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Correntropy is a local similarity measure defined in kernel space, hence can combat large outliers in robust signal processing and machine learning. So far, many robust learning algorithms have been developed under the maximum correntropy criterion (MCC), among which, a Gaussian kernel is generally used in correntropy. To further improve the learning performance, in this paper we propose the concept of mixture correntropy, which uses the mixture of two Gaussian functions as the kernel function. Some important properties of the mixture correntropy are presented. Applications of the maximum mixture correntropy criterion (MMCC) to extreme learning machine (ELM) and kernel adaptive filtering (KAF) for function approximation and data regression are also studied. Experimental results show that the learning algorithms under MMCC can perform very well and achieve better performance than the conventional MCC based algorithms as well as several other state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

Although multi-view clustering has received widespread attention due to its far superior performance to single-view clustering, it still faces the following issues: (1) high computational cost, considering the introduction of multi-view information, reduces the clustering efficiency greatly; (2) complex noises and outliers, existed in real-world data, pose a huge challenge to the robustness of clustering algorithms. Currently, how to increase the efficiency and robustness has become two important issues of multi-view clustering. To cope with the above issues, an efficient correntropy-based multi-view clustering algorithm (ECMC) is proposed in this paper, which can not only improve clustering efficiency by constructing embedded anchor graph and utilizing nonnegative matrix factorization (NMF), but also enhance the robustness by exploring correntropy to suppress various noises and outliers. To further improve clustering efficiency, one of the factors of NMF is constrained to be an indicator matrix instead of a traditional non-negative matrix, so that the categories of samples can be obtained directly without any extra operation. Subsequently, a novel half-quadratic-based strategy is proposed to optimize the non-convex objective function of ECMC. Finally, extensive experiments on eight real-world datasets and eighteen noisy datasets show that ECMC can guarantee faster speed and better robustness than other state-of-the-art multi-view clustering algorithms. [ABSTRACT FROM AUTHOR]

Multi-view clustering (MVC) often provides superior effectiveness to single-view clustering due to the integration of information from diverse views. Nonetheless, existing MVC methods are limited to large-scale real-world data by the drawbacks of low efficiency and poor robustness. To address these issues, we propose a novel robust anchor-based MVC model via spectral embedded concept factorization (RAMCSF). RAMCSF builds anchor graphs to approximate full-sample graphs and decomposes these anchor graphs by concept factorization (CF). To improve the clustering effectiveness, factor matrices of CF are constrained as orthogonal matrices to reduce the freedom of decomposition, and a novel small-scale anchor-based spectral embedding is designed to explore the high-order neighbor relationships. To restrain complex noises distributed in real-world data, we employ correntropy to measure the error between the original data and the learned representation. Moreover, RAMCSF can get a clustering indicator matrix directly, avoiding additional post-processing and ensuring that changes in data dimensions have a limited impact on efficiency. The model is then optimized by a novel fast half-quadratic-based optimization strategy that combines the orthogonal properties and the traces of matrices. Extensive experiments indicate that RAMCSF can achieve higher efficiency and robustness while maintaining comparable effectiveness to other state-of-the-art methods. [ABSTRACT FROM AUTHOR]

Concept factorization (CF) has shown the effectiveness in the field of data clustering. In this paper, a novel and robust semi-supervised CF method, called correntropy based semi-supervised concept factorization with adaptive neighbors (CSCF), is proposed with improved performance in clustering applications. Specifically, on the one hand, the CSCF method adopts correntropy as the cost function to increase the robustness for non-Gaussian noise and outliers, and combines two different types of supervised information simultaneously for obtaining a compact low-dimensional representation of the original data. On the other hand, CSCF assigns the adaptive neighbors for each data point to construct a good data similarity matrix for reducing the sensitiveness of data. Moreover, a generalized version of CSCF is derived for enlarging the clustering application ranges. Analysis is also presented for the relationship of CSCF with several typical CF methods. Experimental results have shown that CSCF has better clustering performance than several state-of-the-art CF methods. [ABSTRACT FROM AUTHOR]

Multiview clustering (MVC) has attracted considerable attention owing to its remarkable capacity to reconcile diverse information from multiple perspectives. However, traditional MVC generally has a narrow scope of application owing to its limited efficiency. Consequently, various efficient MVC (EMVC) methods have emerged recently. Despite their promising performance, these EMVC methods still have several unresolved issues: (1) They suffer from reduced effectiveness caused by representation non-alignment across views and information mismatch between stages, and (2) they fail to efficiently resist complex noises and outliers. To address these issues, we propose an efficient correntropy-based multiview clustering method with alignment discretization (ECMCAD). Specifically, a correntropy-based multipartition learning model was developed to efficiently learn view-specific robust partition-level representations. Additionally, a novel alignment discretization strategy was designed to align the learned cross-view representations into a consensus discrete indicator to integrate representation learning, representation alignment, and discrete label acquisition into a unified framework. Furthermore, an efficient alternating optimization method was developed to solve the model. Numerous experiments illustrated the superiority of the proposed method over state-of-the-art baselines. [ABSTRACT FROM AUTHOR]

Concept factorization (CF), unlike nonnegative matrix factorization (NMF), can handle data with negative values by approximating the original data with two low-dimensional nonnegative matrices and itself. Nevertheless, existing CF-based methods continue to suffer from the two issues specified as follows: (1) Their effectiveness is reduced by the high degree of factorization freedom and the two-stage mismatch between factorization and category acquisition, and (2) their robustness drops significantly when dealing with complex noise. In response to the aforementioned issues, we propose a robust spectral-embedded bilateral orthogonal concept factorization (RSOCF) model for clustering. It constrains the factor matrices as orthogonal matrices to decrease the freedom and obtain samples' categories directly after factorization, which can significantly improve clustering effectiveness. Moreover, correntropy is introduced into RSOCF to improve its robustness to complex noise. To optimize the non-convex RSOCF model, a half-quadratic-based algorithm is devised. Numerous experiments demonstrate that RSOCF surpasses other state-of-the-art methods in terms of clustering effectiveness and robustness. • A novel robust concept factorization-based clustering model is proposed. • A fast algorithm is proposed to optimize the non-convex model. • Numerous experiments validate its clustering effectiveness and robustness. [ABSTRACT FROM AUTHOR]

Owing to its ability to handle negative data and promising clustering performance, concept factorization (CF), an improved version of non-negative matrix factorization, has been incorporated into multi-view clustering recently. Nevertheless, existing CF-based multi-view clustering methods still have the following issues: (1) they directly conduct factorization in the original data space, which means its efficiency is sensitive to the feature dimension; (2) they ignore the high degree of factorization freedom of standard CF, which may lead to non-uniqueness factorization thereby causing reduced effectiveness; (3) traditional robust norms they used are unable to handle complex noises, significantly challenging their robustness. To address these issues, we establish a fast multi-view clustering via correntropy-based orthogonal concept factorization (FMVCCF). Specifically, FMVCCF executes factorization on a learned consensus anchor graph rather than directly decomposing the original data, lessening the dimensionality sensitivity. Then, a lightweight graph regularization term is incorporated to refine the factorization process with a low computational burden. Moreover, an improved multi-view correntropy-based orthogonal CF model is developed, which can enhance the effectiveness and robustness under the orthogonal constraint and correntropy criterion, respectively. Extensive experiments demonstrate that FMVCCF can achieve promising effectiveness and robustness on various real-world datasets with high efficiency. [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]

• A novel correntropy based semi-supervised NMF method is proposed for image clustering. • The proposed method is analysed in terms of convergence, robustness, and computational complexity. • The relationships between the proposed method and several typical NMF based methods are discussed. • Experimental results show the effectiveness and robustness of the proposed method in image clustering tasks. Nonnegative matrix factorization (NMF) is a powerful dimension reduction method, and has received increasing attention in various practical applications. However, most traditional NMF based algorithms are sensitive to noisy data, or fail to fully utilize the limited supervised information. In this paper, a novel robust semi-supervised NMF method, namely correntropy based semi-supervised NMF (CSNMF), is proposed to solve these issues. Specifically, CSNMF adopts a correntropy based loss function instead of the squared Euclidean distance (SED) in constrained NMF to suppress the influence of non-Gaussian noise or outliers contaminated in real world data, and simultaneously uses two types of supervised information, i.e., the pointwise and pairwise constraints, to obtain the discriminative data representation. The proposed method is analyzed in terms of convergence, robustness and computational complexity. The relationships between CSNMF and several previous NMF based methods are also discussed. Extensive experimental results show the effectiveness and robustness of CSNMF in image clustering tasks, compared with several state-of-the-art methods. [ABSTRACT FROM AUTHOR]

Nonnegative matrix factorization (NMF) has been a vital data representation technique, and has demonstrated significant potential in the field of machine learning and data mining. Nonnegative matrix tri-factorization (NMTF) is an extension of NMF, and provides more degrees of freedom than NMF. In this paper, we propose the correntropy based orthogonal nonnegative matrix tri-factorization (CNMTF) algorithm, which is robust to noisy data contaminated by non-Gaussian noise and outliers. Different from previous NMF algorithms, CNMTF firstly applies correntropy to NMTF to measure the similarity, and preserves double orthogonality conditions and dual graph regularization. We adopt the half-quadratic technique to solve the optimization problem of CNMTF, and derive the multiplicative update rules. The complexity issue of CNMTF is also presented. Furthermore, the robustness of the proposed algorithm is analyzed, and the relationships between CNMTF and several previous NMF based methods are discussed. Experimental results demonstrate that the proposed CNMTF method has better performance on real world image and text datasets for clustering tasks, compared with several state-of-the-art methods. • The correntropy based orthogonal nonnegative matrix tri-factorization (CNMTF) algorithm is proposed. • The robustness of CNMTF is analyzed by make a comparison with several robust NMF methods. • The relationships between CNMTF and several previous NMF methods are also discussed. [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]

• Correntropy is introduced to the registration problem as a distance metric. • A closed-form solution is given out at each iterative step of the algorithm. • Pointwise correspondences are used to make sure the efficiency. • It's a general framework for m-D point set registration. The iterative closest point (ICP) algorithm is fast and accurate for rigid point set registration, but it works badly when handling noisy data or point clouds with outliers. This paper instead proposes a novel method based on the ICP algorithm to deal with this problem. Firstly, correntropy is introduced into the rigid registration problem which could handle noises and outliers well, and then a new energy function based on maximum correntropy criterion is proposed. After that, a new ICP algorithm based on correntropy is proposed, which performs well in dealing with rigid registration with noises and outliers. This new algorithm converges monotonically from any given parameters, which is similar to the ICP algorithm. Experimental results demonstrate its accuracy and robustness compared with the traditional ICP algorithm. [ABSTRACT FROM AUTHOR]

The adaptive variable step-size technique is an effective way to improve the convergence rate of an adaptive filtering algorithm. However, for most existing variable step-size sign algorithm against impulsive noise, either the performance is not good enough, or the calculation is complex. In this paper, a correntropy inspired variable step-size method for sign algorithm is proposed. The new variable step-size method is computationally simple and robust to impulsive noises. Theoretical analysis and simulation results demonstrate that the proposed algorithm can achieve desirable performance with low computational complexity in presence of impulsive noises. [ABSTRACT FROM AUTHOR]