Search Results (24)

In semi-supervised learning scenarios, the presence of limited labeled data and abundant unlabeled samples poses significant challenges to model robustness and generalization. Although the semi-supervised broad learning system (SSBLS) effectively exploits manifold structure through graph Laplacian regularization, its optimization is typically formulated under the mean square error (MSE) criterion, which is sensitive to noise and outliers. To address this limitation, this paper introduces the maximum mixture correntropy criterion (MMC) into the SSBLS framework and proposes a model termed M2C-SSBLS. By replacing the conventional MSE loss with a mixture correntropy-based objective, the proposed method enhances robustness against non-Gaussian noise and abnormal samples while preserving the computational efficiency and analytical solution property of the BLS. Furthermore, to improve representation diversity and reduce model variance, a multi-view ensemble extension, named EC-SSBLS, is proposed. This method constructs multiple feature views through a random feature subspace strategy, and independently trains an M2C-SSBLS base learner on each subspace. Finally, the predicted results of each view are fused through a voting mechanism. Experiments on benchmark UCI datasets under noise-free, 10% and 20% label noise settings demonstrate that the proposed M2C-SSBLS consistently outperforms conventional SSBLS and other advanced semi-supervised learning approaches. The ensemble extension EC-SSBLS further enhances performance, particularly in noisy environments, validating the effectiveness of combining MMC-based optimization with multi-view ensemble learning. Full article

To address the challenges of nonlinearity, strong temporal dependence, and accuracy degradation caused by sudden disturbances in power grid customer service telephone traffic forecasting, this paper proposes a novel forecasting method based on an ensemble model pairing Gated Recurrent Unit (GRU) with Correntropy loss (CL) (called EnsCL-GRU). First, to overcome the sensitivity of the traditional Mean Squared Error (MSE) loss to abnormal spikes and its difficulty in capturing the overall trend consistency of the sequence, a CL is introduced as the loss function for the GRU model. This loss function calculates the normalized Correntropy coefficient between the predicted sequence and the true sequence in the time-delay domain, guiding the model to focus on the overall shape matching of the time series data rather than point-wise error fitting. Furthermore, the gated memory mechanism of the GRU can capture long-term dependencies in the time series, while the CL constrains the consistency of the predicted dynamic trends from the sequence level. This preserves the GRU’s temporal modeling capability while enhancing the model’s response accuracy to sudden disturbances and trend changes. Second, to improve the generalization ability of a single GRU model, an ensemble strategy is employed to train multiple CL-enhanced GRU base models serially. By adaptively adjusting sample weights, the fitting capability for difficult samples (such as telephone traffic spikes) is improved, further improving the model’s robustness. Finally, Bayesian optimization is introduced to automatically search for the optimal hyperparameters of the ensemble model, efficiently approximating the global optimal configuration within a limited number of evaluations. Experimental results demonstrate that the proposed method outperforms traditional approaches. Specifically, compared with the standard GRU model, the proposed method reduces MAPE from 29.15% to 22.61%. It also consistently outperforms the ensemble baseline EnsGRU, achieving a MAPE reduction of 4.73 percentage points. The results indicate that the proposed model significantly improves forecasting accuracy and robustness, particularly under scenarios with nonlinear fluctuations and sudden disturbances, providing reliable support for optimal resource allocation in power grid customer service systems. Full article

Traditional non-negative matrix factorization (NMF) faces challenges when dealing with complex data, primarily characterized by sensitivity to noise, neglect of data geometric structure, and inability to effectively utilize supervised information. To address these limitations, this paper proposes a class-driven robust non-negative matrix factorization with dual-hypergraph regularization (CRNMFDH) framework. The core contributions of this framework include the following: Firstly, the design of a novel dual-hypergraph regularization term that symmetrically captures and preserves the higher-order geometric structures of both the sample space and feature space, establishing a mutually reinforcing topological relationship between them. Secondly, an introduction of a class-driven mechanism to effectively integrate label information into the decomposition process, significantly enhancing the discriminative capability of the low-dimensional representations. Finally, the employment of a loss function based on correntropy to replace the traditional Euclidean distance, thereby enhancing the model’s robustness against noise and outliers. Extensive experiments across nine datasets demonstrate that CRNMFDH significantly outperforms existing state-of-the-art algorithms in multiple clustering evaluation metrics and noise robustness, providing an effective new solution for complex data clustering tasks. Full article

Global Navigation Satellite System (GNSS) receivers may produce measurement outliers in real-world applications owing to various circumstances, including poor signal quality, multipath effects, data loss, satellite signal loss, or electromagnetic interference. This can lead to a noise distribution that is non-Gaussian heavy-tailed, affecting the effectiveness of satellite navigation filters. This paper presents a robust Extended Kalman Filter (EKF) based on the Maximum Correntropy Criterion with a Student’s t kernel (STMCCEKF) for GPS navigation under non-Gaussian noise. Unlike traditional EKF and Gaussian-kernel MCCEKF, the proposed method enhances robustness by leveraging the heavy-tailed Student’s t kernel, which effectively suppresses outliers and dynamic observation noise. A fixed-point iterative algorithm is used for state update, and a new posterior error covariance expression is derived. The simulation results demonstrate that STMCCEKF outperforms conventional filters in positioning accuracy and robustness, particularly in environments with impulsive noise and multipath interference. The Student’s t-distribution kernel efficiently mitigates heavy-tailed non-Gaussian noise, while it adaptively adjusts process and measurement noise covariances, leading to improved estimation performance. A detailed explanation of several key concepts along with practical examples are discussed to aid in understanding and applying the Global Positioning System (GPS) navigation filter. By integrating cutting-edge reinforcement learning with robust statistical approaches, this work advances adaptive signal processing and estimation, offering a significant contribution to the field. Full article

Gyros/star sensor integration provides a potential method to obtain high-accuracy spatial orientation for turntable structures. However, it is subjected to the problem of accuracy loss when the measurement noises become non-Gaussian due to the complex spatial environment. This paper presents an event-driven maximum correntropy filter based on Cauchy kernel to handle the above problem. In this method, a direct installation mode of gyros/star sensor integration is established and the associated mathematical model is derived to improve the turntable’s control stability. Based on this, a Cauchy kernel-based maximum correntropy filter is developed to curb the influence of non-Gaussian measurement noise for enhancing the gyros/star sensor integration’s robustness. Subsequently, an event-driven mechanism is constructed based on the filter’s innovation information for further reducing the unnecessary computational cost to optimize the real-time performance. The effectiveness of the proposed method has been validated by simulations of the gyros/star sensor integration for spatial orientation. This shows that the proposed filtering methodology not only has strong robustness to deal with the influence of non-Gaussian measurement noise but can also achieve superior real-time spatial applications with a small computational cost, leading to enhanced performance for the turntable’s spatial orientation using gyros/star sensor integration. Full article

In this study, we address the challenge of noise reduction in environments characterized by impulsive noise and missing input data in active noise control (ANC) systems, where existing algorithms often fail to deliver satisfactory results. Background noise, especially impulsive noise, poses a significant obstacle to signal processing and noise reduction. Furthermore, data loss during transmission or acquisition further complicates the noise reduction task. In this paper, a filtered-x imputation of the missing data maximum correntropy criterion (FxImdMCC) algorithm is proposed based on an imputation model, least mean square, and the maximum correntropy criterion (MCC), which can effectively reduce the impact of outliers and missing input data. The simulation results demonstrate the efficacy of the proposed FxImdMCC algorithm, which significantly outperforms existing algorithms in the context of active impulsive noise control. Full article

In this paper, a Toeplitz construction method based on eigenvalues and eigenvectors is proposed to combine with traditional denoising algorithms, including fractional low-order moment (FLOM), phased fractional low-order moment (PFLOM), and correntropy-based correlation (CRCO) methods. It can improve the direction of arrival (DOA) estimation of signals in impulsive noise. Firstly, the algorithm performs eigenvalue decomposition on the received covariance matrix to obtain eigenvectors and eigenvalues, and then the Toeplitz matrix is created according to the eigenvectors corresponding to its eigenvalues. Secondly, the spatial averaging method is used to obtain an unbiased estimate of the Toeplitz matrix, which is then weighted and added based on the corresponding eigenvalues. Next, the noise subspace of the Toeplitz matrix is reconstructed to obtain the one that has less angle information. Finally, the DOA of the coherent signal is estimated using the Multiple Signal Classification (MUSIC) algorithm. The improved method based on the Toeplitz matrix can not only suppress the effect of impulsive noise but can also solve the problem of aperture loss due to its decoherence. A series of simulations have shown that they have better performances than other algorithms. Full article

Direction of arrival (DOA) estimation is an important research topic in array signal processing and widely applied in practical engineering. However, when signal sources are highly correlated or coherent, conventional subspace-based DOA estimation algorithms will perform poorly due to the rank deficiency in the received data covariance matrix. Moreover, conventional DOA estimation algorithms are usually developed under Gaussian-distributed background noise, which will deteriorate significantly in impulsive noise environments. In this paper, a novel method is presented to estimate the DOA of coherent signals in impulsive noise environments. A novel correntropy-based generalized covariance (CEGC) operator is defined and proof of boundedness is given to ensure the effectiveness of the proposed method in impulsive noise environments. Furthermore, an improved Toeplitz approximation method combined CEGC operator is proposed to estimate the DOA of coherent sources. Compared to other existing algorithms, the proposed method can avoid array aperture loss and perform more effectively, even in cases of intense impulsive noise and low snapshot numbers. Finally, comprehensive Monte-Carlo simulations are performed to verify the superiority of the proposed method under various impulsive noise conditions. Full article

Extreme learning machines (ELMs) have recently attracted significant attention due to their fast training speeds and good prediction effect. However, ELMs ignore the inherent distribution of the original samples, and they are prone to overfitting, which fails at achieving good generalization performance. In this paper, based on expectile penalty and correntropy, an asymmetric C-loss function (called AC-loss) is proposed, which is non-convex, bounded, and relatively insensitive to noise. Further, a novel extreme learning machine called L₁ norm robust regularized extreme learning machine with asymmetric C-loss (L₁-ACELM) is presented to handle the overfitting problem. The proposed algorithm benefits from L₁ norm and replaces the square loss function with the AC-loss function. The L₁-ACELM can generate a more compact network with fewer hidden nodes and reduce the impact of noise. To evaluate the effectiveness of the proposed algorithm on noisy datasets, different levels of noise are added in numerical experiments. The results for different types of artificial and benchmark datasets demonstrate that L₁-ACELM achieves better generalization performance compared to other state-of-the-art algorithms, especially when noise exists in the datasets. Full article

Robust nonlinear filtering is an important method for tracking maneuvering targets in non-Gaussian noise environments. Although there are many robust filters for nonlinear systems, few of them have ideal performance for mixed Gaussian noise and non-Gaussian noise (such as scattering noise) in practical applications. Therefore, a novel cubature formula and maximum correntropy criterion (MCC)-based robust cubature Kalman filter is proposed. First, the fully symmetric cubature criterion and high-order divided difference are used to construct a new fifth-degree cubature formula using fewer symmetric cubature points. Then, a new cost function is obtained by combining the weighted least-squares method and the MCC loss criterion to deal with the abnormal values of non-Gaussian noise, which enhances the robustness; and statistical linearization methods are used to calculate the approximate result of the measurement process. Thus, the final fifth-degree divided difference–maximum correntropy cubature Kalman filter (DD-MCCKF) framework is constructed. A typical surface-maneuvering target-tracking simulation example is used to verify the tracking accuracy and robustness of the proposed filter. Experimental results indicate that the proposed filter has a higher tracking accuracy and better numerical stability than other common nonlinear filters in non-Gaussian noise environments with fewer cubature points used. Full article

In this paper, angles-only target tracking (AoT) problem is investigated in the non Gaussian environment. Since the conventional minimum mean square error criterion based estimators tend to give poor accuracy in the presence of large outliers or impulsive noises in measurement, a maximum correntropy criterion (MCC) based framework is presented. Accordingly, three new estimation algorithms are developed for AoT problems based on the conventional sigma point filters, termed as MC-UKF-CK, MC-NSKF-GK and MC-NSKF-CK. Here MC-NSKF-GK represents the maximum correntropy new sigma point Kalman filter realized using Gaussian kernel and MC-NSKF-CK represents realization using Cauchy kernel. Similarly, based on the unscented Kalman filter, MC-UKF-CK has been developed. The performance of all these estimators is evaluated in terms of root-mean-square error (RMSE) in position and % track loss. The simulations were carried out for 2D as well as 3D AoT scenarios and it was inferred that, the developed algorithms performed with improved estimation accuracy than the conventional ones, in the presence of non Gaussian measurement noise. Full article

The constrained recursive maximum correntropy criterion (CRMCC) combats the non-Gaussian noise effectively. However, the performance surface of maximum correntropy criterion (MCC) is highly non-convex, resulting in low accuracy. Inspired by the smooth kernel risk-sensitive loss (KRSL), a novel constrained recursive KRSL (CRKRSL) algorithm is proposed, which shows higher filtering accuracy and lower computational complexity than CRMCC. Meanwhile, a modified update strategy is developed to avoid the instability of CRKRSL in the early iterations. By using Isserlis’s theorem to separate the complex symmetric matrix with fourth-moment variables, the mean square stability condition of CRKRSL is derived, and the simulation results validate its advantages. Full article

The robust Kalman filter with correntropy loss has received much attention in recent years for forecasting-aided state estimation in power systems, since it efficiently reduces the negative influence of various abnormal situations, such as non-Gaussian communication, changing environment, and instrument failures, and obviously improves the stability of power systems. However, the existing correntropy-based robust Kalman filters usually use the Gaussian function with a fixed center as the kernel function in correntropy, which may not be a suitable choice in practical applications of power system forecasting-aided state estimation (PSSE). To address this issue, a new and robust unscented Kalman filter, called the maximum correntropy with variable center unscented Kalman filter (MCVUKF), is proposed in this paper for PSSE. Specifically, MCVUKF adopts an extended version of correntropy, whose center can be located at any position, to replace the original correntropy in an unscented Kalman filter to improve the performance in PSSE. Moreover, by using an exponential function of the innovation vector to adjust a covariance matrix, an enhanced MCVUKF (En-MCVUKF) method is also developed for suppressing the influence of bad data to the innovation vector and further improving the accuracy of PSSE. Finally, extensive simulations have been conducted on IEEE 14-bus, 30-bus, and 57-bus test power systems, and the simulation results have shown the superiority of the proposed MCVUKF and En-MCVUKF methods compared with several related state-of-the-art Kalman filter methods. Full article

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. Full article

State of charge (SOC) estimation plays a crucial role in battery management systems. Among all the existing SOC estimation approaches, the model-driven extended Kalman filter (EKF) has been widely utilized to estimate SOC due to its simple implementation and nonlinear property. However, the traditional EKF derived from the mean square error (MSE) loss is sensitive to non-Gaussian noise which especially exists in practice, thus the SOC estimation based on the traditional EKF may result in undesirable performance. Hence, a novel robust EKF method with correntropy loss is employed to perform SOC estimation to improve the accuracy under non-Gaussian environments firstly. Secondly, a novel robust EKF, called C-WLS-EKF, is developed by combining the advantages of correntropy and weighted least squares (WLS) to improve the digital stability of the correntropy EKF (C-EKF). In addition, the convergence of the proposed algorithm is verified by the Cramér–Rao low bound. Finally, a C-WLS-EKF method based on an equivalent circuit model is designed to perform SOC estimation. The experiment results clarify that the SOC estimation error in terms of the MSE via the proposed C-WLS-EKF method can efficiently be reduced from 1.361% to 0.512% under non-Gaussian noise conditions. Full article