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To date, most linear and nonlinear Kalman filters (KFs) have been developed under the Gaussian assumption and the well-known minimum mean square error (MMSE) criterion. In order to improve the robustness with respect to impulsive (or heavy-tailed) non-Gaussian noises, the maximum correntropy criterion (MCC) has recently been used to replace the MMSE criterion in developing several robust Kalman-type filters. To deal with more complicated non-Gaussian noises such as noises from multimodal distributions, in this article, we develop a new Kalman-type filter, called minimum error entropy KF (MEE-KF), by using the minimum error entropy (MEE) criterion instead of the MMSE or MCC. Similar to the MCC-based KFs, the proposed filter is also an online algorithm with the recursive process, in which the propagation equations are used to give prior estimates of the state and covariance matrix, and a fixed-point algorithm is used to update the posterior estimates. In addition, the MEE extended KF (MEE-EKF) is also developed for performance improvement in the nonlinear situations. The high accuracy and strong robustness of MEE-KF and MEE-EKF are confirmed by experimental results. [ABSTRACT FROM AUTHOR]

Recently, maximum correntropy criterion (MCC) has been widely and successfully used in robust signal processing and machine learning, in which the correntropy is maximized instead of minimizing the popular mean square error (MSE) to improve the robustness with respect to outliers or impulsive noises. A lot of efforts have been devoted to derive different adaptive algorithms under MCC, but to date, little insight has been gained as to how the MCC solution will be influenced by outliers. In this paper, we investigate this problem and our focus is mainly on the parameter estimation of a simple linear errors-in-variables (EIVs) model with scalar variables. Under some conditions, we derive an upper bound on the absolute value of the estimation error and show that the MCC solution can get very close to the true value of the unknown parameter even with arbitrarily large outliers in both the input and output variables. Illustrative examples are provided to verify and clarify the theory. [ABSTRACT FROM AUTHOR]

Due to the effectiveness in learning the subspace structures, low-rank representation (LRR) and its variations have been widely applied in various fields, such as computer vision and pattern recognition. However, in real applications, it is a challenge to handle the complex noises. To address this problem, we propose a novel robust LRR method based on kernel risk-sensitive loss (KRSL) with high-order manifold constraint, called RHLRR, in which the KRSL is introduced to deal with the noises and the multiple hypergraph regularization term is used as a high order manifold constraint to effectively capture the locality, similarity and the intrinsic geometric information in data. Besides, an iterative algorithm based on the half-quadratic (HQ) and the accelerated block coordinate update (BCU) is developed. The experimental results demonstrate that the proposed method can outperform other state-of-the-art LRR variants. [ABSTRACT FROM AUTHOR]

Common spatial pattern (CSP) is a classic method commonly used in multichannel electroencephalogram (EEG) signal processing, which aims to extract effective features for binary classification by solving spatial filters that maximize the ratio of filtered dispersion between two classes. The aim of this paper is to improve the performance of the conventional CSP method, which will be badly influenced by noises. The recently proposed quantized minimum error entropy (QMEE) criterion is applied to structure a new objective function instead of the ${L} _{2}$ -norm in the conventional CSP. Quantization is utilized to reduce the computational complexity. The new objective function is optimized by a gradient-based iterative algorithm. The desirable performance of the QMEE-based CSP method, namely CSP-QMEE, is demonstrated with a toy example and two real EEG datasets, including Dataset IIb of the brain–computer interfaces (BCIs) Competition IV (three channels) and Dataset IIIa of the BCI Competition III (60 channels). The new method can achieve satisfactory performance compared to existing methods on all datasets. The promising results in this paper suggest that the CSP-QMEE may become a powerful tool for BCIs. [ABSTRACT FROM AUTHOR]

Nonlinear similarity measures defined in kernel space, such as correntropy, can extract higher order statistics of data and offer potentially significant performance improvement over their linear counterparts especially in non Gaussian signal processing and machine learning. In this paper, we propose a new similarity measure in kernel space, called the kernel risk-sensitive loss (KRSL), and provide some important properties. We apply the KRSL to adaptive filtering and investigate the robustness, and then develop the MKRSL algorithm and analyze the mean square convergence performance. Compared with correntropy, the KRSL can offer a more efficient performance surface, thereby enabling a gradient-based method to achieve faster convergence speed and higher accuracy while still maintaining the robustness to outliers. Theoretical analysis results and superior performance of the new algorithm are confirmed by simulation. [ABSTRACT FROM PUBLISHER]

As a robust nonlinear similarity measure in kernel space, correntropy has received increasing attention in domains of machine learning and signal processing. In particular, the maximum correntropy criterion (MCC) has recently been successfully applied in robust regression and filtering. The default kernel function in correntropy is the Gaussian kernel, which is, of course, not always the best choice. In this paper, we propose a generalized correntropy that adopts the generalized Gaussian density (GGD) function as the kernel, and present some important properties. We further propose the generalized maximum correntropy criterion (GMCC) and apply it to adaptive filtering. An adaptive algorithm, called the GMCC algorithm, is derived, and the stability problem and steady-state performance are studied. We show that the proposed algorithm is very stable and can achieve zero probability of divergence (POD). Simulation results confirm the theoretical expectations and demonstrate the desirable performance of the new algorithm. [ABSTRACT FROM AUTHOR]

Abstract: The minimum mean-square error (MMSE) and minimum error entropy (MEE) are two important criteria in the estimation related problems. The MMSE can be viewed as a robust MEE criterion in the minimax sense, as its minimization is equivalent to minimizing an upper bound (the maximum value) of the error entropy. This note gives a new and more meaningful interpretation on the robustness of MMSE for problems in which there exists uncertainty in the probability model. It is shown that the MMSE estimator imposes an upper bound on error entropy for the true model. The upper bound consists of two terms. The first term quantifies the “MMSE performance” under nominal conditions, and the second term measures the “distance” between the true and nominal models. This robustness property is parallel to that of the risk-sensitive estimation. Illustration examples are included to confirm the robustness of MMSE. [Copyright &y& Elsevier]

Multi-view clustering has received widespread attention owing to its effectiveness by integrating multi-view data appropriately, but traditional algorithms have limited applicability to large-scale real-world data due to their high computational complexity and low robustness. Focusing on the aforementioned issues, we propose an efficient and robust multi-view clustering algorithm with anchor graph regularization (ERMC-AGR). In this work, a novel anchor graph regularization (ARG) is designed to improve the quality of the learned embedded anchor graph (EAG), and the obtained EAG is decomposed by nonnegative matrix factorization (NMF) under correntropy criterion to acquire clustering results directly. Different from the traditional graph regularization that needs to construct a large-scale Laplacian matrix pertaining to the all-sample graph, our lightweight AGR, constructed from the perspective of anchors, can reduce the computational complexity significantly while improving the EAG quality. Moreover, a factor matrix of NMF is constrained to be the cluster indicator matrix to omit additional k-means after optimization. Subsequently, correntropy is utilized to improve the effectiveness and robustness of ERMC-AGR owing to its promising performance to complex noises and outliers. Extensive experiments on real-world datasets and noisy datasets show that ERMC-ARG can improve the clustering efficiency and robustness while ensuring comparable or even better effectiveness. [ABSTRACT FROM AUTHOR]

An adaptive estimation algorithm based on the Lorentzian norm is proposed for echo cancellation in vehicle hands-free communication systems and video teleconferencing systems, namely the affine-projection Lorentzian (APL) algorithm. By minimizing the Lorentzian norm of the a posteriori error vector with a suitable constraint on the weight vector and providing a dynamic Lorentzian-norm-controlling parameter, the proposed APL algorithm achieves robustness against impulsive disturbances and speeds up convergence for colored input signals. The computational complexity of the APL algorithm is analyzed and a fast recursive filtering method is employed to reduce its complexity. The stability analysis, based on energy-conservation arguments, shows that the APL algorithm converges. Furthermore, its tracking behavior is also investigated and a step size optimizing the tracking performance is derived. Simulation results agree well with the theoretical analysis. Simulation results for channel estimation and in-car echo cancellation scenarios demonstrate that the APL algorithm achieves better performance compared to the maximum-correntropy-criterion, affine-projection-generalized-maximum-correntropy, affine-projection-sign, affine-projection-like M-estimate, and Lorentzian adaptive filtering algorithms in various impulsive interference environments. [ABSTRACT FROM AUTHOR]

In order to efficiently utilize the information in the data and eliminate the negative effects of outliers in the principal component analysis (PCA) method, in this paper, we propose a novel robust sparse PCA method based on maximum correntropy criterion (MCC) with high-order manifold constraints called the RHSPCA. Compared with the traditional PCA methods, the proposed RHSPCA has the following benefits: 1) the MCC regression term is more robust to outliers than the MSE-based regression term; 2) thanks to the high-order manifold constraints, the low-dimensional representations can preserve the local relations of the data and greatly improve the clustering and classification performance for image processing tasks; and 3) in order to further counteract the adverse effects of outliers, the MCC-based samples’ mean is proposed to better centralize the data. We also propose a new solver based on the half-quadratic technique and accelerated block coordinate update strategy to solve the RHSPCA model. Extensive experimental results show that the proposed method can outperform the state-of-the-art robust PCA methods on a variety of image processing tasks, including reconstruction, clustering, and classification, on outliers contaminated datasets. [ABSTRACT FROM AUTHOR]

High-dimensional data contain not only redundancy but also noises produced by the sensors. These noises are usually non-Gaussian distributed. The metrics based on Euclidean distance are not suitable for these situations in general. In order to select the useful features and combat the adverse effects of the noises simultaneously, a robust sparse subspace learning method in unsupervised scenario is proposed in this paper based on the maximum correntropy criterion that shows strong robustness against outliers. Furthermore, an iterative strategy based on half quadratic and an accelerated block coordinate update is proposed. The convergence analysis of the proposed method is also carried out to ensure the convergence to a reliable solution. Extensive experiments are conducted on real-world data sets to show that the new method can filter out the outliers and outperform several state-of-the-art unsupervised feature selection methods. [ABSTRACT FROM AUTHOR]

In hyperspectral images, some spectral bands suffer from low signal-to-noise ratio due to noisy acquisition and atmospheric effects, thus requiring robust techniques for the unmixing problem. This paper presents a robust supervised spectral unmixing approach for hyperspectral images. The robustness is achieved by writing the unmixing problem as the maximization of the correntropy criterion subject to the most commonly used constraints. Two unmixing problems are derived: the first problem considers the fully constrained unmixing, with both the nonnegativity and sum-to-one constraints, while the second one deals with the nonnegativity and the sparsity promoting of the abundances. The corresponding optimization problems are solved using an alternating direction method of multipliers (ADMM) approach. Experiments on synthetic and real hyperspectral images validate the performance of the proposed algorithms for different scenarios, demonstrating that the correntropy-based unmixing with ADMM is particularly robust against highly noisy outlier bands. [ABSTRACT FROM PUBLISHER]