of knowledge of MCC-based adaptive filtering and providing a fast convergence rate. Theoretical analysis of the steady-state performance of the algorithm is carried out and verified by simulations. The experimental results show that, compared to the conventional MCC adaptive filter, the MCC-based Newtonian-type method converges faster and still maintains a good steady-state performance under impulsive noise. The practicability of the algorithm is also verified in the experiment of acoustic echo cancellation.

Quantized generalized maximum correntropy criterion based kernel recursive least squares for online time series prediction

With the rapid development of information theoretic learning, the maximum correntropy criterion (MCC) has been widely used in time series prediction area. Especially, the kernel recursive least squares (KRLS) based on MCC is studied recently due to its online recursive form and the ability to resist noise and be robust in non-Gaussian environments. However, it is not always an optimal choice that using the correntropy, which is calculated by default Gaussian kernel function, to describe the local similarity between variables. Besides, the computational burden of MCC based KRLS will raise as data size increases, thus causing difficulties in accommodating time-varying environments. Therefore, this paper proposes a quantized generalized MCC (QGMCC) to solve the above problem. Specifically, a generalized MCC (GMCC) is utilized to enhance the accuracy and flexibility in calculating the correntropy. In order to solve the problem of computational complexity, QGMCC quantizes the input space and upper bounds the network size by vector quantization (VQ) method. Furthermore, QGMCC is applied to KRLS and forming a computationally efficient and precisely predictive algorithm. After that, the improved algorithm named quantized kernel recursive generalized maximum correntropy (QKRGMC) is set up and the derivation process is also given. Experimental results of one benchmark dataset and two real-world datasets are present to verify the effectiveness of the online prediction algorithm.

An Adaptive Channel Estimation Based on Fixed-Point Generalized Maximum Correntropy Criterion

Many conventional adaptive channel estimation methods are based on minimum mean square error (MMSE) criterion, maximum correntropy criterion (MCC) or least p-norm criterion. However, these criteria are not always desirable in the presence of the various kinds of noises in different wireless channels. To further enhance the adaptability of the channel estimation to different noises, this paper introduces a new criterion named generalized maximum correntropy criterion (GMCC), and calculates the estimated channel parameters using the fixed-point iteration. The convergence analysis of the fixed-point iteration based on GMCC is discussed theoretically and is verified by experiments. More experiments are implemented to show the steady-state performance of the algorithm under different noise environments and the guide of parameter selection is provided.

Nearest Kronecker Product Decomposition Based Generalized Maximum Correntropy and Generalized Hyperbolic Secant Robust Adaptive Filters

Robust adaptive signal processing algorithms based on a generalized maximum correntropy criterion (GMCC) suffers from high steady state misalignment. In an endeavour to achieve lower steady state misalignment, in this letter we propose a generalized hyperbolic secant function (GHSF) as a robust norm and derive the generalized hyperbolic secant adaptive filter (GHSAF). The new algorithm is seen to offer robust system identification performance over the conventional GMCC algorithm. To further improve the convergence performance under non-Gaussian noise environments, we propose the nearest Kronecker product decomposition based GMCC and GHSAF algorithms. Extensive simulation study show the improved convergence performance provided by the proposed algorithms for system identification.

Robust Generalized Maximum Correntropy Criterion Algorithms for Active Noise Control

As a robust nonlinear similarity measure, the maximum correntropy criterion (MCC) has been successfully applied to active noise control (ANC) for impulsive noise. The default kernel function of the filtered-x maximum correntropy criterion (FxMCC) algorithm is the Gaussian kernel, which is desirable in many cases for its smooth and strict positive-definite. However, it is not always the best choice. In this study, a filtered-x generalized maximum correntropy criterion (FxGMCC) algorithm is proposed, which adopts the generalized Gaussian density (GGD) function as its kernel. The FxGMCC algorithm has greater robust ability against non-Gaussian environments, but, it still adopts a single error norm which exhibits poor convergence rate and noise reduction performance. To surmount this problem, an improved FxGMCC (IFxGMCC) algorithm with continuous mixed Lp- norm is proposed. Moreover, to make a trade-off between fast convergence rate and low steady-state misalignment, a convexly combined IFxGMCC (C-IFxGMCC) algorithm is further developed. The stability mechanism and computational complexity of the proposed algorithms are analyzed. Simulation results in the context of different impulsive noises as well as the real noise signals verify that the proposed algorithms are superior to most of the existing robust adaptive algorithms.