Federated Multi-View Clustering has gained increasing attention for its ability to discover complementary clustering structures of distributed multi-view data while preserving data privacy. However, real-world clients often only have access to partial views, and the view incompleteness poses great challenges to federated multi-view feature fusion to exploit consistent and complementary information. Moreover, efficiency is highly expected in federated scenarios due to the limited resources of each client. To alleviate these issues, we propose Federated Incomplete Multi-View Clustering with Tensorized Low-Rank Constraint (FIMVC-TLRC), which incorporates anchors to improve efficiency and is able to address prevalent view incompleteness issue in federated scenarios. FIMVC-TLRC aligns the local anchor graphs and employs a tensorized low-rank constraint based on the tensor Schatten p-norm to enforce the consistency of the data representations learned by each client. Besides, a federated optimization framework is developed to jointly optimize the construction and alignment of anchor graphs, thus enabling collaborative and privacy-preserving training. Experimental results on multiple datasets demonstrate its effectiveness.

Marginal Fisher Analysis (MFA) is a classical dimensionality reduction (DR) method that leverages dual graphs to capture intra-class compactness and inter-class separability. However, MFA’s reliance on high-quality labels limits its practical application. For another, existing unsupervised DR methods neglect data’s local manifold relationship, resulting in poor discriminativeness. To address these limitations, we propose a novel DR method named Discriminative Graph Embedding Framework (DGEF) via Label-Free Marginal Fisher Analysis. Our approach uses the adjacency matrix and cluster indicator matrix derived from centerless K-Means to construct intrinsic graph and penalty graph, which preserve the local manifold structure of the data. Additionally, we have derived the convertible relationship between centerless K-Means and Manifold learning and unified them within a graph embedding framework. By adopting the intrinsic graph and penalty graph, our DGEF avoids centroid initialization and ensures robustness and discriminativeness. This method achieves dimensionality reduction adaptively without relying on labeled data. Extensive experiments on benchmark datasets show that our approach outperforms conventional methods in clustering performance.

Fair incomplete multi-view clustering (FIMVC) confronts a critical yet unresolved challenge, as existing methods often fail to address the intertwined issues of data missingness and algorithmic bias simultaneously. In this paper, we propose a novel FIMVC method named Adversarial Fair Incomplete Multi-View Clustering (AFIMVC). The core of AFIMVC is a new adaptive adversarial disentanglement mechanism. This mechanism trains the feature encoder to produce representations that are invariant to sensitive attributes by adversary learning, where the adversarial intensity is dynamically controlled by the model's real-time bias. Additionally, we develop a probabilistic cross-view contrastive learning strategy to achieve semantic consistency in latent space. To handle missing data, AFIMVC employs a context-aware fusion strategy that leverages cross-sample attention to robustly synthesize a unified representation from incomplete views. Extensive experiments demonstrate that AFIMVC achieves a state-of-the-art balance between clustering accuracy and fairness, significantly outperforming existing methods.

Locality Preserving Projections (LPP) aims to find a projection matrix to map the high-dimensional data into a low-dimensional subspace while preserving the local manifold structure, which is a classical unsupervised subspace learning method. However, the lack of label guidance makes LPP not able to fully exploit the discriminative information of the data. To solve the problem, we propose a Self-Guided Discriminative LPP algorithm employing pseudo labels learned by K-Means to guide the subspace learning. In this way, it facilitates the discovery of discriminative cluster information while preserving inherent manifold structure. Besides, considering K-Means' sensitivity to selection of cluster centroids, we introduce a centerless K-Means method to improve robustness by eliminating the need of centroid initialization. We also discuss the internal relationship between K-Means and LPP, and prove that K-Means can be written in the form of LPP under certain conditions. Experiments on seven benchmark datasets demonstrate that our method greatly improves the clustering performance.

Current deep multi-modal graph clustering methods primarily rely on Graph Neural Network (GNN) to fully exploit attribute features and graph structures, including message propagation and low-dimensional feature embedding. However, these methods lack further exploration of graph structural information, such as the relationship between nodes and shortest paths. Additionally, they may not sufficiently mine complementary information among multi-modal graph data. To address these issues, we propose a novel Deep Multi-modal Graph Clustering via Graph Transformer Network method, called DMGC-GTN. This method thoroughly dissects and utilizes graph structural information, applying graph smoothing to node features and incorporating various forms of embeddings into the transformer architecture. This achieves a unified embedding of graph structure and multi-modal feature attributes, fully exploiting the complementary information within multi-modal graph data. Extensive experiments demonstrate the effectiveness of our algorithm.

Multi-view clustering (MVC) methods have garnered considerable attention within centralized data frameworks. However, real-world multi-view data are often collected and stored by different organizations, complicating the practical deployment of MVC and motivating the emergence of federated multi-view clustering (FMVC). Existing FMVC approaches typically necessitate post-processing to derive clustering labels and confront challenges in effectively exploring the complementary and consistent information across multi-view data residing in different entities. To address these limitations, we propose a novel framework termed Scalable Federated One-Step Multi-View Clustering with Tensorized Regularization (SFOMVC-TR). This framework facilitates one-step clustering at each client and employs tensor learning to capture consistent and complementary information through a centralized server. Additionally, it adopts anchor graphs to enhance clustering efficiency and scalability in high-dimensional data. By incorporating a Lp,q sparse regularization on the projection matrix, SFOMVC-TR enables the direct projection of anchors into clustering assignments to mitigate redundancy. A federated optimization framework is developed to support collaborative and privacy-preserving training under the coordination of the server. Extensive experiments on multiple datasets validate the privacy and effectiveness of our method.

Multi-view clustering aims to identify consistent and complementary information across multiple views to partition data into clusters, emerging as a popular unsupervised method for multi-view data analysis. However, existing methods often design view-specific encoders to extract distinct features from each view, lacking exploration of their complementarity. Additionally, current contrastive-based multi-view clustering methods may lead to erroneous negative sample pairs conflicting with the clustering objective. To address these challenges, we propose a novel Contrastive Multi-view Subspace Clustering via Tensor Transformers Autoencoder (TTAE). On the one hand, it facilitates information exchange between views by tensor transformers autoencoder, thereby enhancing complementarity. On the other hand, It learns a consistent subspace with a self-expression layer. Meanwhile, adaptive contrastive learning helps to provide more discriminative features for the self-expression learning layer, and the self-expression learning layer in turn supervises contrastive learning. Moreover, our method adaptively selects positive and negative samples for contrastive learning to mitigate the impact of inappropriate negative sample pairs. Extensive experiments on several multi-view datasets demonstrate the effectiveness and superiority of our model.

Multi-view graph clustering methods have been widely concerned due to the ability of dealing with arbitrarily shaped datasets. However, many methods with higher time and space complexity make them challenging to deal with large-scale datasets. Besides, many fuzzy clustering methods needs additional regularization terms or hyper-parameters to obtain the membership matrix or avoid trivial solutions, which weakens the model generalization ability. Furthermore, inconsistent clustering labels can arise when there are significant discrepancies between views, making it challenging to effectively leverage the complementary information from different views. To this end, we propose Tensorized Label Learning based Fast Fuzzy Clustering (TLLFFC). Specifically, we design a novel balanced regularization term to reduce pressure of tuning regularization parameters for fuzzy clustering. The label transmission strategy with the anchor graph makes TLLFFC suitable for large-scale datasets. Moreover, incorporating the Schatten p-norm regularization on the label matrices can effectively unearth the complementary information distributed among views, thereby align the labels across views more consistently. Extensive experiments verify the superiority of TLLFFC.

Multi-view clustering is effective in unsupervised multi-view data analysis and has received considerable attention. However, most existing methods excessively emphasize certain attributes, resulting in unfair clustering outcomes, i.e., certain sensitive attributes dominate the clustering results. Moreover, existing methods struggle to effectively capture complex nonlinear relationships and interactions across views, limiting their ability to achieve optimal clustering performance. Therefore, in this work, we propose a novel method, Deep Fair Multi-View Clustering with Attention Kolmogorov-Arnold Network (DFMVC-AKAN), to generate fair clustering results while maintaining robust performance. DFMVC-AKAN integrates attention mechanisms into Kolmogorov-Arnold Networks (KAN) to exploit the complex nonlinear inter-view relationships. Specifically, KAN provides a nonlinear feature representation capable of efficiently approximating arbitrary multivariate continuous functions, augmented by a hybrid attention mechanism which enables the model to dynamically focus on the most relevant features. Finally, we refine the clustering assignments with a distribution alignment module to ensure fair outcomes across diverse groups while maintaining discriminative ability. Experimental results on four datasets containing sensitive attributes demonstrate that DFMVC-AKAN significantly improves fairness and clustering performance compared to state-of-the-art methods.

The success of existing deep multi-view graph clustering methods is based on the assumption that node attributes are fully available across all views. However, in practical scenarios, node attributes are frequently missing due to factors such as data privacy concerns or failures in data collection devices. Although some methods have been proposed to address the issue of missing node attributes, they come with the following limitations: i) Existing methods are often not tailored specifically for clustering tasks and struggle to address missing attributes effectively. ii) They tend to ignore the relational dependencies between nodes and their neighboring nodes. This oversight results in unreliable imputations, thereby degrading clustering performance. To address the above issues, we propose an Attribute-Missing Multi-view Graph Clustering (AMMGC). Specifically, we first impute missing node attributes by leveraging neighbor-hood information through an adjacency matrix. Then, to improve the consistency, we integrate a dual structure consistency module that aligns graph structures across multiple views, reducing redundancy and retaining key information. Furthermore, we introduce a high-confidence guidance module to improve the reliability of clustering. Extensive experiment results showcase the effectiveness and superiority of our proposed method on multiple benchmark datasets.

K-Means clustering is a classical and effective unsupervised learning method attributed to its simplicity and efficiency. However, it faces notable challenges, including sensitivity to random initial centroid selection, a limited ability to discover the intrinsic manifold structures within nonlinear datasets, and difficulty in achieving balanced clustering in practical scenarios. To overcome these weaknesses, we introduce a novel framework for K-Means that leverages manifold learning. This approach eliminates the need for centroid calculation and utilizes a cluster indicator matrix to align the manifold structures, thereby enhancing clustering accuracy. Beyond the traditional Euclidean distance, our model incorporates Gaussian kernel distance, K-nearest neighbor distance, and low-pass filtering distance to effectively manage data that is not linearly separable. Furthermore, we introduce a balanced regularizer to achieve balanced clustering results. The detailed experimental results demonstrate the efficacy of our proposed methodology.

Linear Discriminant Analysis (LDA) is a classical supervised dimensionality reduction algorithm. However, LDA focuses more on global structure and overly depends on reliable data labels. For data with outliers and nonlinear structures, LDA cannot effectively capture the true structure of the data. Moreover, the subspace dimension learned by LDA must be smaller than cluster number, which limits its practical applications. To address these issues, we propose a novel unsupervised LDA method that combines centerless K-means and LDA. This method eliminates the need to calculate cluster centroids and improves model robustness. By fusing centerless K-means and LDA into a unified framework and deducing the connection between K-means and manifold learning, this method captures the local manifold structure and discriminative structure. Additionally, the dimensionality of the subspace is not restricted. This method not only overcomes the limitations of traditional LDA but also improves the model’s adaptability to complex data. Extensive experiments on seven datasets demonstrate the effectiveness of the proposed method.

Contrastive multi-view clustering has demonstrated remarkable potential in complex data analysis, yet existing approaches face two critical challenges: difficulty in constructing high-quality positive and negative pairs and high computational overhead due to static optimization strategies. To address these challenges, we propose an innovative efficient Multi-View Clustering framework with Reinforcement Contrastive Learning (EMVCRCL). Our key innovation is developing a reinforcement contrastive learning paradigm for dynamic clustering optimization. First, we leverage multi-view contrastive learning to obtain latent features, which are then sent to the reinforcement learning module to refine low-quality features. Specifically, it selects high-confident features to guide the positive/negative pair construction of contrastive learning. For the low-confident features, it utilizes the prior balanced distribution to adjust their assignment. Extensive experimental results showcase the effectiveness and superiority of our proposed method on multiple benchmark datasets.

Hypergraph Clustering has gained significant attention due to its capability of capturing high order structural information. Among different approaches, contrastive learning-based methods leverage self-supervised learning and data augmentation, exhibiting impressive performance. However, most of them come with the following limitations: 1) Augmentation strategies like feature dropout can potentially disrupt the intrinsic clustering structure of hypergraphs. 2) High computational demands hinder their real-world application. To address the above issues, we propose a simple yet effective Hypergraph Clustering Network framework (HCN). Specifically, HCN replaces the hypergraph convolution operation with smoothing preprocessing, which avoids high computational complexity. Besides, to retain intrinsic structure, it develops two key modules: the self-diagonal consistency module and the structure alignment mod ule. They respectively align the similarity matrix with the identity matrix and the structural affinity matrix, which ensures intra-cluster compact ness and inter-cluster separability. Extensive experiments on five benchmark datasets demonstrate HCN’s superiority over state-of-the-art methods.

Federated Multi-View Clustering (FedMVC) aims to uncover consistent clustering structures from distributed multi-view data for clustering while preserving data privacy. However, existing FedMVC methods under vertical settings either ignore the ubiquitous incomplete view issue or require uploading data features, which may lead to privacy leakage or induce high communication costs. To mitigate the view incompleteness issue and simultaneously maintain privacy and efffciency, we propose a novel Federated Multiview Graph Clustering with Incomplete Attribute Imputation (FMVC-IAI). This method constructs a consensus graph structure through complementary multi-view data and then utilizes a non-parametric graph neural network (GNN) to impute missing features. Additionally, it utilizes the adjacency graph as the knowledge carrier to share and fuse the multi-view information. To alleviate the high communication cost due to graph sharing, we proposed to share the anchor graph for global adjacency graph construction, which reduces communication cost and also helps to reduce privacy leakage risk. Extensive experiments demonstrate the superiority of our method in FedMVC tasks with incomplete views.

Multi-view clustering (MVC) has emerged as an important unsupervised multi-view learning method that leverages consistent and complementary information to enhance clustering performance. Recently, tensorized MVC, which processes multi-view data as a tensor to capture their cross-view information, has received considerable attention. However, existing tensorized MVC methods generally overlook deep structures within each view and rely on post-processing to derive clustering results, leading to potential information loss and degraded performance. To address these issues, we develop Tensorial Multi-view Clustering with Deep Anchor Graph Projection (TMVC-DAGP), which performs deep projection on the anchor graph, thus improving model scalability. Besides, we utilize a sparsity regularization to eliminate the redundancy and enforce the projected anchor graph to retain a clear clustering structure. Furthermore, TMVC-DAGP leverages weighted Tensor Schatten $p$-norm to exploit the consistent and complementary information. Extensive experiments on multiple datasets demonstrate TMVC-DAGP's effectiveness and superiority.

Incomplete multi-view clustering (IMVC) extracts consistent and complementary information from multi-source/modality data with missing views, aiming to partition the data into different clusters. It can effectively address the problem of unsupervised multi-source data analysis in complex environments and has gained considerable attention. However, the fairness of IMVC remains underexplored, particularly when data contains sensitive features ({e.g.}, gender, marital status, and age). To tackle the problem, this work presents a novel Fair Incomplete Multi-View Clustering (FIMVC) method. The proposed FIMVC introduces fairness constraints to ensure clustering results are independent of sensitive features. Additionally, it learns consensus representations to enhance clustering performance by maximizing mutual information and aligning the distributions of different views. Experimental results on three datasets containing sensitive features demonstrate that our method improves the fairness of clustering results while outperforming state-of-the-art IMVC methods in clustering performance.

Remote sensing image classification with noisy labels is receiving increasing attention. However, the existing methods ignore the context information of the training sample and judge whether the label is a noise label only by monitoring the loss value of a single sample, which may lead to misjudgment of the sample label. Additionally, these algorithms do not consider constructing pairs of confidence instances to obtain robust potential representations after identifying confidence instances. In this paper, a Multi-view Collaborative Representation Learning (MCRL) approach from noisy labels is proposed to improve the classification performance of very high resolution (VHR) remote sensing images. Specifically, we design a correction strategy based on spatial consistency and confidence-aware mechanisms. This strategy quantitatively measures label reliability by mining the contextual information of labelled samples within the adaptive region. Leveraging the spatial consistency principle and the confidence-aware mechanism to correct and smooth the noisy labels progressively. Moreover, we construct confidence sample pairs by establishing relationships between samples within and between views to obtain robust latent representations, which improves the model's tolerance to noisy labels. Experiments show that the MCRL can significantly reduce the impact of noisy labels on the model and is more competitive than homologous algorithms.

Although numerous clustering algorithms have been developed, many existing methods still rely on the K-means technique to identify clusters of data points. However, the performance of K-means is highly dependent on the accurate estimation of cluster centers, which is challenging to achieve optimally. Furthermore, it struggles to handle linearly non-separable data. To address these limitations, from the perspective of manifold learning, we reformulate multi-view K-means into a manifold-based multi-view clustering formulation that eliminates the need for computing centroid matrix. This reformulation ensures consistency between the manifold structure and the data labels. Building on this, we propose a novel multi-view K-means model incorporating the tensor rank constraint. Our model employs the indicator matrices from different views to construct a third-order tensor, whose rank is minimized via the tensor Schatten p-norm. This approach effectively leverages the complementary information across views. By utilizing different distance functions, our proposed model can effectively handle linearly non-separable data. Extensive experimental results on multiple databases demonstrate the superiority of our proposed model.

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.

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.

Partial multi-view clustering is a challenging and practical research problem for data analysis in real-world applications, due to the potential data missing issue in different views. However, most existing methods have not fully explored the correlation information among various incomplete views. In addition, these existing clustering methods always ignore discovering discriminative features inside the data itself in this unsupervised task. To tackle these challenges, we propose Partial Multi-View Clustering via Self-Supervised \textbf{N}etwork (PVC-SSN) in this paper. Specifically, we employ contrastive learning to obtain a more discriminative and consistent subspace representation, which is guided by a self-supervised module. Self-supervised learning can exploit effective cluster information through the data itself to guide the learning process of clustering tasks. Thus, it can pull together embedding features from the same cluster and push apart these from different clusters. Extensive experiments on several benchmark datasets show that the proposed PVC-SCN method outperforms several state-of-the-art clustering methods.

Graph-based multimedia data clustering has attracted much attention due to the impressive clustering performance for arbitrarily shaped multimedia data. However, existing graph-based clustering methods need post-processing to get labels for multimedia data with high computational complexity. Moreover, it is sub-optimal for label learning due to the fact that they exploit the complementary information embedded in data with different types pixel by pixel. To handle these problems, we present a novel label learning model with good interpretability for clustering. To be specific, our model decomposes anchor graph into the products of two matrices with orthogonal non-negative constraint to directly get soft label without any post-processing, which remarkably reduces the computational complexity. To well exploit the complementary information embedded in multimedia data, we introduce tensor Schatten p-norm regularization on the label tensor which is composed of soft labels of multimedia data. The solution can be obtained by iteratively optimizing four decoupled sub-problems, which can be solved more efficiently with good convergence. Experimental results on various datasets demonstrate the efficiency of our model.

Recently, anchor graph-based multi-view clustering has been proven to be highly efficient for large-scale data processing. However, most existing anchor graph-based clustering methods necessitate post-processing to obtain clustering labels and are unable to effectively utilize the information within anchor graphs. To solve these problems, we propose an Embedded Feature Selection on Graph-Based Multi-View Clustering (EFSGMC) approach to improve the clustering performance. Our method decomposes anchor graphs, taking advantage of memory efficiency, to obtain clustering labels in a single step without the need for post-processing. Furthermore, we introduce the l2,p-norm for graph-based feature selection, which selects the most relevant data for efficient graph factorization. Lastly, we employ the tensor Schatten p-norm as a tensor rank approximation function to capture the complementary information between different views, ensuring similarity between cluster assignment matrices. Experimental results on five real-world datasets demonstrate that our proposed method outperforms state-of-the-art approaches.

Multi-view clustering method based on anchor graph has been widely concerned due to its high efficiency and effectiveness. In order to avoid post-processing, most of the existing anchor graph-based methods learn bipartite graphs with connected components. However, such methods have high requirements on parameters, and in some cases it may not be possible to obtain bipartite graphs with clear connected components. To end this, we propose a label learning method based on tensor projection (LLMTP). Specifically, we project anchor graph into the label space through an orthogonal projection matrix to obtain cluster labels directly. Considering that the spatial structure information of multi-view data may be ignored to a certain extent when projected in different views separately, we extend the matrix projection transformation to tensor projection, so that the spatial structure information between views can be fully utilized. In addition, we introduce the tensor Schatten p-norm regularization to make the clustering label matrices of different views as consistent as possible. Extensive experiments have proved the effectiveness of the proposed method.

Multi-view clustering (MVC) methods based on non-negative matrix factorization (NMF) have gained popularity owing to their ability to provide interpretable clustering results. However, these NMF-based MVC methods generally process each view independently and thus ignore the potential relationship between views. Besides, they are limited in the ability to capture nonlinear data structures. To overcome these weaknesses and inspired by deep learning, we propose a multi-view clustering method based on deep non-negative tensor factorization (MVC-DNTF). With deep tensor factorization, our method can well exploit the spatial structure of the original data and is capable of extracting more deep and nonlinear features embedded in different views. To further extract the complementary information of different views, we adopt the weighted tensor Schatten p-norm regularization term. An optimization algorithm is developed to effectively solve the MVC-DNTF objective. Extensive experiments are performed to demonstrate the effectiveness and superiority of our method.

Multi-view clustering has emerged as an important unsupervised method to process unlabelled multi-view data that provides a comprehensive description of an object. Existing multi-view clustering methods focus on centralized settings but ignore the fact that real-world multi-view data may be distributed across different entities. The sensitive information embedded in multi-view data hinders the cooperative training of multi-view clustering, since data of different views cannot be directly shared, leading to a great challenge to cooperatively exploit the consistent and complementary information of different views. To validate the multi-view clustering in distributed scenarios, in this paper, we propose a novel federated multi-view method named Federated Multi-View Fuzzy C-means with Schatten-p Norm Minimization (FMVFCMSP) which is based on fuzzy C-means and tensor Schatten p-norm. Specifically, we utilize the membership degrees to replace conventional hard clustering assignment in K-means, enabling improved uncertainty handling and less information loss. Moreover, we introduce a tensor Schatten p-norm-based regularizer to fully explore the inter-view complementary information and global spatial structure. We also develop a federated optimization algorithm enabling clients to collaboratively learn the clustering results. Extensive experiments on several datasets demonstrate that our proposed method exhibits superior performance in federated multi-view clustering.

Fair multi-view clustering aims to achieve both satisfactory clustering performance and non-discriminatory outcomes with respect to sensitive attributes. Existing fair multi-view clustering methods impose a constraint that requires the distribution of sensitive attributes to be uniform within each cluster. However, this constraint can lead to misallocation of samples with sensitive attributes. To solve this problem, we propose a novel Deep Fair Multi-View Clustering (DFMVC) method that learns a consistent and discriminative representation instructed by a fairness constraint constructed from the cluster distribution. Specifically, we incorporate contrastive constraints on semantic features from different views to obtain consistent and discriminative representations for each view. Additionally, we align the distribution of sensitive attributes with the target cluster distribution to achieve optimal fairness in clustering results. Experimental results on four datasets with sensitive attributes demonstrate that our method improves fairness and clustering performance compared with state-of-the-art multi-view clustering methods.

Mobile Crowdsourcing (MCS) is a widely adopted data collection method that utilizes ubiquitous mobile devices as sensors. The centralized nature of traditional MCS introduces certain weaknesses, leading to a growing interest in blockchainbased MCS. Although decentralized MCS proves to be effective, it also presents several privacy and trust concerns. Specifically, ensuring node trust authentication in an anonymous and decentralized manner is critical due to the susceptibility of a trustworthy and decentralized MCS platform to various attacks. Nevertheless, the absence of a centralized and trusted entity in blockchain poses significant challenges in managing node keys for authentication. Moreover, trust often conflicts with privacy, and the transparency of blockchain further complicates the achievement of anonymous authentication while preserving privacy. To address these challenges, we propose a scheme for decentralized anonymous authentication based on threshold and partial blind signature, which provides a key alternation service. The proposed scheme enables trust credential issuance without disclosing the linkable relationship between the public keys before and after the alternation. Extensive analyses and experiments are conducted to demonstrate the security and efficiency of the proposed scheme.

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.

Cross-view subspace clustering has become a popular unsupervised method for cross-view data analysis because it can extract both the consistent and complementary features of data for different views. Nonetheless, existing methods usually ignore the discriminative features due to a lack of label supervision, which limits its further improvement in clustering performance. To address this issue, we design a novel model that leverages the self-supervision information embedded in the data itself by combining contrastive learning and self-expression learning, i.e., unsupervised cross-view subspace clustering via adaptive contrastive learning (CVCL). Specifically, CVCL employs an encoder to learn a latent subspace from the cross-view data and convert it to a consistent subspace with a self-expression layer. In this way, contrastive learning helps to provide more discriminative features for the self-expression learning layer, and the self-expression learning layer in turn supervises contrastive learning. Besides, CVCL adaptively chooses positive and negative samples for contrastive learning to reduce the noisy impact of improper negative sample pairs. Ultimately, the decoder is designed for reconstruction tasks, operating on the output of the self-expressive layer, and strives to faithfully restore the original data as much as possible, ensuring that the encoded features are potentially effective. Extensive experiments conducted across multiple cross-view datasets showcase the exceptional performance and superiority of our model.

Self-supervised learning (SSL) has been successfully applied to remote sensing image classification by designing pretext tasks to extract valuable feature representations of targets. However, existing SSL methodologies overlook the edge information integral to ground objects, culminating in frequent misclassifications at target boundaries. Additionally, the scarcity of training samples often restricts the full utilization of the knowledge encapsulated in the pre-training model. To address these issues, we propose a novel self-supervised edge perception learning framework (SEPLF) to improve the classification performance of high-resolution remote sensing images (HRSI). The framework comprises self-supervised edge perception learning (SEPL) and training sample augmentation (TSA) algorithms. On the one hand, the SEPL approach leverages morphological data enhancement strategies to render the extracted invariant features more robust. It also effectively mines the potential information concealed at target edges, augmenting ground objects’s edge separability. On the other hand, the TSA algorithm not only obtains a large number of training samples but also enhances the intra-class diversity of the samples by considering different spectral features of the same category of ground objects. Experimental results validate that our proposed method outperforms state-of-the-art algorithms, particularly with limited labeled samples.

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.

The goal of mixed-modality clustering, which differs from typical multi-modality/view clustering, is to divide samples derived from various modalities into several clusters. This task has to solve two critical semantic gap problems: i) how to generate the missing modalities without the pairwise-modality data; and ii) how to align the representations of heterogeneous modalities. To tackle the above problems, this paper proposes a novel mixedmodality clustering model, which integrates the missing-modality generation and the heterogeneous modality alignment into a unified framework. During the missing-modality generation process, a bidirectional mapping is established between different modalities, enabling generation of preliminary representations for the missing-modality using information from another modality. Then the intra-modality bipartite graphs are constructed to help generate better missing-modality representations by weighted aggregating existing intra-modality neighbors. In this way, a pairwise-modality representation for each sample can be obtained. In the process of heterogeneous modality alignment, each modality is modelled as a graph to capture the global structure among intra-modality samples and is aligned against the heterogeneous modality representations through the adaptive heterogeneous graph matching module. Experimental results on three public datasets show the effectiveness of the proposed model compared to multiple state-of-the-art multi-modality/view clustering methods.

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.

Recently, multi-view clustering methods have been widely used in handling multi-media data and have achieved impressive performances. Among the many multi-view clustering methods, anchor graph-based multi-view clustering has been proven to be highly efficient for large-scale data processing. However, most existing anchor graph-based clustering methods necessitate post-processing to obtain clustering labels and are unable to effectively utilize the information within anchor graphs. To address this issue, we draw inspiration from regression and feature selection to proposeAnchorGraph-BasedFeatureSelection forOne-stepMulti-ViewClustering (AGFS-OMVC). Our method combines embedding learning and sparse constraint to perform feature selection, allowing us to remove noisy anchor points and redundant connections in the anchor graph. This results in a clean anchor graph that can be projected into the label space, enabling us to obtain clustering labels in a single step without post-processing. Lastly, we employ the tensor Schatten$p$-norm as a tensor rank approximation function to capture the complementary information between different views, ensuring similarity between cluster assignment matrices. Experimental results on five real-world datasets demonstrate that our proposed method outperforms state-of-the-art approaches.

Recently, deep multi-view clustering (MVC) has attracted increasing attention in multi-view learning owing to its promising performance. However, most existing deep multi-view methods use single-pathway neural networks to extract features of each view, which cannot explore comprehensive complementary information and multilevel features. To tackle this problem, we propose a deep structured multi-pathway network (SMpNet) for multi-view subspace clustering task in this brief. The proposed SMpNet leverages structured multi-pathway convolutional neural networks to explicitly learn the subspace representations of each view in a layer-wise way. By this means, both low-level and high-level structured features are integrated through a common connection matrix to explore the comprehensive complementary structure among multiple views. Moreover, we impose a low-rank constraint on the connection matrix to decrease the impact of noise and further highlight the consensus information of all the views. Experimental results on five public datasets show the effectiveness of the proposed SMpNet compared with several state-of-the-art deep MVC methods.

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 graph clustering aims to leverage different views to obtain consistent information and improve clustering performance by sharing the graph structure. Existing multi-view graph clustering algorithms generally adopt a single-pathway network reconstruction and consistent feature extraction, building on top of auto-encoders and graph convolutional networks (GCN). Despite their promising results, these single-pathway methods may ignore the significant complementary information between different layers and the rich multi-level context inside. On the other hand, GCN usually employs a shallow network structure (2-3 layers) due to the over-smoothing with the increase of network depth, while few multi-view graph clustering methods explore the performance of deep networks. In this work, we propose a novel Dropping Pathways strategy toward building a deep Multi-view Graph Subspace Clustering network, namely DPMGSC, to fully exploit the deep and multi-level graph network representations. The proposed method implements a multi-pathway self-expressive network to capture pairwise affinities of graph nodes among multiple views. Moreover, we empirically study the impact of a series of dropping methods on deep multi-pathway networks. Extensive experiments demonstrate the effectiveness of the proposed DPMGSC compared with its deep counterpart and state-of-the-art methods.

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.

Despite the impressive clustering performance and efficiency in characterizing both the relationship between the data and cluster structure, most existing graph-based multi-view clustering methods still have the following drawbacks. They suffer from the expensive time burden due to both the construction of graphs and eigen-decomposition of Laplacian matrix. Moreover, none of them simultaneously considers the similarity of inter-view and similarity of intra-view. In this article, we propose a variance-based de-correlation anchor selection strategy for bipartite construction. The selected anchors not only cover the whole classes but also characterize the intrinsic structure of data. Following that, we present a tensorized bipartite graph learning for multi-view clustering (TBGL). Specifically, TBGL exploits the similarity of inter-view by minimizing the tensor Schatten p-norm, which well exploits both the spatial structure and complementary information embedded in the bipartite graphs of views. We exploit the similarity of intra-view by using the [Formula: see text]-norm minimization regularization and connectivity constraint on each bipartite graph. So the learned graph not only well encodes discriminative information but also has the exact connected components which directly indicates the clusters of data. Moreover, we solve TBGL by an efficient algorithm which is time-economical and has good convergence. Extensive experimental results demonstrate that TBGL is superior to the state-of-the-art methods. Codes and datasets are available: https://github.com/xdweixia/TBGL-MVC.

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.

The existing deep multiview clustering (MVC) methods are mainly based on autoencoder networks, which seek common latent variables to reconstruct the original input of each view individually. However, due to the view-specific reconstruction loss, it is challenging to extract consistent latent representations over multiple views for clustering. To address this challenge, we propose adversarial MVC (AMvC) networks in this article. The proposed AMvC generates each view’s samples conditioning on the fused latent representations among different views to encourage a more consistent clustering structure. Specifically, multiview encoders are used to extract latent descriptions from all the views, and the corresponding generators are used to generate the reconstructed samples. The discriminative networks and the mean squared loss are jointly utilized for training the multiview encoders and generators to balance the distinctness and consistency of each view’s latent representation. Moreover, an adaptive fusion layer is developed to obtain a shared latent representation, on which a clustering loss and the${\ell _ {1,2}}$-norm constraint are further imposed to improve clustering performance and distinguish the latent space. Experimental results on video, image, and text datasets demonstrate that the effectiveness of our AMvC is over several state-of-the-art deep MVC methods.

Human action recognition which recognizes human actions in a video is a fundamental task in computer vision field. Although multiple existing methods with single-view or multi-view have been presented for human action recognition, these recognition approaches cannot be extended into new action recognition or action classification tasks, as well as discover underlying correlations among different views. To tackle the above problem, this paper proposes a new lifelong multi-view subspace learning framework for continuous human action recognition, which could exploit the complementary information amongst different views from a lifelong learning perspective. More specifically, a set of view-specific libraries is established to gradually store the useful information within multiple views. As a new action recognition task comes, we decompose the model parameters into a set of embedded parameters over view-specific libraries. A latent representation subspace is constructed via encouraging it to be close to different view-specific libraries, which can leverage the high-order correlations among different views and further avoid partial information for action recognition task. Meanwhile, we propose to employ an alternating direction strategy to optimize our proposed method. Empirical studies on real-world multi-view action recognition datasets have shown that our proposed framework attains the superior recognition performance and saves the computational time when continually learning new action recognition tasks.

Incomplete multiview clustering is a challenging problem in the domain of unsupervised learning. However, the existing incomplete multiview clustering methods only consider the similarity structure of intraview while neglecting the similarity structure of interview. Thus, they cannot take advantage of both the complementary information and spatial structure embedded in similarity matrices of different views. To this end, we complete the incomplete graph with missing data referring to tensor complete and present a novel and effective model to handel the incomplete multiview clustering task. To be specific, we consider the similarity of the interview graphs via the tensor Schatten p -norm-based completion technique to make use of both the complementary information and spatial structure. Meanwhile, we employ the connectivity constraint for similarity matrices of different views such that the connected components approximately represent clusters. Thus, the learned entire graph not only has the low-rank structure but also well characterizes the relationship between unmissing data. Extensive experiments show the promising performance of the proposed method comparing with several incomplete multiview approaches in the clustering tasks.

Despite the promising preliminary results, existing graph convolutional network (GCN) based multi-view learning methods directly use the graph structure as view descriptor, which may inhibit the ability of multi-view learning for multimedia data. The major reason is that, in real multimedia applications, the graph structure may contain outliers. Moreover, they fail to take advantage of the information embedded in the inaccurate clustering labels obtained from their proposed methods, resulting in inferior clustering results. These observations motivate us to study whether there is a better alternative GCN based framework for multi-view clustering. To this end, in this paper, we propose an end-to-end self-supervised graph convolutional network for multi-view clustering (SGCMC). Specifically, SGCMC constructs a new view descriptor for graph-structured data by mapping the raw node content into the complex space via Euler transformation, which not only suppresses outliers but also reveals non-linear patterns embedded in data. Meanwhile, the proposed SGCMC uses the clustering labels to guide the learning of the latent representation and coefficient matrix, and the latter in turn is used to conduct the subsequent node clustering. By this way, clustering and representation learning are seamlessly connected, with the aim to achieve better clustering results. Extensive experiments indicate that the proposed SGCMC outperforms the state-of-the-art methods.

Consider the lifelong machine learning paradigm whose objective is to learn a sequence of tasks depending on previous experiences, e.g., knowledge library or deep network weights. However, the knowledge libraries or deep networks for most recent lifelong learning models are of prescribed size and can degenerate the performance for both learned tasks and coming ones when facing with a new task environment (cluster). To address this challenge, we propose a novel incremental clustered lifelong learning framework with two knowledge libraries: feature learning library and model knowledge library, called Flexible Clustered Lifelong Learning (FCL3). Specifically, the feature learning library modeled by an autoencoder architecture maintains a set of representation common across all the observed tasks, and the model knowledge library can be self-selected by identifying and adding new representative models (clusters). When a new task arrives, our FCL3 model firstly transfers knowledge from these libraries to encode the new task, i.e., effectively and selectively soft-assigning this new task to multiple representative models over feature learning library. Then: 1) the new task with a higher outlier probability will be judged as a new representative, and used to redefine both feature learning library and representative models over time; or 2) the new task with lower outlier probability will only refine the feature learning library. For model optimization, we cast this lifelong learning problem as an alternating direction minimization problem as a new task comes. Finally, we evaluate the proposed framework by analyzing several multitask data sets, and the experimental results demonstrate that our FCL3 model can achieve better performance than most lifelong learning frameworks, even batch clustered multitask learning models.

Existing multi-modal subspace clustering methods, aiming to exploit the correlation information between different modalities, have achieved promising preliminary results. However, these methods might be incapable of handling real problems with complex heterogeneous structures between different modalities, since the large heterogeneous structure makes it difficult to directly learn a discriminative shared self-representation for multi-modal clustering. To tackle this problem, in this paper, we propose a deep Self-supervised t-SNE method (StSNE) for multi-modal subspace clustering, which learns soft label features by multi-modal encoders and utilizes the common label feature to supervise soft label feature of each modal by adversarial training and reconstruction networks. Specifically, the proposed StSNE consists of four components: 1) multi-modal convolutional encoders; 2) a self-supervised t-SNE module; 3) a self-expressive layer; 4) multi-modal convolutional decoders. Multi-modal data are fed to encoders to obtain soft label features, for which the self-supervised t-SNE module is added to make full use of the label information among different modalities. Simultaneously, the latent representations given by encoders are constrained by a self-expressive layer to capture the hierarchical information of each modal, followed by decoders reconstructing the encoded features to preserve the structure of the original data. Experimental results on several public datasets demonstrate the superior clustering performance of the proposed method over state-of-the-art methods.

Nowadays, with the rapid development of data collection sources and feature extraction methods, multi-view data are getting easy to obtain and have received increasing research attention in recent years, among which, multi-view clustering (MVC) forms a mainstream research direction and is widely used in data analysis. However, existing MVC methods mainly assume that each sample appears in all the views, without considering the incomplete view case due to data corruption, sensor failure, equipment malfunction, etc. In this study, we design and build a generative partial multi-view clustering model with adaptive fusion and cycle consistency, named as GP-MVC, to solve the incomplete multi-view problem by explicitly generating the data of missing views. The main idea of GP-MVC lies in two-fold. First, multi-view encoder networks are trained to learn common low-dimensional representations, followed by a clustering layer to capture the shared cluster structure across multiple views. Second, view-specific generative adversarial networks with multi-view cycle consistency are developed to generate the missing data of one view conditioning on the shared representation given by other views. These two steps could be promoted mutually, where the learned common representation facilitates data imputation and the generated data could further explores the view consistency. Moreover, an weighted adaptive fusion scheme is implemented to exploit the complementary information among different views. Experimental results on four benchmark datasets are provided to show the effectiveness of the proposed GP-MVC over the state-of-the-art methods.

Recently, deep convolutional neural networks have demonstrated remarkable progresses on single image super-resolution (SR) problem. However, most of them use more deeper and wider networks to improve SR performance, which is not practical in real-world applications due to large complexity, high computation cost, and low efficiency. In addition, they cannot provide high perception quality and guarantee objective quality simultaneously. To address these limitations, we in this paper propose a novel Adversarial Multipath Residual Network (AMPRN), which can largely suppress the number of network parameters and achieve a higher SR performance compared with the state-of-the-art methods. More specifically, we propose a multi-path residual block (MPRB) for multi-path residual network (MPRN) with fewer network parameters, which can extract abundant local features by fully using features from different paths generated by channel slices. These hierarchical features from all the MPRBs are then jointly aggregated by global gradual feature fusion. Following MPRN, we construct an adversarial gradient network with a gradient loss to make the gradient distribution of the generated SR images and ground truth image closer. In this way, the generated SR images of our model can provide high perception quality and objective quality. Finally, several experimental results demonstrate that our AMPRN achieves better performance in comparison with fewer parameters than the state-of-the-art methods.

Cross-modal clustering aims to cluster the high-similar cross-modal data into one group while separating the dissimilar data. Despite the promising cross-modal methods have developed in recent years, existing state-of-the-arts cannot effectively capture the correlations between cross-modal data when encountering with incomplete cross-modal data, which can gravely degrade the clustering performance. To well tackle the above scenario, we propose a novel incomplete cross-modal clustering method that integrates canonical correlation analysis and exclusive representation, named incomplete Cross-modal Subspace Clustering (i.e., iCmSC). To learn a consistent subspace representation among incomplete cross-modal data, we maximize the intrinsic correlations among different modalities by deep canonical correlation analysis (DCCA), while an exclusive self-expression layer is proposed after the output layers of DCCA. We exploit a ℓ1,2-norm regularization in the learned subspace to make the learned representation more discriminative, which makes samples between different clusters mutually exclusive and samples among the same cluster attractive to each other. Meanwhile, the decoding networks are employed to reconstruct the feature representation, and further preserve the structural information among the original cross-modal data. To the end, we demonstrate the effectiveness of the proposed iCmSC via extensive experiments, which can justify that iCmSC achieves consistently large improvement compared with the state-of-the-arts.

Deep multi-view subspace clustering has achieved promising performance compared with other multi-view clustering. However, existing deep multi-view subspace clustering only considers the global structure for all views, and they ignore the local geometric structure among each view. In addition, they cannot learn discriminative feature on different clusters of different views, i.e., inter-cluster difference. To solve these problems, in this paper, we propose a novel Deep Multi-view Subspace Clustering with Unified and Discriminative Learning (DMSC-UDL). DMSC-UDL combines global and local structures with self-expression layer. The global and local structures help each other forward and achieve small distance between samples of the same cluster. To make samples in different clusters of different views farther, DMSC-UDL uses a discriminative constraint between different views. In this way, DMSC-UDL makes the same cluster's samples have large weights, while different clusters' samples have small weights. Thus, it can learn a better shared connection matrix for multi-view clustering. Extensive experimental results reveal that the proposed multi-view clustering method is superior to several state-of-the-art multi-view clustering methods in terms of performance.

For cross-modal subspace clustering, the key point is how to exploit the correlation information between cross-modal data. However, most hierarchical and structural correlation information among cross-modal data cannot be well exploited due to its high-dimensional non-linear property. To tackle this problem, in this paper, we propose an unsupervised framework named Cross-Modal Subspace Clustering via Deep Canonical Correlation Analysis (CMSC-DCCA), which incorporates the correlation constraint with a self-expressive layer to make full use of information among the inter-modal data and the intra-modal data. More specifically, the proposed model consists of three components: 1) deep canonical correlation analysis (Deep CCA) model; 2) self-expressive layer; 3) Deep CCA decoders. The Deep CCA model consists of convolutional encoders and correlation constraint. Convolutional encoders are used to obtain the latent representations of cross-modal data, while adding the correlation constraint for the latent representations can make full use of the information of the inter-modal data. Furthermore, self-expressive layer works on latent representations and constrain it perform self-expression properties, which makes the shared coefficient matrix could capture the hierarchical intra-modal correlations of each modality. Then Deep CCA decoders reconstruct data to ensure that the encoded features can preserve the structure of the original data. Experimental results on several real-world datasets demonstrate the proposed method outperforms the state-of-the-art methods.

In the past decades, spectral clustering (SC) has become one of the most effective clustering algorithms. However, most previous studies focus on spectral clustering tasks with a fixed task set, which cannot incorporate with a new spectral clustering task without accessing to previously learned tasks. In this paper, we aim to explore the problem of spectral clustering in a lifelong machine learning framework, i.e., Lifelong Spectral Clustering (L2SC). Its goal is to efficiently learn a model for a new spectral clustering task by selectively transferring previously accumulated experience from knowledge library. Specifically, the knowledge library of L2SC contains two components: 1) orthogonal basis library: capturing latent cluster centers among the clusters in each pair of tasks; 2) feature embedding library: embedding the feature manifold information shared among multiple related tasks. As a new spectral clustering task arrives, L2SC firstly transfers knowledge from both basis library and feature library to obtain encoding matrix, and further redefines the library base over time to maximize performance across all the clustering tasks. Meanwhile, a general online update formulation is derived to alternatively update the basis library and feature library. Finally, the empirical experiments on several real-world benchmark datasets demonstrate that our L2SC model can effectively improve the clustering performance when comparing with other state-of-the-art spectral clustering algorithms.

Object clustering, aiming at grouping similar objects into one cluster with an unsupervised strategy, has been extensively-studied among various data-driven applications. However, most existing state-of-the-art object clustering methods (e.g., single-view or multi-view clustering methods) only explore visual information, while ignoring one of most important sensing modalities, i.e., tactile information which can help capture different object properties and further boost the performance of object clustering task. To effectively benefit both visual and tactile modalities for object clustering, in this paper, we propose a deep Auto-Encoder-like Non-negative Matrix Factorization framework for visual-tactile fusion clustering. Specifically, deep matrix factorization constrained by an under-complete Auto-Encoder-like architecture is employed to jointly learn hierarchical expression of visual-tactile fusion data, and preserve the local structure of data generating distribution of visual and tactile modalities. Meanwhile, a graph regularizer is introduced to capture the intrinsic relations of data samples within each modality. Furthermore, we propose a modality-level consensus regularizer to effectively align the visual and tactile data in a common subspace in which the gap between visual and tactile data is mitigated. For the model optimization, we present an efficient alternating minimization strategy to solve our proposed model. Finally, we conduct extensive experiments on public datasets to verify the effectiveness of our framework.

Graph neural networks (GNNs) have made considerable achievements in processing graph-structured data. However, existing methods can not allocate learnable weights to different nodes in the neighborhood and lack of robustness on account of neglecting both node attributes and graph reconstruction. Moreover, most of multi-view GNNs mainly focus on the case of multiple graphs, while designing GNNs for solving graph-structured data of multi-view attributes is still under-explored. In this paper, we propose a novel Multi-View Attribute Graph Convolution Networks (MAGCN) model for the clustering task. MAGCN is designed with two-pathway encoders that map graph embedding features and learn the view-consistency information. Specifically, the first pathway develops multi-view attribute graph attention networks to reduce the noise/redundancy and learn the graph embedding features for each multi-view graph data. The second pathway develops consistent embedding encoders to capture the geometric relationship and probability distribution consistency among different views, which adaptively finds a consistent clustering embedding space for multi-view attributes. Experiments on three benchmark graph datasets show the superiority of our method compared with several state-of-the-art algorithms.

Multi-view clustering has attracted increasing attention in recent years by exploiting common clustering structure across multiple views. Most existing multi-view clustering algorithms use shallow and linear embedding functions to learn the common structure of multi-view data. However, these methods cannot fully utilize the non-linear property of multi-view data, which is important to reveal complex cluster structure underlying multi-view data. In this paper, we propose a novel multi-view clustering method, named Deep Adversarial Multi-view Clustering (DAMC) network, to learn the intrinsic structure embedded in multi-view data. Specifically, our model adopts deep auto-encoders to learn latent representations shared by multiple views, and meanwhile leverages adversarial training to further capture the data distribution and disentangle the latent space. Experimental results on several real-world datasets demonstrate that the proposed method outperforms the state-of art methods.

Multi-view clustering, as one of the most important methods to analyze multi-view data, has been widely used in many real-world applications. Most existing multi-view clustering methods perform well on the assumption that each sample appears in all views. Nevertheless, in real-world application, each view may well face the problem of the missing data due to noise, or malfunction. In this paper, a new consistent generative adversarial network is proposed for partial multi-view clustering. We learn a common low-dimensional representation, which can both generate the missing view data and capture a better common structure from partial multi-view data for clustering. Different from the most existing methods, we use the common representation encoded by one view to generate the missing data of the corresponding view by generative adversarial networks, then we use the encoder and clustering networks. This is intuitive and meaningful because encoding common representation and generating the missing data in our model will promote mutually. Experimental results on three different multi-view databases illustrate the superiority of the proposed method.

Recently, many ℓ1-norm-based PCA approaches have been developed to improve the robustness of PCA. However, most existing approaches solve the optimal projection matrix by maximizing ℓ1-norm-based variance and do not best minimize the reconstruction error, which is the true goal of PCA. Moreover, they do not have rotational invariance. To handle these problems, we propose a generalized robust metric learning for PCA, namely, ℓ2,p-PCA, which employs ℓ2,p-norm as the distance metric for reconstruction error. The proposed method not only is robust to outliers but also retains PCA's desirable properties. For example, the solutions are the principal eigenvectors of a robust covariance matrix and the low-dimensional representation have rotational invariance. These properties are not shared by ℓ1-norm-based PCA methods. A new iteration algorithm is presented to solve ℓ2,p-PCA efficiently. Experimental results illustrate that the proposed method is more effective and robust than PCA, PCA-L1 greedy, PCA-L1 nongreedy, and HQ-PCA.

Recently, discriminant locality preserving projection based on L1-norm (DLPP-L1) was developed for robust subspace learning and image classification. It obtains projection vectors by greedy strategy, i.e., all projection vectors are optimized individually through maximizing the objective function. Thus, the obtained solution does not necessarily best optimize the corresponding trace ratio optimization algorithm, which is the essential objective function for general dimensionality reduction. It results in insufficient recognition accuracy. To tackle this problem, we propose a nongreedy algorithm to solve the trace ratio formula of DLPP-L1, and analyze its convergence. Experimental results on three databases illustrate the effectiveness of our proposed algorithm.

Two-dimensional principle component analysis (2DPCA) has been widely used for face image representation and recognition. But it is sensitive to the presence of outliers. To alleviate this problem, we propose a novel robust 2DPCA, namely 2DPCA with F-norm minimization (F-2DPCA), which is intuitive and directly derived from 2DPCA. In F-2DPCA, distance in spatial dimensions (attribute dimensions) is measured in F-norm, while the summation over different data points uses 1-norm. Thus it is robust to outliers and rotational invariant as well. To solve F-2DPCA, we propose a fast iterative algorithm, which has a closed-form solution in each iteration, and prove its convergence. Experimental results on face image databases illustrate its effectiveness and advantages.

Recently, many ℓ1-norm based PCA methods have been developed for dimensionality reduction, but they do not explicitly consider the reconstruction error. Moreover, they do not take into account the relationship between reconstruction error and variance of projected data. This reduces the robustness of algorithms. To handle this problem, a novel formulation for PCA, namely angle PCA, is proposed. Angle PCA employs ℓ2-norm to measure reconstruction error and variance of projected da-ta and maximizes the summation of ratio between variance and reconstruction error of each data. Angle PCA not only is robust to outliers but also retains PCA’s desirable property such as rotational invariance. To solve Angle PCA, we propose an iterative algorithm, which has closed-form solution in each iteration. Extensive experiments on several face image databases illustrate that our method is overall superior to the other robust PCA algorithms, such as PCA, PCA-L1 greedy, PCA-L1 nongreedy and HQ-PCA.

Sparse representation shows impressive results for image classification, however, it cannot well characterize the discriminant structure of data, which is important for classification. This paper aims to seek a projection matrix such that the low-dimensional representations well characterize the discriminant structure embedded in high-dimensional data and simultaneously well fit sparse representation-based classifier (SRC). To be specific, Fisher discriminant criterion (FDC) is used to extract the discriminant structure, and sparse representation is simultaneously considered to guarantee that the projected data well satisfy the SRC. Thus, our method, called SRC-FDC, characterizes both the spatial Euclidean distribution and local reconstruction relationship, which enable SRC to achieve better performance. Extensive experiments are done on the AR, CMU-PIE, Extended Yale B face image databases, the USPS digit database, and COIL20 database, and results illustrate that the proposed method is more efficient than other feature extraction methods based on SRC.