Tensor-based multi-view subspace clustering (MVSC) has achieved significant success by capturing high-order inter-view correlations. However, existing approaches face two principal limitations. First, most methods either exclusively emphasize the inter-view low‑rankness (R) prior while neglecting the intra-view local smoothness (S) prior, or treat R and S as two separate regularizers—complicating joint optimization. Second, conventional tensor‑based methods impose only low‑rank constraints on the representation tensor, which limits their ability to simultaneously model consistency and complementary information. To address these issues, we propose a Unified View Extraction with Low‑Rankness and Smoothness Fusion (UVELRS) method. Our framework first extracts a consistent cross‑view representation and then constructs a tensor by stacking these representations. We introduce a novel tensor total variation Schatten-p norm that simultaneously encodes both R and S priors while offering flexible singular‑value control. This unified formulation effectively captures both high-order inter-view correlations and intra-view local smoothness. Extensive experiments on real‑world datasets demonstrate UVELRS's superior performance and robustness.

The multi-view clustering methods based on tensor regression can make full use of the potential structural information between views and achieve data-level fusion. However, existing tensor regression-based approaches for anchor graph often overlook the probabilistic nature of anchor graph, focusing solely on sample labels while ignoring the influence of anchor labels on clustering results. To overcome these limitations, we introduce Tensorized Label Learning via Balanced Tensor Regression (TLL-BTR). Our key idea is to exploit the probabilistic nature of the anchor graph by regarding the sample labels as a projection tensor that maps the anchor graph into the label space, thereby producing anchor labels. By enforcing constraints on these anchor labels, we guide the concurrent learning of sample labels and achieve co-label learning between anchors and samples. To prevent trivial solutions, we maximize the nuclear norm to promote an even distribution of samples across clusters. Extensive experiments on benchmark datasets demonstrate that TLL-BTR consistently outperforms state-of-the-art methods.

Multi-view clustering (MVC) is intended to enhance clustering performance by integrating complementary information from diverse sources. However, prevailing low-rank tensor based MVC methods often exhibit suboptimal performance, as they tend to treat singular values equally and lack structured sparsity constraints. A novel framework termed EUGL-WTSN is proposed to address the drawbacks of existing methods. It enhances unified graph learning and low-rank tensor learning model through the joint application of weighted tensor Schatten$p$-norm and$\ell \_{1,2}$-norm. Specifically, weighted tensor Schatten$p$-norm is employed in our model to more accurately capture inter-view relationships and spatial structures embedded within the multi-view data. This approach yields a tighter relaxation bound for the tensor rank through adaptive truncation of singular values. Furthermore, the$\ell \_{1,2}$-norm regularization is applied to the view-specific affinity matrices to induce row sparsity, which enhances the discriminability and robustness of the learned graph structures. To optimize the proposed model, we propose an efficient iterative optimization algorithm with provable convergence guarantees. Experimental evaluations reveal that our proposed framework achieves better performance than existing methodologies, demonstrating significant improvements in clustering performance and model robustness. Codes and datasets are available:https://github.com/yangming1984/EUGL-WTSN.

Existing multi-view clustering methods often separate feature learning from clustering, leading to suboptimal preservation of global structure and increased reliance on heuristic post-processing. Recently risen tensor-based approaches better model cross-view correlations but still fail to fully capture intrinsic sample relationships. To tackle these shortcomings, we propose a unified one-step multi-view clustering framework (MCOC) that combines contrastive learning, tensor-based self-representation, and nonnegative symmetric matrix factorization. View-specific self-representation matrices are obtained via contrastive learning and arranged along the third mode to form a third-order tensor to capture global consensus across multiple views, then view-specific self-representation matrices are symmetrized to construct affinity graphs. Joint factorization of degree-normalized affinity matrices yields a shared nonnegative indicator matrix, enabling direct cluster assignment. Experiments on real-world datasets validate the superior clustering performance of the proposed method, effectively fusing local view-specific and global structural information.

Multi-view clustering (MVC) aims to uncover the consistent structure and latent distribution of data by integrating information from diverse perspectives. A series of MVC models have been developed, but most of them are limited. They either naively fuse multi-view data into a single view or process each view in isolation, thereby neglecting the complex relationships between views. Among which, multi-stage approaches are heavily dependent on pre-learning and post-processing steps. To overcome these limitations, a one-stage MVC model, namely the embedded multi-view clustering approach with tensor self-representation and adaptive graph learning (EMCTGL), is proposed. In the proposed model, a step-structured data tensor is constructed and then decomposed to learn a cross-view self-representation tensor, effectively capturing the global topological relationships across all views. To achieve a clearer global subspace structure, a novel TLog-induced non-convex low-rank regularization is imposed on the rotated representation tensor. Under relaxed symmetry constraints, the self-representative tensor guides the learning of view-specific affinity graphs and a σ-norm penalty is applied to promote approximation of symmetry of affinity graphs. Subsequently, the normalized view-specific graphs are adaptively fused and factorized into the final clustering indicator matrix by embedding the semi-non-negative decomposition within a one-stage framework. To reduce the computational complexity, EMCTGL is extended to an anchor-driven MVC through determining anchors based on an adaptive density-peak strategy. Effective optimization schemes are devised to solve these non-convex models. Extensive experiments on various real-world datasets demonstrate that EMCTGL outperforms current state-of-the-art techniques.

Multi-view clustering based on anchor graphs has attracted significant attention due to its ability to substantially reduce computational complexity, enabling the efficient processing of large-scale multimedia data. However, most existing anchor graph-based clustering methods fail to fully exploit the intrinsic properties of anchor graphs when applying regression techniques. Moreover, some approaches focus solely on sample labels while overlooking the crucial role of anchor labels in clustering. To address these limitations, we leverage the probabilistic information of the anchor graph by employing probabilistic projection to map the anchor graph into the label space, thereby obtaining anchor labels. By clustering both anchors and samples simultaneously, the anchor graph serves as a guide to induce anchor labels, which are then used to generate sample labels, facilitating anchor-guided sample clustering. Furthermore, we propose a novel regularization paradigm based on the matrix nuclear norm, ensuring that the obtained results remain discrete and that the sample distribution across clusters is balanced. Additionally, we introduce a new matrix nuclear norm optimization method based on the first-order Taylor expansion. Extensive experiments on real-world datasets demonstrate the effectiveness and robustness of our proposed method, achieving superior performance compared to state-of-the-art approaches. Our code is available at:https://github.com/harunakai/ADMC

Manifold learning and $K$K-means are two powerful techniques for data analysis in the field of artificial intelligence. When used for label learning, a promising strategy is to combine them directly and optimize both models simultaneously. However, a significant drawback of this approach is that it represents a naive and crude integration, requiring the optimization of all variables in both models without achieving a truly essential combination. Additionally, it introduces an extra hyperparameter and cannot ensure cluster balance. These challenges motivate us to explore whether a meaningful integration can be developed for dimensionality reduction clustering. In this paper, we propose a novel self-supervised manifold clustering framework that reformulates the two models into a unified framework, eliminating the need for additional hyperparameters while achieving dimensionality reduction clustering. Specifically, by analyzing the relationship between $K$K-means and manifold learning, we construct a meaningful low-dimensional manifold clustering model that directly produces the label matrix of the data. The label information is then used to guide the learning of the manifold structure, ensuring consistency between the manifold structure and the labels. Notably, we identify a valuable role of ${\ell _{2,p}}$ℓ2,p-norm regularization in clustering: maximizing the ${\ell _{2,p}}$ℓ2,p-norm naturally maintains class balance during clustering, and we provide a theoretical proof of this property. Extensive experimental results demonstrate the efficiency of our proposed model.

Multi-view clustering (MVC) strives to reveal the hidden correlations and potential distribution of data from multiple views. However, most existing methods separate feature extraction and clustering processes, relying heavily on pre-learning and post-processing, leading to information loss and suboptimal clustering results. Therefore, we propose a novel embedded multi-view clustering model EMVCTM via collaborative tensor subspace representation and adaptive multi-graph fusion. The tensor self-representation framework is designed to capture global structural information. Symmetry constraints are relaxed synchronously to adaptively learn view-specific affinity graphs and dynamically generate fusion graph. The near-global optimal clustering result is derived through an efficient embedded clustering framework with activated view interactions, providing a more interpretable explanation for cluster division. Experimental results on various real-world datasets confirm that EMVCTM outperforms existing state-of-the-art techniques.

Multi-view clustering leverages the complementary and compatible information among various views to achieve superior clustering outcomes. The approach of multi-view clustering through non-negative matrix factorization (NMF) has garnered extensive interest, attributed to its remarkable interpretability and clustering efficacy. Nonetheless, existing NMF-based multi-view subspace clustering methods fall short in thoroughly harnessing the complementary information across different views, potentially impairing clustering performance. To mitigate this issue, we introduce an orthogonal semi-nonnegative matrix tri-factorization model. This model excels in clustering interpretability, enabling the direct derivation of cluster labels from the clustering indicator matrix, thereby eliminating the need for post-processing. Our model employs tensor Schatten p-norm as a constraint, adeptly capturing both the complementary information and spatial structure information across views. Extensive experimental evaluations on a variety of benchmark datasets affirm the superior clustering performance of our proposed method.

Large-scale multi-view clustering for image data has achieved impressive clustering performance and efficiency. However, most methods lack interpretability in clustering and do not fully consider the complementarity of distributions between different views. To address these problems, we introduce Multi-View Clustering with Transition Probabilities Learning (MVC-TPL). Specifically, we construct an anchor graph factorization model from the perspective of transition probabilities, while simultaneously learning transition probability matrices from samples to clusters and from anchor points to clusters, serving as soft label matrices for samples and anchor points, respectively. This model enables one-step label acquisition and provides the model with a sound probability interpretation. Moreover, since the clusters of samples and anchor points should be consistent across all views, we employ Schatten p-norm regularization on the two matrices, effectively mining the complementary information distributed among the views, thereby aligning the labels across views more consistently. Comprehensive testing on four small-scale datasets and three large-scale datasets confirms the effectiveness of this model.

Late fusion-based algorithms have attracted extensive attention because of their low time and space complexity for handling in-complete multiview data. However, these methods have certain limitations. First, the basic clustering indicator matrices generated by incomplete views are susceptible to low-quality imputation. Second, traditional methods often fail to adequately consider the high-order correlations between these basic clustering indicator matrices, leading to suboptimal performance. Third, conventional methods focus primarily on improving speed, with less emphasis on enhancing clustering performance. To address these issues, we propose two novel models. The first is called tensor-based late fusion incomplete multiview clustering (TLF-IMVC-1). Specifical-ly, TLF-IMVC-1 first seeks a consensus clustering matrix from the basic clustering indicator matrices and subsequently imputes the incomplete portions of these matrices via the learned consen-sus matrix. This approach seamlessly integrates the clustering process with the imputation of missing elements into a unified framework. Furthermore, we construct a third-order tensor from these basic clustering matrices, constrained by the tensor nuclear norm, to capture their high-order correlations. Although this model is effective, it lacks proper guidance in the learning process of the basic clustering indicator matrices, making them susceptible to low-quality imputation. Therefore, we introduce the second novel model, i.e., TLF-IMVC-2, to address this issue. Specifically, TLF-IMVC-2 uses the learned consensus representation matrix as a new component to construct the third-order tensor. This strategy leverages the robust clustering structure inherent in the consensus matrix to guide the learning process of the basic clustering matrices. The experimental results demonstrate that both models outperform state-of-the-art methods in clustering.

Recently, a strong interest has been in multiview high-dimensional data collected through cross-domain or various feature extraction mechanisms. Nonnegative matrix factorization (NMF) is an effective method for clustering these high-dimensional data with clear physical significance. However, existing multiview clustering based on NMF only measures the difference between the elements of the coefficient matrix without considering the spatial structure relationship between the elements. And they often require postprocessing to achieve clustering, making the algorithms unstable. To address this issue, we propose minimizing the Schatten p-norm of the tensor, which consists of a coefficient matrix of different views. This approach considers each element's spatial structure in the coefficient matrices, crucial for effectively capturing complementary information presented in different views. Furthermore, we apply orthogonal constraints to the cluster index matrix to make it sparse and provide a strong interpretation of the clustering. This allows us to obtain the cluster label directly without any postprocessing. To distinguish the importance of different views, we utilize adaptive weights to assign varying weights to each view. We introduce an unsupervised optimization scheme to solve and analyze the computational complexity of the model. Through comprehensive evaluations of six benchmark datasets and comparisons with several multiview clustering algorithms, we empirically demonstrate the superiority of our proposed method.

Tensor robust principal component analysis (TRPCA) is a classical way for low-rank tensor recovery, which minimizes the convex surrogate of tensor rank by shrinking each tensor singular value equally. However, for real-world visual data, large singular values represent more significant information than small singular values. In this paper, we propose a nonconvex TRPCA (N-TRPCA) model based on the tensor adjustable logarithmic norm. Unlike TRPCA, our N-TRPCA can adaptively shrink small singular values more and shrink large singular values less. In addition, TRPCA assumes that the whole data tensor is of low rank. This assumption is hardly satisfied in practice for natural visual data, restricting the capability of TRPCA to recover the edges and texture details from noisy images and videos. To this end, we integrate nonlocal self-similarity into N-TRPCA, and further develop a nonconvex and nonlocal TRPCA (NN-TRPCA) model. Specifically, similar nonlocal patches are grouped as a tensor and then each group tensor is recovered by our N-TRPCA. Since the patches in one group are highly correlated, all group tensors have strong low-rank property, leading to an improvement of recovery performance. Experimental results demonstrate that the proposed NN-TRPCA outperforms existing TRPCA methods in visual data recovery. The demo code is available at https://github.com/qguo2010/NN-TRPCA.

Significant advances in graph-oriented clustering methods can be attributed to their effectiveness in leveraging relationships and complex structures within multiview data. However, several limitations persist in most existing graph-based multiview clustering approaches. First, quadratic or cubic complexity is required for graph construction or eigendecomposition of the Laplacian matrix in many existing methods. Second, certain methods overlook the differences between views and employ an identical indicator matrix, which can lead to over-learning in practical scenarios. Third, existing methods often neglect spatial structure and complementary information, focusing primarily on calculating error feature-by-feature using different norms. In order to tackle these drawbacks, we propose a new multiview spectral clustering model called A nchor G raph-based M ultiview S pectral C lustering(AG-MSC). AG-MSC incorporates an adaptive weighting mechanism that assigns weights to each view, enhancing the robustness of the algorithm. Using a tensor Schatten p -norm constraint minimizes the discrepancy between indicator matrices obtained from different views, thereby preserving high-order information and spatial structure. To improve computational efficiency, we replace the full adjacency matrices of the corresponding views with anchor graphs. AG-MSC offers a distinct advantage over conventional spectral clustering by directly obtaining all sample categories without additional post-processing steps. We have validated the efficiency of our method through extensive experimental evaluations.

How to handle large multidimensional datasets, such as hyperspectral images and video information, efficiently and effectively plays a critical role in big-data processing. The characteristics of low-rank tensor decomposition in recent years demonstrate the essentials in describing the tensor rank, which often leads to promising approaches. However, most current tensor decomposition models consider the rank-1 component simply to be the vector outer product, which may not fully capture the correlated spatial information effectively for large-scale and high-order multidimensional datasets. In this article, we develop a new novel tensor decomposition model by extending it to the matrix outer product or called Bhattacharya-Mesner product, to form an effective dataset decomposition. The fundamental idea is to decompose tensors structurally in a compact manner as much as possible while retaining data spatial characteristics in a tractable way. By incorporating the framework of the Bayesian inference, a new tensor decomposition model on the subtle matrix unfolding outer product is established for both tensor completion and robust principal component analysis problems, including hyperspectral image completion and denoising, traffic data imputation, and video background subtraction. Numerical experiments on real-world datasets demonstrate the highly desirable effectiveness of the proposed approach.

Nowadays, data in the real world often comes from multiple sources, but most existing multi-view ${K}$ -Means perform poorly on linearly non-separable data and require initializing the cluster centers and calculating the mean, which causes the results to be unstable and sensitive to outliers. This paper proposes an efficient multi-view ${K}$ -Means to solve the above-mentioned issues. Specifically, our model avoids the initialization and computation of clusters centroid of data. Additionally, our model use the Butterworth filters function to transform the adjacency matrix into a distance matrix, which makes the model is capable of handling linearly inseparable data and insensitive to outliers. To exploit the consistency and complementarity across multiple views, our model constructs a third tensor composed of discrete index matrices of different views and minimizes the tensor's rank by tensor Schatten ${p}$ -norm. Experiments on two artificial datasets verify the superiority of our model on linearly inseparable data, and experiments on several benchmark datasets illustrate the performance.

Due to many unmarked data, there has been tremendous interest in developing unsupervised feature selection methods, among which graph-guided feature selection is one of the most representative techniques. However, the existing feature selection methods have the following limitations: (1) All of them only remove redundant features shared by all classes and neglect the class-specific properties; thus, the selected features cannot well characterize the discriminative structure of the data. (2) The existing methods only consider the relationship between the data and the corresponding neighbor points by Euclidean distance while neglecting the differences with other samples. Thus, existing methods cannot encode discriminative information well. (3) They adaptively learn the graph in the original or embedding space. Thus, the learned graph cannot characterize the data’s cluster structure. To solve these limitations, we present a novel unsupervised discriminative feature selection via contrastive graph learning, which integrates feature selection and graph learning into a uniform framework. Specifically, our model adaptively learns the affinity matrix, which helps characterize the data’s intrinsic and cluster structures in the original space and the contrastive learning. We minimize ℓ1,2-norm regularization on the projection matrix to preserve class-specific features and remove redundant features shared by all classes. Thus, the selected features encode discriminative information well and characterize the discriminative structure of the data. Generous experiments indicate that our proposed model has state-of-the-art performance.

Due to the excellent interpretability of non-negative matrix factorization (NMF), NMF-based multi-view clustering has attracted much attention for multi-media data analysis and processing. However, the existing clustering methods leverage NMF to cluster data matrix, resulting in high computational complexity. Moreover, they are sub-optimal to exploit the complementary information between views because they all measure the between-views error pixel by pixel. To tackle this problem, inspired by orthogonal NMF and anchor graph, we present an efficient anchor graph factorization model with orthogonal, non-negative, and tensor low-rank constraints. We use an anchor graph instead of a data matrix to get an indicator matrix without post-processing, which remarkably reduces the computational complexity. To exploit the between-views complementary information well, we introduce tensor Schatten$p$-norm regularization on the third tensor, composed of soft label matrices of views. The solution can be obtained by iteratively optimizing four decoupled sub-problems, which can be solved more efficiently with good convergence. Through experimental results on the six multi-view datasets, our approach ensures the enhancement of clustering performance while improving efficiency.

Although K-Means clustering has been widely studied due to its simplicity, these methods still have the following fatal drawbacks. Firstly, they need to initialize the cluster centers, which causes unstable clustering performance. Secondly, they have poor performance on non-Gaussian datasets. Inspired by the affinity matrix, we propose a novel multi-view K-Means based on the adjacency matrix. It maps the affinity matrix to the distance matrix according to the principle that every sample has a small distance from the points in its neighborhood and a large distance from the points outside of the neighborhood. Moreover, this method well exploits the complementary information embedded in different views by minimizing the tensor Schatten p-norm regularize on the third-order tensor which consists of cluster assignment matrices of different views. Additionally, this method avoids initializing cluster centroids to obtain stable performance. And there is no need to compute the means of clusters so that our model is not sensitive to outliers. Experiment on a toy dataset shows the excellent performance on non-Gaussian datasets. And other experiments on several benchmark datasets demonstrate the superiority of our proposed method.

Multi-view clustering (MVC) based on non-negative matrix factorization (NMF) and its variants have attracted much attention due to their advantages in clustering interpretability. However, existing NMF-based multi-view clustering methods perform NMF on each view respectively and ignore the impact of between-view. Thus, they can't well exploit the within-view spatial structure and between-view complementary information. To resolve this issue, we present orthogonal non-negative tensor factorization (Orth-NTF) and develop a novel multi-view clustering based on Orth-NTF with one-side orthogonal constraint. Our model directly performs Orth-NTF on the 3rd-order tensor which is composed of anchor graphs of views. Thus, our model directly considers the between-view relationship. Moreover, we use the tensor Schatten $p$-norm regularization as a rank approximation of the 3rd-order tensor which characterizes the cluster structure of multi-view data and exploits the between-view complementary information. In addition, we provide an optimization algorithm for the proposed method and prove mathematically that the algorithm always converges to the stationary KKT point. Extensive experiments on various benchmark datasets indicate that our proposed method is able to achieve satisfactory clustering performance.

Multi-modal clustering (MMC) aims to explore complementary information from diverse modalities for clustering performance facilitating. This article studies challenging problems in MMC methods based on deep neural networks. On one hand, most existing methods lack a unified objective to simultaneously learn the inter- and intra-modality consistency, resulting in a limited representation learning capacity. On the other hand, most existing processes are modeled for a finite sample set and cannot handle out-of-sample data. To handle the above two challenges, we propose a novel Graph Embedding Contrastive Multi-modal Clustering network (GECMC), which treats the representation learning and multi-modal clustering as two sides of one coin rather than two separate problems. In brief, we specifically design a contrastive loss by benefiting from pseudo-labels to explore consistency across modalities. Thus, GECMC shows an effective way to maximize the similarities of intra-cluster representations while minimizing the similarities of inter-cluster representations at both inter- and intra-modality levels. So, the clustering and representation learning interact and jointly evolve in a co-training framework. After that, we build a clustering layer parameterized with cluster centroids, showing that GECMC can learn the clustering labels with given samples and handle out-of-sample data. GECMC yields superior results than 14 competitive methods on four challenging datasets. Codes and datasets are available: https://github.com/xdweixia/GECMC.

Multi-view clustering aims to capture the multiple views inherent information by identifying the data clustering that reflects distinct features of datasets. Since there is a consensus in literature that different views of a dataset share a common latent structure, most existing multi-view subspace learning methods rely on the nuclear norm to seek the low-rank representation of the underlying subspace. However, the nuclear norm often fails to distinguish the variance of features for each cluster due to its convex nature and data tends to fall in multiple non-linear subspaces for multi-dimensional datasets. To address these problems, we propose a new and novel multi-view clustering method (HL-L21-TLD-MSC) that unifies the Hyper-Laplacian (HL) and exclusive ℓ 2,1 (L21) regularization with the Tensor Log-Determinant Rank Minimization (TLD) setting. Specifically, the hyper-Laplacian regularization maintains the local geometrical structure that makes the estimation prune to nonlinearities, and the mixed ℓ 2,1 and ℓ 1,2 regularization provides the joint sparsity within-cluster as well as the exclusive sparsity between-cluster. Furthermore, a log-determinant function is used as a tighter tensor rank approximation to discriminate the dimension of features. An efficient alternating algorithm is then derived to optimize the proposed model, and the construction of a convergent sequence to the Karush-Kuhn-Tucker (KKT) critical point solution is mathematically validated in detail. Extensive experiments are conducted on ten well-known datasets to demonstrate that the proposed approach outperforms the existing state-of-the-art approaches with various scenarios, in which, six of them achieve perfect results under our framework developed in this article, demonstrating highl effectiveness for the proposed approach.

Multi-view clustering method tries to improve the performance of clustering by using the information existing in different views. The tensorial representation is more suitable to capture the high order correlations across different views while keep local geometrical structure in specific view. In this paper, we propose a sliced sparse gradient induced multi-view subspace clustering method via tensorial arctangent rank minimization, named SSG-TAR method. Firstly, a tensorial arctangent rank (TAR) is defined, which is a tighter surrogate of the tensor rank and more effective to explore the consistency among multiple views. Secondly, a sliced sparse gradient regularization (SSG) is firstly proposed to enhance the discrimination between clusters and better capture the complementary information in view-specific feature space. Finally, we unify these two terms together and establish an efficient algorithm to optimize the proposed model. Furthermore, the constructed sequence was proved to converge to the stationary KKT point. We have carried out extensive experiments on ten datasets across different types and sizes to verify the performance of our model. The experimental results show that our method have achieved the state-of-the-art performance.

Graph-based multi-view clustering method has attracted considerable attention in multi-media data analyse community due to its good clustering performance and efficiency in characterizing the relationship between data. But the existing graph-based clustering methods still have many shortcomings. Firstly, they have high computational complexity due to the eigenvalue decomposition. Secondly, the complementary information and spatial structure embedded in different views can affect the clustering performance. However, some existing graph-based clustering methods do not consider these two points. In this article, we use the anchor graphs of different views as input, which effectively reduces the computational complexity. And then we explicitly consider the complementary information and spatial structure between anchor graphs of different views by minimizing the tensor Schatten$p$-norm, aiming to achieve a better tensor with low-rank approximation. Finally, we learn the view-consensus anchor graph with connectivity constraints, which can directly indicate clusters by self-weighted strategy. An efficient alternating algorithm is then derived to optimize the proposed multi-view special clustering model. Furthermore, the constructed sequence was proved to converge to the stationary KKT point. Experiments show that our proposed method not only reduces the time cost, but also outperforms the most advanced methods.

Attributed graph clustering, which learns node representation from node attribute and topological graph for clustering, is a fundamental and challenging task for multimedia network-structured data analysis. Recently, graph contrastive learning (GCL)-based methods have obtained impressive clustering performance on this task. Nevertheless, there still remain some limitations to be solved: 1) most existing methods fail to consider the self-consistency between latent representations and cluster structures; and 2) most methods require a post-processing operation to get clustering labels. Such a two-step learning scheme results in models that cannot handle newly generated data,i.e., out-of-sample (OOS) nodes. To address these issues in a unified framework, aSelf-consistentContrastiveAttributedGraphClustering (SCAGC) network with pseudo-label prompt is proposed in this article. In SCAGC, by clustering labels prompt information, a self-consistent contrastive loss, which aims to maximize the consistencies of intra-cluster representations while minimizing the consistencies of inter-cluster representations, is designed for representation learning. Meanwhile, a clustering module is built to directly output clustering labels by contrasting the representation of different clusters. Thus, for the OOS nodes, SCAGC can directly calculate their clustering labels. Extensive experimental results on seven benchmark datasets have shown that SCAGC consistently outperforms 16 competitive clustering methods.

In this article, we present a novel general framework for incomplete multi-view clustering by integrating graph learning and spectral clustering. In our model, a tensor low-rank constraint are introduced to learn a stable low-dimensional representation, which encodes the complementary information and takes into account the cluster structure between different views. A corresponding algorithm associated with augmented Lagrangian multipliers is established. In particular, tensor Schatten p -norm is used as a tighter approximation to the tensor rank function. Besides, both consistency and specificity are jointly exploited for subspace representation learning. Extensive experiments on benchmark datasets demonstrate that our model outperforms several baseline methods in incomplete multi-view clustering.

Multi-view spectral clustering has become appealing due to its good performance in capturing the correlations among all views. However, on one hand, many existing methods usually require a quadratic or cubic complexity for graph construction or eigenvalue decomposition of Laplacian matrix; on the other hand, they are inefficient and unbearable burden to be applied to large scale data sets, which can be easily obtained in the era of big data. Moreover, the existing methods cannot encode the complementary information between adjacency matrices, i.e., similarity graphs of views and the low-rank spatial structure of adjacency matrix of each view. To address these limitations, we develop a novel multi-view spectral clustering model. Our model well encodes the complementary information by Schatten p -norm regularization on the third tensor whose lateral slices are composed of the adjacency matrices of the corresponding views. To further improve the computational efficiency, we leverage anchor graphs of views instead of full adjacency matrices of the corresponding views, and then present a fast model that encodes the complementary information embedded in anchor graphs of views by Schatten p -norm regularization on the tensor bipartite graph. Finally, an efficient alternating algorithm is derived to optimize our model. The constructed sequence was proved to converge to the stationary KKT point. Extensive experimental results indicate that our method has good performance.

In this paper, we study the image multiview subspace clustering problem via a nonconvex low-rank representation under the framework of tensors. Most of the recent studies of tensor based multiview subspace clustering use the tensor nuclear norm as a convex surrogate of the tensor rank, i.e., the t-SVD based multiview subspace clustering model. However, since the tensor nuclear norm is linearly proportional to the sum of singular values, the tensor rank approximation by using the tensor nuclear norm may become problematic if the ratios of the nonzero singular values are far from 1. In this paper, a nonconvex tensor log-determinant function is proposed as the objective function regularizer, aiming to achieve a better tensor low-rank approximation. Instead of directly solving the minimization problem in its original setting, the corresponding non-convex optimization is conducted in the Fourier domain, which is shown not only to be feasible but also to be quite effective. A corresponding algorithm associated with the augmented Lagrangian multipliers is established and the constructed convergent sequence to the desirable Karush--Kuhn--Tucker critical point solution is mathematically validated in detail. Extensive simulations on eight benchmark image datasets are provided, along with full comparisons with the latest existing approaches. The obtained results demonstrate that our proposed method significantly outperforms those convex approaches currently available in the literature.

Recommender systems play an increasingly important role in online applications to help users find what they need or prefer. Collaborative filtering algorithms that generate predictions by analyzing the user-item rating matrix perform poorly when the matrix is sparse. To alleviate this problem, this paper proposes a simple recommendation algorithm that fully exploits the similarity information among users and items and intrinsic structural information of the user-item matrix. The proposed method constructs a new representation which preserves affinity and structure information in the user-item rating matrix and then performs recommendation task. To capture proximity information about users and items, two graphs are constructed. Manifold learning idea is used to constrain the new representation to be smooth on these graphs, so as to enforce users and item proximities. Our model is formulated as a convex optimization problem, for which we need to solve the well known Sylvester equation only. We carry out extensive empirical evaluations on six benchmark datasets to show the effectiveness of this approach.

Recovering low-rank matrices is a problem common in many applications of data mining and machine learning, such as matrix completion and image denoising. Robust Principal Component Analysis (RPCA) has emerged for handling such kinds of problems; however, the existing RPCA approaches are usually computationally expensive, due to the fact that they need to obtain the singular value decomposition (SVD) of large matrices. In this paper, we propose a novel RPCA approach that eliminates the need for SVD of large matrices. Scalable algorithms are designed for several variants of our approach, which are crucial for real world applications on large scale data. Extensive experimental results confirm the effectiveness of our approach both quantitatively and visually.

We propose a new subspace clustering method that integrates feature selection into subspace clustering. Rather than using all features to construct a low-rank representation of the data, we find such a representation using only relevant features, which helps in revealing more accurate data relationships. Two variants are proposed by using both convex and nonconvex rank approximations. Extensive experimental results confirm the effectiveness of the proposed method and models.