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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]

In this paper, robust first and second-order divided difference filtering algorithms based on correntropy are proposed, which not only retain the advantages of divided difference filters, but also exhibit robustness in the presence of non-Gaussian noises, especially when the measurements are contaminated by heavy-tailed noises. The proposed filters are then applied to the problem of ship positioning. In order to improve the accuracy and reliability of ship positioning, the positioning method combines the Dead Reckoning (DR) algorithm and the Global Positioning System (GPS). Experimental results of an illustrative example show the superior performance of the new algorithms when applied to ship positioning. [ABSTRACT FROM AUTHOR]

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]

Graph-based clustering commonly provides promising clustering effectiveness as it can preserve samples' local geometric information. Inspired by it, multi-view graph clustering was developed to integrate complementary information among graphs of diverse views and it has received intensive attention recently. Nevertheless, on the one hand, most existing methods require extra k-means after obtaining embedding representations to generate a discrete cluster indicator, which reduces effectiveness due to the two-stage mismatch. On the other hand, numerous complex noises in real-world multi-view data challenge the robustness of existing clustering methods. In this paper, we established a discrete correntropy-based multi-view anchor-graph clustering (DCMAC) model that not only emphasizes the aforementioned issues but also makes use of anchor graphs to improve the efficiency of the graph construction stage. To optimize this non-convex model, we propose a fast half-quadratic-based coordinate descent strategy to acquire the discrete cluster indicator directly without extra k-means. Furthermore, we extend the DCMAC model to a single-view form and provide optimization strategies for it. Extensive experiments illustrate that the proposed method is effective and robust compared to those advanced baselines. • A new discrete correntropy-based multi-view anchor-graph clustering (DCMAC) model is proposed. • A novel half-quadratic-based coordinate descent algorithm is proposed to solve the DCMAC model. • To handle single-view clustering instances, DCMAC is extended to a single-view form named DCAC. • Numerous experiments demonstrate the outstanding effectiveness and robustness of DCMAC. [ABSTRACT FROM AUTHOR]

Nonnegative matrix factorization (NMF) has attracted increasing attention in data mining and machine learning. However, existing NMF methods have some limitations. For example, some NMF methods seriously suffer from noisy data contaminated by outliers, or fail to preserve the geometric information of the data and guarantee the sparse parts-based representation. To overcome these issues, in this paper, a robust and sparse NMF method, called correntropy based dual graph regularized nonnegative matrix factorization with local coordinate constraint (LCDNMF) is proposed. Specifically, LCDNMF incorporates the geometrical information of both the data manifold and the feature manifold, and the local coordinate constraint into the correntropy based objective function. The half-quadratic optimization technique is utilized to solve the nonconvex optimization problem of LCDNMF, and the multiplicative update rules are obtained. Furthermore, some properties of LCDNMF including the convergence, relation with gradient descent method, robustness, and computational complexity are analyzed. Experiments of clustering demonstrate the effectiveness and robustness of the proposed LCDNMF method in comparison to several state-of-the-art methods on six real world image datasets. • The LCDNMF algorithm is proposed. • The convergence and relation with gradient descent method of LCDNMF is analyzed. • The robustness and computational complexity of LCDNMF is also analyzed. • Experiment results show the effectiveness and robustness of LCDNMF. [ABSTRACT FROM AUTHOR]

Robust matrix completion aims to recover a low-rank matrix from a subset of noisy entries perturbed by complex noises. Traditional matrix completion algorithms are always based on $l_2$ -norm minimization and are sensitive to non-Gaussian noise with outliers. In this paper, we propose a novel robust and fast matrix completion method based on the maximum correntropy criterion (MCC). The correntropy-based error measure is utilized instead of the $l_2$ -based error norm to improve robustness against noise. By using the half-quadratic optimization technique, the correntropy-based optimization can be transformed into a weighted matrix factorization problem. Two efficient algorithms are then derived: an alternating minimization-based algorithm and an alternating gradient descent-based algorithm. These algorithms do not require the singular value decomposition (SVD) to be calculated for each iteration. Furthermore, an adaptive kernel width selection strategy is proposed to accelerate the convergence speed as well as improve the performance. A comparison with existing robust matrix completion algorithms is provided by simulations and shows that the new methods can achieve better performance than the existing state-of-the-art algorithms. [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]

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]