Mixture Correntropy Research Articles

Iterated Maximum Mixture Correntropy Kalman Filter and Its Applications in Tracking and Navigation

Iterated Maximum Mixture Correntropy Kalman Filter and Its Applications in Tracking and Navigation

Stochastic configuration network modeling method based on information superposition and mixture correntropy

Stochastic configuration network modeling method based on information superposition and mixture correntropy

Sequence homology score-based deep fuzzy network for identifying therapeutic peptides

The detection of therapeutic peptides is a topic of immense interest in the biomedical field. Conventional biochemical experiment-based detection techniques are tedious and time-consuming. Computational biology has become a useful tool for improving the detection efficiency of therapeutic peptides. Most computational methods do not consider the deviation caused by noise. To improve the generalization performance of therapeutic peptide prediction methods, this work presents a sequence homology score-based deep fuzzy echo-state network with maximizing mixture correntropy (SHS-DFESN-MMC) model. Our method is compared with the existing methods on eight types of therapeutic peptide datasets. The model parameters are determined by 10 fold cross-validation on their training sets and verified by independent test sets. Across the 8 datasets, the average area under the receiver operating characteristic curve (AUC) values of SHS-DFESN-MMC are the highest on both the training (0.926) and independent sets (0.923).

Improved mixture correntropy cubature Kalman filter for attitude estimation

Abstract This work proposes an algorithm based on improved mixture correntropy cubature Kalman filtering (IMC-CKF) to address the issues of low accuracy and susceptibility to complex noise and outlier interference in inertial navigation attitude estimation. First, a combination of Gaussian kernel and Cauchy kernel is suggested to construct mixture correntropy to tackle the problem of single kernel-based correntropy being insufficient to confronted with complex noise. Second, the model fitting loss based on mean square error and measurement fitting loss based on mixture correntropy are used to establish the objective function. The maximum correntropy criterion (MCC) replaces the minimum mean square error (MMSE) criterion, and the fixed-point iteration method is used to solve the objective function, deriving the mixture correntropy matrix to adjust the measurement noise variance. Finally, the semi-trapezoidal membership function is used to determine the mixture correntropy coefficient. Accordingly, the algorithm can adaptively select the proportions of each kernel function according to the respective noise interference situation. Simulations and dynamic–static experiments have been conducted, and the algorithm has been compared with single kernel-based correntropy algorithms and other robust algorithms to confirm its superior precision and stability under complex noise and outlier interference.

Mixture correntropy-based robust distance metric learning for classification

Metric learning is a branch of machine learning that aims to learn from the given training data a valid distance metric, with which the similarity between samples can be more effectively evaluated for classification. Metric learning has attracted significant attention, and a large number of models have been proposed in the past few years. However, the traditional methods adopt hinge loss which easily leads to noise sensitivity and instability. In this paper, to improve the robustness performance, we develop a mixture correntropy criterion where two Laplacian kernel functions are combined as the kernel function and induce a more general nonconvex robust loss function by the mixture correntropy. The properties related to the loss function are analysed and presented. The induced loss amalgamates the superiors of the state-of-the-art robust loss functions and is more effective. With this induced loss, we establish a robust metric learning model (called MCML) and design an effective iterative algorithm to optimize the nonconvex challenging problem. The computational complexity and convergence of algorithm are discussed in theory. Furthermore, a boosting version of MCML (BMCML) is derived, where the low-rank basis learning is jointly optimized with the metric to better uncover the data structure. Finally, extensive experiments are conducted on artificial datasets, UCI benchmark datasets and image datasets. The experimental results verify the robustness and effectiveness of the proposed methods.

Stacking integrated learning model via ELM and GRU with mixture correntropy loss for robust state of health estimation of lithium-ion batteries

Accurate estimation of the state of health (SOH) is crucial for the safe and stable operation of lithium-ion batteries. However, since the labeled values may contain non-Gaussian noise which may lead to a decrease in the effectiveness of traditional data-driven based estimation methods. Therefore, a novel robust stacking integrated learning model (ILM) is proposed to enable accurate SOH estimation under non-Gaussian noises (or outliers) conditions. The mixture correntropy loss (MCL) is used in original extreme learning machine (ELM) and the gated recurrent unit (GRU) frameworks to develop novel robust learning models, i.e MCL-ELM and MCL-GRU, and they are used as the sub-models of the proposed ILM, which takes into account the generalization performance of the model and the overall trend of SOH over the time series. In addition, the entropy weighting method that can well reflect the differences between the sub-models is utilized to reduce the complexity of the stacked ILM. Furthermore, the local tangent space alignment is used to capture the local relationships between different loops to enhance the effectiveness of the extracted health features. Several numerical experiments are performed under different cases to validate the estimation effect of the proposed model by using two publicly available datasets, and the experimental results demonstrate that the maximum RMSE, MAE, and MAPE values of the proposed model are 1.391%, 0.932%, and 1.480%, respectively, under non-Gaussian noises conditions.

Enhanced square root CKF with mixture correntropy loss for robust state of charge estimation of lithium-ion battery

The measurement data of lithium-ion battery collected in complex operating conditions may be contaminated by non-Gaussian noises (or outliers), a novel robust state of charge (SOC) estimation approach that enhances the robustness of square-root cubature Kalman filter (SRCKF) by incorporating a mixture correntropy loss (MCL) is proposed to overcome the issue of non-Gaussian measurement noise interference. Although the SRCKF can perform non-destructive state estimation for nonlinear system, it is sensitive to the non-Gaussian noises (or outliers) due to the use of mean square error (MSE) loss. To overcome this limitation, the MCL is used as a cost to replace the MSE in CKF framework, which is constructed by mixture of two Gaussian kernel functions with different kernel widths and has outstanding robustness. Moreover, we establish an effective nonlinear regression model that incorporates noise and state error information into the MCL function, and then a fixed-point iteration method is utilized to update the posterior state estimation. Additionally, to further suppress the influence of abnormal noise on the posterior state estimation, we introduce the exponential function of the innovation vector to adjust the measurement covariance matrix in real-time. Accordingly, an enhanced MCL-SRCKF is developed for SOC estimation considering the measurement noises with non-Gaussian distribution. Results from various simulation environments demonstrate that the proposed method achieves high estimation accuracy in different cases.

Multi-Sensor Fusion Target Tracking Based on Maximum Mixture Correntropy in Non-Gaussian Noise Environments with Doppler Measurements

This paper addresses the multi-sensor fusion target tracking problem based on maximum mixture correntropy in non-Gaussian noise environments exclusively using Doppler measurements. As Doppler measurements are non-linear, a statistical linear regression model is constructed using the unscented transformation. Then, a centralized measurement model is developed, and the mixture correntropy is determined, which contains the high-order statistics of state prediction and the measurement error caused by noise. Then, a robust fusion filter is proposed by maximizing the mixture-correntropy-based cost. To improve numerical stability, the information filter and corresponding square root version are also derived. Furthermore, the performance of the proposed algorithm is analyzed, and the selection of the kernel width is discussed. Experiments are performed using simulated data and automatic driving software. The results show that the estimation performance of the proposed algorithm is better with respect to outliers and mixture Gaussian noise than that of traditional methods.

A diffusion strategy for robust distributed estimation based on streaming graph signals

The problem of robust distributed estimation over dynamic and streaming graph signals is investigated in this paper. Existing works related to distributed estimation over dynamic and streaming graph signals are mainly derived from the Mean-Square-Error criterion, and they are vulnerable to non-Gaussian noise. Therefore, a new kind of diffusion Mixture correntropy (d-MC) algorithm is developed to deal with the disadvantage in this paper. Incorporating the diffusion strategy and a novel cost function, the proposed algorithm could accurately estimate the graph filter parameter with the dynamic and streaming graph signals, and achieve desirable performance under both Gaussian and impulsive noise environment. Besides, the theoretical analysis results of mean and mean-square stability are derived. Simulations on various case studies indicate the desirable performance of proposed d-MC algorithm by comparing it to other benchmarks.

Fractional-order ascent maximum mixture correntropy criterion for FLANNs based multi-channel nonlinear active noise control

The filtered-s maximum correntropy criterion (FsMCC) algorithm was developed for nonlinear active noise control (NANC) in impulsive noise environments with the use of functional linked artificial neural networks (FLANNs) structure. However, the kernel-width of the FsMCC is constant, which is dull and cannot self-regulate to achieve both the fast convergence and low steady-state error performance. For better convergence ability, in this paper, a fractional-order gradient ascent filtered-s maximum correntropy criterion algorithm (FGA-FsMCC) is presented for multi-channel NANC system. The fractional lower-order moments supersede the non-existent second-order moments. To come up with a more reliable algorithm, by merging two kernels with complementary width, the fractional-order gradient ascent filtered-s mixture correntropy criterion (FGA-FsMMCC) was presented. The computational complexity and convergence conditions are analyzed. To verify the robustness of proposed algorithms, simulations are carried out to discuss parameters and control effects of algorithms for alpha-stable noise in different nonlinear environments.

Robust Subband Adaptive Filter Algorithms-Based Mixture Correntropy and Application to Acoustic Echo Cancellation

To acquire an improvement of the performance of the subband adaptive filter with impulsive interference, the normalized subband adaptive filter (NSAF) algorithm-based maximum correntropy criterion (MCC), called MCC-NSAF, has been developed. However, it is hard for the MCC criterion to take into account both the fast convergence rate and low steady-state error with a fixed kernel bandwidth. To handle this dilemma, in this paper, the normalized subband adaptive filter algorithm-based maximum mixture correntropy criterion (MMC) algorithm, called MMC-NSAF, is proposed. The MMC-NSAF algorithm integrates two correntropies with complementary control sizes of Gaussian kernel and can not only converge quickly but also has a small misalignment. Yet the MMC-NSAF still has some limitations because of its fixed step size. Therefore, a convexly combined MMC-NSAF algorithm, namely MMC-CNSAF, is proposed. The MMC-CNSAF algorithm utilizes two Gaussian kernels of different size and can combine overall improvement between convergence rate and steady-state error simultaneously. Eventually, the convergence and the computational complexity are analyzed. To achieve the test and verification of the robustness of proposed algorithms, simulations are carried out to discuss the effect of the parameters algorithm under colored input signals in impulsive interference environments for system identification. Meanwhile, the performances of the proposed algorithms under the influence of the acoustic echo cancellation in practical application are studied.

Mixture correntropy based robust multi-view K-means clustering

Multi-view clustering has been a significant research problem in unsupervised clustering in recent years and has important applications in computer vision, data mining and other fields. To explore more clustering information from different views and improve performance, researchers have developed a variety of multi-view clustering algorithms by applying the same L1 or L2,1 norm constraints for different views, which essentially assumes that the errors satisfy the characteristics described by the corresponding norms. It is clear that such assumption is not always satisfied in the real-world datasets. Therefore, the performance of existing algorithms can decrease under the complex noise that may be contained in the data. To solve the above problem, we introduce an information theoretic learning-based metric into a multi-view model to address noise. First, we propose a new mixture correntropy (MC) metric. Then, we propose a MC based robust multi-view K-means clustering (MC-RMVKM) method by applying the MC to an existing model. Furthermore, an efficient iterative algorithm is derived to solve the joint MC-RMVKM learning problem. Extensive results on real-world multi-view data show that the MC-based algorithm outperforms other state-of-the-art algorithms.

Multikernel Correntropy for Robust Learning.

As a novel similarity measure that is defined as the expectation of a kernel function between two random variables, correntropy has been successfully applied in robust machine learning and signal processing to combat large outliers. The kernel function in correntropy is usually a zero-mean Gaussian kernel. In a recent work, the concept of mixture correntropy (MC) was proposed to improve the learning performance, where the kernel function is a mixture Gaussian kernel, namely, a linear combination of several zero-mean Gaussian kernels with different widths. In both correntropy and MC, the center of the kernel function is, however, always located at zero. In the present work, to further improve the learning performance, we propose the concept of multikernel correntropy (MKC), in which each component of the mixture Gaussian kernel can be centered at a different location. The properties of the MKC are investigated and an efficient approach is proposed to determine the free parameters in MKC. Experimental results show that the learning algorithms under the maximum MKC criterion (MMKCC) can outperform those under the original maximum correntropy criterion (MCC) and the maximum MC criterion (MMCC).

A Runs Test-Based Kalman Filter With Both Adaptability and Robustness With Application to INS/GNSS Integration

Kalman filter (KF) is one of the most efficient solutions applied for the integration of inertial navigation system (INS) and global navigation satellite system (GNSS). However, for standard KF derived from the ideal system model assumption, various disturbance factors inevitably decrease its estimation accuracy in practical scenarios. Therefore, it is necessary to suppress the interference factors such as inaccurate noise covariance or irregular process uncertainty during filtering, thus improving the integrated system’s stability and accuracy. Nevertheless, existing solutions usually target specific individual issues and lack compatibility with nonstationary scenarios in that multiple uncertain factors coexist. In this article, an improved KF with a switching scheme based on runs hypothesis test is designed to enhance the algorithm’s performance in nonstationary environments, and a process uncertainty robust filter based on mixture correntropy is proposed to suppress the potential diverge risks. By integrating with the variational Bayesian approach into the switching scheme, the noise covariance adaptability of the proposed scheme is further improved, and an improved KF with both adaptivity and robustness is obtained. The simulation and field test results demonstrate that the proposed filter achieved the expected superior performance in challenging nonstationary conditions.

Short-term Wind Power Forecasting Using the Hybrid Model of Improved Variational Mode Decomposition and Maximum Mixture Correntropy Long Short-term Memory Neural Network

With the development of emerging technology, wind power forecasting hybrid with artificial intelligence methods has become a research hotspot. Most of these methods are based on Mean Square Error (MSE) loss. However, when conducting the forecasting studies, the forecasting models built based on the traditional MSE loss have a poor effect, and the wind power data also lack the sensitivity to the nuclear parameters, make it difficult to achieve satisfactory results. Therefore, a wind power forecasting method based on Mixture Correntropy (MC) Long Short-term Memory (LSTM) neural network and Improved Variational Mode Decomposition (IVMD) is proposed in this paper. Aiming at the fact that the mixing coefficient and kernel parameters in Maximum Mixture Correntropy Criterion (MMCC) loss have an impact on its performance, Particle Swarm Optimization (PSO) algorithm is used to optimize the parameters, and PMC(PSO-MC)-LSTM model is constructed. Meanwhile, an IVMD-SE data preprocessing strategy combining Sample Entropy (SE) and IVMD is proposed. The IVMD-SE-PMC-LSTM hybrid forecasting model is constructed. Finally, four groups original data from a wind farm are simulated to verify the forecasting performance of the proposed method. The results show that the hybrid forecasting method proposed in this paper can be better applied to the forecasting with higher data complexity.

Robust Maximum Mixture Correntropy Criterion Based One-Class Classification Algorithm

One-class classification achieves anomaly/outlier detection by exploiting the characteristics of target data. As a local similarity measure defined in kernel space, correntropy is generally more robust than the mean square error (MSE) based criterion in dealing with large outliers. In this article, the maximum mixture correntropy criterion (MMCC) with multiple kernels are applied to the shallow and hierarchical one-class extreme learning machine to enhance the model robustness and learning speed. Experiments on benchmark University of California, Irvine (UCI) classification datasets, urban acoustic classification dataset, and four synthetic datasets are carried out to show the effectiveness and comparisons with several state-of-the-art methods are provided to demonstrate the superiority of the proposed algorithms.

Mixture Correntropy-Based Kernel Extreme Learning Machines.

Kernel-based extreme learning machine (KELM), as a natural extension of ELM to kernel learning, has achieved outstanding performance in addressing various regression and classification problems. Compared with the basic ELM, KELM has a better generalization ability owing to no needs of the number of hidden nodes given beforehand and random projection mechanism. Since KELM is derived under the minimum mean square error (MMSE) criterion for the Gaussian assumption of noise, its performance may deteriorate under the non-Gaussian cases, seriously. To improve the robustness of KELM, this article proposes a mixture correntropy-based KELM (MC-KELM), which adopts the recently proposed maximum mixture correntropy criterion as the optimization criterion, instead of using the MMSE criterion. In addition, an online sequential version of MC-KELM (MCOS-KELM) is developed to deal with the case that the data arrive sequentially (one-by-one or chunk-by-chunk). Experimental results on regression and classification data sets are reported to validate the performance superiorities of the new methods.

Variational Bayesian-Based Improved Maximum Mixture Correntropy Kalman Filter for Non-Gaussian Noise.

The maximum correntropy Kalman filter (MCKF) is an effective algorithm that was proposed to solve the non-Gaussian filtering problem for linear systems. Compared with the original Kalman filter (KF), the MCKF is a sub-optimal filter with Gaussian correntropy objective function, which has been demonstrated to have excellent robustness to non-Gaussian noise. However, the performance of MCKF is affected by its kernel bandwidth parameter, and a constant kernel bandwidth may lead to severe accuracy degradation in non-stationary noises. In order to solve this problem, the mixture correntropy method is further explored in this work, and an improved maximum mixture correntropy KF (IMMCKF) is proposed. By derivation, the random variables that obey Beta-Bernoulli distribution are taken as intermediate parameters, and a new hierarchical Gaussian state-space model was established. Finally, the unknown mixing probability and state estimation vector at each moment are inferred via a variational Bayesian approach, which provides an effective solution to improve the applicability of MCKFs in non-stationary noises. Performance evaluations demonstrate that the proposed filter significantly improves the existing MCKFs in non-stationary noises.

Robust Power System Forecasting-Aided State Estimation With Generalized Maximum Mixture Correntropy Unscented Kalman Filter

As an effective method for power system forecasting-aided state estimation (FASE), the unscented Kalman filter (UKF) based on correntropy has been widely used in recent years, ensuring the safe and reliable operation of power systems. In this article, to address the impulsive noise, Laplacian noise, bad measurement data, and sudden load change, a robust UKF algorithm based on generalized maximum mixture correntropy (GMMC-UKF) criterion is proposed for FASE, in which the kernel is composed of two generalized Gaussian functions. Specifically, we use a statistical linearization technique to unify the state error and measurement error in the cost function and obtain the optimal value of state estimation by fixed-point iteration. The effectiveness of the proposed algorithm for FASE is verified on IEEE 14-, 30-, and 57-bus test systems under a variety of abnormal situations. Compared with traditional correntropy algorithms, the GMMC-UKF shows more accurate estimation and stronger robustness.

Mixture quantized error entropy for recursive least squares adaptive filtering

Error entropy is a well-known learning criterion in information theoretic learning (ITL), and it has been successfully applied in robust signal processing and machine learning. To date, many robust learning algorithms have been devised based on the minimum error entropy (MEE) criterion, and the Gaussian kernel function is always utilized as the default kernel function in these algorithms, which is not always the best option. To further improve learning performance, two concepts using a mixture of two Gaussian functions as kernel functions, called mixture error entropy and mixture quantized error entropy, are proposed in this paper. We further propose two new recursive least-squares algorithms based on mixture minimum error entropy (MMEE) and mixture quantized minimum error entropy (MQMEE) optimization criteria. The convergence analysis, steady-state mean-square performance, and computational complexity of the two proposed algorithms are investigated. In addition, the reason why the mixture mechanism (mixture correntropy and mixture error entropy) can improve the performance of adaptive filtering algorithms is explained. Simulation results show that the proposed new recursive least-squares algorithms outperform other RLS-type algorithms, and the practicality of the proposed algorithms is verified by the electro-encephalography application.