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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]

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]

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]

• 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]

• A novel hypergraph based semi-supervised SNMF method is proposed for image clustering. • A new hypergraph based pairwise constraints propagation algorithm is presented. • The proposed method is analysed in terms of convergence, supervisory information, and computational complexity. • Extensive experiments confirm the effectiveness of the proposed method in clustering applications. Semi-supervised symmetric nonnegative matrix factorization (SNMF) has been shown to be a significant method for both linear and nonlinear data clustering applications. Nevertheless, existing SNMF-based methods only adopt a simple graph to construct the similarity matrix, and cannot fully use the limited supervised information for the construction of the similarity matrix. To overcome the drawbacks of previous SNMF-based methods, a new semi-supervised SNMF-based method called hypergraph based semi-supervised SNMF (HSSNMF), is proposed in this paper for image clustering. Specifically, HSSNMF adopts a predefined hypergraph to build a similarity matrix for capturing the high-order relationships of samples. By exploiting a new hypergraph based pairwise constraints propagation (HPCP) algorithm, HSSNMF propagates the pairwise constraints of the limited data points to the entire data points, which can make full use of the limited supervised information and construct a more informative similarity matrix. Using the multiplicative updating algorithm, a discriminative assignment matrix can then be obtained by solving the optimization problem of HSSNMF. Moreover, analyses of the convergence, supervisory information, and computational complexity of HSSNMF are presented. Finally, extensive clustering experiments have been conducted on six real-world image datasets, and the experimental results have demonstrated the superiority of HSSNMF while compared with several state-of-the-art methods. [ABSTRACT FROM AUTHOR]