Multi-View Clustering (MVC) is a pivotal multi-view learning paradigm widely adopted across various fields. Despite recent advances, existing methods primarily focus on enhancing the performance of fused multi-view representation, often neglecting the issue of Representation Degradation (RD) arising from discrepancies in the intrinsic quality of different views. To address the limitations, we propose a novel Granular-ball Fuzzy Split and Attention Fusion (GFSAF) learning, which leverages the nature of granular-ball to extract mutual and complementary representation separately. Meanwhile, the proposed method introduces an attention variant for fused representations to mitigate the RD issue. GFSAF mainly consists of two training stages: Split-Extract Stage and Views-Fusion Stage. Specifically, we design a novel Granular-ball Fuzzy Contrastive Learning to extract mutual representation, and introduce Noise Stripping Loss to reduce the influence of noise for complementary representation. Then, a novel multi-head Cross Views Attention is proposed to employ attention mechanism from multi-view perspectives for comprehensive fused representations. Experimental results on eight databases demonstrate that our GFSAF achieves superior performance compared to several state-of-the-art MVC methods.

Graph-based methods have proven to be effective in capturing relationships among points for 3D point cloud analysis. However, these methods often suffer from suboptimal graph structures, particularly due to sparse connections at boundary points and noisy connections in junction areas. To address these challenges, we propose a novel method that integrates a graph smoothing module with an enhanced local geometry learning module. Specifically, we identify the limitations of conventional graph structures, particularly in handling boundary points and junction areas. In response, we introduce a graph smoothing module designed to optimize the graph structure and minimize the negative impact of unreliable sparse and noisy connections. Based on the optimized graph structure, we improve the feature extract function with local geometry information. These include shape features derived from adaptive geometric descriptors based on eigenvectors and distribution features obtained through cylindrical coordinate transformation. Experimental results on real-world datasets validate the effectiveness of our method in various point cloud learning tasks, i.e., classification, part segmentation, and semantic segmentation.

Multi-view clustering (MVC) has recently garnered increasing attention for its ability to partition unlabeled samples into distinct clusters by leveraging complementary and consistent information from different views. Existing MVC methods primarily combine deep neural networks with contrastive learning for cross-view representation learning, yet often overlook the inherent global-local structural relationships among samples. While GNN-based methods capture local structures, they struggle to model global dependencies, leading to inferior inter-cluster separability. In contrast, Transformer-based methods excel at global aggregation but suffer from quadratic complexity, and their attention smoothing effect weakens fine-grained local structures, resulting in suboptimal intra-cluster compactness. To address these limitations, we propose a novel end-to-end MVC framework called Mamba-Driven Multi-View Discriminative Clustering via Global-Local Cross-View Sequence Modeling (MGLC). By flexibly constructing multi-view sequences, MGLC fully exploits the efficient sequence modeling capabilities of Mamba to jointly model cross-view dependencies and global-local structural relationships among samples. Furthermore, MGLC introduces a Cross-Mamba Fusion module to dynamically integrate cross-view and global-local structural representations. Additionally, MGLC incorporates a Dual Calibration Contrastive Learning module, guided by high-confidence pseudo-labels, that adaptively refines both feature and semantic representations while mitigating false negatives among semantically similar samples. Extensive comparative experiments and ablation studies demonstrate the effectiveness of MGLC.

Incomplete multi-view clustering (IMVC) has attracted increasing attention in recent years, owing to the prevalence of missing data in real-world multi-view scenarios. Existing imputation-based IMVC methods partially mitigate the impact of missing information but still face three key limitations: (i) overlooking latent structural relationships among samples, which leads to imputed representations deviating from the true distribution; (ii) decoupling imputation from clustering, which reduces the discriminability of the recovered representations; and (iii) exhibiting low efficiency, which makes it difficult to balance recovery quality and inference speed under complex missing scenarios. To address these issues, we propose a Structure-Aware Conditional Diffusion Generation (SACDG) framework. During training, SACDG first models local structural relationships via adaptive neighborhood graphs and injects them as conditional priors into the diffusion model, where a cross-attention mechanism integrates these priors into the noise prediction process to learn structure-aware generative capability. Meanwhile, a semantic distribution alignment module is introduced to leverage pseudo-labels for enforcing cross-view consistency, thereby enhancing semantic discriminability. During inference, SACDG integrates cross-view structural information through cross-view adjacency fusion to guide the reverse denoising trajectory, and employs deterministic DDIM sampling to efficiently and stably recover the representations of missing views. Extensive comparative experiments and ablation studies on multiple benchmark datasets demonstrate that SACDG achieves superior clustering performance and improved efficiency over state-of-the-art methods. Our code is available athttps://github.com/zhangyuanyang21/SACDG.

Incomplete multi-view clustering (IMVC) has garnered increasing attention in recent years due to the common issue of missing data in multi-view datasets. The primary approach to address this challenge involves recovering the missing views before applying conventional multi-view clustering methods. Although imputation-based IMVC methods have achieved significant improvements, they still encounter notable limitations: 1) heavy reliance on paired data for training the data recovery module, which is impractical in real scenarios with high missing data rates; 2) the generated data often lacks diversity and discriminability, resulting in suboptimal clustering results. To address these shortcomings, we propose a novel IMVC method called Diffusion Contrastive Generation (DCG). Motivated by the consistency between the diffusion and clustering processes, DCG learns the distribution characteristics to enhance clustering by applying forward diffusion and reverse denoising processes to intra-view data. By performing contrastive learning on a limited set of paired multi-view samples, DCG can align the generated views with the real views, facilitating accurate recovery of views across arbitrary missing view scenarios. Additionally, DCG integrates instance-level and category-level interactive learning to exploit the consistent and complementary information available in multi-view data, achieving robust and end-to-end clustering. Extensive experiments demonstrate that our method outperforms state-of-the-art approaches.

Recently, multi-view learning (MVL) has garnered significant attention due to its ability to fuse discriminative information from multiple views. However, real-world multi-view datasets are often heterogeneous and imperfect, which usually causes MVL methods designed for specific combinations of views to lack application potential and limits their effectiveness. To address this issue, we propose a novel robust MVL method (namely RML) with simultaneous representation fusion and alignment. Specifically, we introduce a simple yet effective multi-view transformer fusion network where we transform heterogeneous multi-view data into homogeneous word embeddings, and then integrate multiple views by the sample-level attention mechanism to obtain a fused representation. Furthermore, we propose a simulated perturbation based multi-view contrastive learning framework that dynamically generates the noise and unusable perturbations for simulating imperfect data conditions. The simulated noisy and unusable data obtain two distinct fused representations, and we utilize contrastive learning to align them for learning discriminative and robust representations. Our RML is self-supervised and can also be applied for downstream tasks as a regularization. In experiments, we employ it in multi-view unsupervised clustering, noise-label classification, and as a plug-and-play module for cross-modal hashing retrieval. Extensive comparison experiments and ablation studies validate RML's effectiveness. Code is available at https://github.com/SubmissionsIn/RML.

Recently, numerous multi-view clustering (MVC) and multi-view graph clustering (MVGC) methods have been proposed. Despite significant progress, they still face two issues: I) MVC and MVGC are often developed independently for multi-view and multi-graph data. They have redundancy but lack a unified methodology to combine their strengths. II) Contrastive learning is usually adopted to explore the associations across multiple views. However, traditional contrastive losses ignore the neighbor relationship in multi-view scenarios and easily lead to false associations in sample pairs. To address these issues, we propose Graph Embedded Contrastive Learning for Multi-View Clustering. Concretely, we propose a process of view-specific pre-training with adaptive graph convolution to make our method compatible with both multi-view and multi-graph data, which aggregates the graph information into data and leverages autoencoders to learn view-specific representations. Furthermore, to explore the view-cross associations, we introduce the process of view-cross contrastive learning and clustering, where we propose the graph-guided contrastive learning that can generate global graph to mitigate the false association issue as well as the cluster-guided contrastive clustering for improving the model robustness. Finally, extensive experiments demonstrate that our method achieves superior performance on both MVC and MVGC tasks.

Multi-modal clustering is an effective method for integrating multiple omics data in identifying and analyzing cancer diseases, enabling the unsupervised discovery of latent cluster patterns within multi-omics cancer data. However, existing multi-modal clustering methods primarily focus on single-level flat partitions, often overlooking the hierarchical subtype structures of real-world data. To address this issue, we propose a novel Multi-modal Hierarchical Clustering method for cancer Subtype identification of multi-omics data, termed Subtype-MHC. Specifically, Subtype-MHC is a hyperbolic neural network incorporating multiple Poincaré autoencoders, where the latent representations of each omic modality are mapped from the Euclidean space to the hyperbolic space, thus explicitly modeling hierarchical subtype structures during multi-omics integration process. On one hand, we leverage inter-omics complementarity by utilizing an inter-omics Poincaré reconstruction loss to capture modality-specific information within each omic, while a hyperbolic diversity loss is introduced to promote cluster separability on the Poincaré ball. On the other hand, in order to exploit cross-omics consistency, we design a self-weighted cross-omics integration loss to extract the shared hierarchies across all omic modalities. Additionally, a prototype-based weighting strategy is applied on the representation alignment, compressing task-relevant cluster information and mitigating the representation degradation caused by the quality differences of all omic modalities. Extensive experiments on ten multi-omics datasets demonstrate the hierarchical representation ability and clustering effectiveness of Subtype-MHC for cancer subtype identification.

Multiview graph clustering (MGC) methods are increasingly being studied due to the explosion of multiview data with graph structural information. The critical point of MGC is to better utilize view-specific and view-common information in features and graphs of multiple views. However, existing works have an inherent limitation that they are unable to concurrently utilize the consensus graph information across multiple graphs and the view-specific feature information. To address this issue, we propose a variational graph generator for MGC (VGMGC). Specifically, a novel variational graph generator is proposed to extract common information among multiple graphs. This generator infers a reliable variational consensus graph based on a priori assumption over multiple graphs. Then, a simple yet effective graph encoder in conjunction with the multiview clustering objective is presented to learn the desired graph embeddings for clustering, which embeds the inferred view-common graph and view-specific graphs together with features. Finally, theoretical results illustrate the rationality of the VGMGC by analyzing the uncertainty of the inferred consensus graph with the information bottleneck (IB) principle. Extensive experiments demonstrate the superior performance of our VGMGC over state-of-the-art methods (SOTAs). The source code is publicly available at: https://github.com/cjpcool/VGMGC.

Cluster analysis plays an indispensable role in machine learning and data mining. Learning a good data representation is crucial for clustering algorithms. Recently, deep clustering (DC), which can learn clustering-friendly representations using deep neural networks (DNNs), has been broadly applied in a wide range of clustering tasks. Existing surveys for DC mainly focus on the single-view fields and the network architectures, ignoring the complex application scenarios of clustering. To address this issue, in this article, we provide a comprehensive survey for DC in views of data sources. With different data sources, we systematically distinguish the clustering methods in terms of methodology, prior knowledge, and architecture. Concretely, DC methods are introduced according to four categories, i.e., traditional single-view DC, semi-supervised DC, deep multiview clustering (MVC), and deep transfer clustering. Finally, we discuss the open challenges and potential future opportunities in different fields of DC.

Multi-view clustering (MVC) aims at exploring category structures among multi-view data in self-supervised manners. Multiple views provide more information than single views and thus existing MVC methods can achieve satisfactory performance. However, their performance might seriously degenerate when the views are noisy in practical multi-view scenarios. In this paper, we formally investigate the drawback of noisy views and then propose a theoretically grounded deep MVC method (namely MVCAN) to address this issue. Specifically, we propose a novel MVC objective that enables un-shared parameters and inconsistent clustering predictions across multiple views to reduce the side effects of noisy views. Furthermore, a two-level multi-view iterative optimization is designed to generate robust learning targets for refining individual views' representation learning. Theoretical analysis reveals that MVCAN works by achieving the multi-view consistency, complementarity, and noise robustness. Finally, experiments on extensive public datasets demonstrate that MVCAN outperforms state-of-the-art methods and is robust against the existence of noisy views.

Recently, federated multi-view clustering (FedMVC) has emerged to explore cluster structures in multi-view data distributed on multiple clients. Many existing approaches tend to assume that clients are isomorphic and all of them belong to either single-view clients or multi-view clients. While these methods have succeeded, they may encounter challenges in practical FedMVC scenarios involving heterogeneous hybrid views, where a mixture of single-view and multi-view clients exhibit varying degrees of heterogeneity. In this paper, we propose a novel FedMVC framework, which concurrently addresses two challenges associated with heterogeneous hybrid views, i.e., client gap and view gap. To address the client gap, we design a local-synergistic contrastive learning approach that helps single-view clients and multi-view clients achieve consistency for mitigating heterogeneity among all clients. To address the view gap, we develop a global-specific weighting aggregation method, which encourages global models to learn complementary features from hybrid views. The interplay between local-synergistic contrastive learning and global-specific weighting aggregation mutually enhances the exploration of the data cluster structures distributed on multiple clients. Theoretical analysis and extensive experiments demonstrate that our method can handle the heterogeneous hybrid views in FedMVC and outperforms state-of-the-art methods.

Contrastive learning has been successfully applied in unsupervised representation learning. However, the generalization ability of representation learning is limited by the fact that the loss of downstream tasks (e.g., classification) is rarely taken into account while designing contrastive methods. In this article, we propose a new contrastive-based unsupervised graph representation learning (UGRL) framework by 1) maximizing the mutual information (MI) between the semantic information and the structural information of the data and 2) designing three constraints to simultaneously consider the downstream tasks and the representation learning. As a result, our proposed method outputs robust low-dimensional representations. Experimental results on 11 public datasets demonstrate that our proposed method is superior over recent state-of-the-art methods in terms of different downstream tasks. Our code is available at https://github.com/LarryUESTC/GRLC.

With the increase of multi-view graph data, multi-view graph clustering (MVGC) that can discover the hidden clusters without label supervision has attracted growing attention from researchers. Existing MVGC methods are often sensitive to the given graphs, especially influenced by the low quality graphs, i.e., they tend to be limited by the homophily assumption. However, the widespread real-world data hardly satisfy the homophily assumption. This gap limits the performance of existing MVGC methods on low homophilous graphs. To mitigate this limitation, our motivation is to extract high-level view-common information which is used to refine each view's graph, and reduce the influence of non-homophilous edges. To this end, we propose dual label-guided graph refinement for multi-view graph clustering (DuaLGR), to alleviate the vulnerability in facing low homophilous graphs. Specifically, DuaLGR consists of two modules named dual label-guided graph refinement module and graph encoder module. The first module is designed to extract the soft label from node features and graphs, and then learn a refinement matrix. In cooperation with the pseudo label from the second module, these graphs are refined and aggregated adaptively with different orders. Subsequently, a consensus graph can be generated in the guidance of the pseudo label. Finally, the graph encoder module encodes the consensus graph along with node features to produce the high-level pseudo label for iteratively clustering. The experimental results show the superior performance on coping with low homophilous graph data. The source code for DuaLGR is available at https://github.com/YwL-zhufeng/DuaLGR.

Federated multi-view clustering has the potential to learn a global clustering model from data distributed across multiple devices. In this setting, label information is unknown and data privacy must be preserved, leading to two major challenges. First, views on different clients often have feature heterogeneity, and mining their complementary cluster information is not trivial. Second, the storage and usage of data from multiple clients in a distributed environment can lead to incompleteness of multi-view data. To address these challenges, we propose a novel federated deep multi-view clustering method that can mine complementary cluster structures from multiple clients, while dealing with data incompleteness and privacy concerns. Specifically, in the server environment, we propose sample alignment and data extension techniques to explore the complementary cluster structures of multiple views. The server then distributes global prototypes and global pseudo-labels to each client as global self-supervised information. In the client environment, multiple clients use the global self-supervised information and deep autoencoders to learn view-specific cluster assignments and embedded features, which are then uploaded to the server for refining the global self-supervised information. Finally, the results of our extensive experiments demonstrate that our proposed method exhibits superior performance in addressing the challenges of incomplete multi-view data in distributed environments.

Recently, numerous studies have demonstrated the effectiveness of contrastive learning (CL), which learns feature representations by pulling in positive samples while pushing away negative samples. Many successes of CL lie in that there exists semantic consistency between data augmentations of the same instance. In multi-view scenarios, however, CL might cause representation degeneration when the collected multiple views inherently have inconsistent semantic information or their representations subsequently do not capture sufficient discriminative information. To address this issue, we propose a novel framework called SEM: SElf-weighted Multi-view contrastive learning with reconstruction regularization. Specifically, SEM is a general framework where we propose to first measure the discrepancy between pairwise representations and then minimize the corresponding self-weighted contrastive loss, and thus making SEM adaptively strengthen the useful pairwise views and also weaken the unreliable pairwise views. Meanwhile, we impose a self-supervised reconstruction term to regularize the hidden features of encoders, to assist CL in accessing sufficient discriminative information of data. Experiments on public multi-view datasets verified that SEM can mitigate representation degeneration in existing CL methods and help them achieve significant performance improvements. Ablation studies also demonstrated the effectiveness of SEM with different options of weighting strategies and reconstruction terms.

Incomplete multi-view clustering (IMVC) analysis, where some views of multi-view data usually have missing data, has attracted increasing attention. However, existing IMVC methods still have two issues: 1) they pay much attention to imputing or recovering the missing data, without considering the fact that the imputed values might be inaccurate due to the unknown label information, 2) the common features of multiple views are always learned from the complete data, while ignoring the feature distribution discrepancy between the complete and incomplete data. To address these issues, we propose an imputation-free deep IMVC method and consider distribution alignment in feature learning. Concretely, the proposed method learns the features for each view by autoencoders and utilizes an adaptive feature projection to avoid the imputation for missing data. All available data are projected into a common feature space, where the common cluster information is explored by maximizing mutual information and the distribution alignment is achieved by minimizing mean discrepancy. Additionally, we design a new mean discrepancy loss for incomplete multi-view learning and make it applicable in mini-batch optimization. Extensive experiments demonstrate that our method achieves the comparable or superior performance compared with state-of-the-art methods.

Multi-view clustering is an important research topic due to its capability to utilize complementary information from multiple views. However, there are few methods to consider the negative impact caused by certain views with unclear clustering structures, resulting in poor multi-view clustering performance. To address this drawback, we proposeself-supervised discriminative feature learning fordeepmulti-viewclustering (SDMVC). Concretely, deep autoencoders are applied to learn embedded features for each view independently. To leverage the multi-view complementary information, we concatenate all views’ embedded features to form the global features, which can overcome the negative impact of some views’ unclear clustering structures. In a self-supervised manner, pseudo-labels are obtained to build a unified target distribution to perform multi-view discriminative feature learning. During this process, global discriminative information can be mined to supervise all views to learn more discriminative features, which in turn are used to update the target distribution. Besides, this unified target distribution can make SDMVC learn consistent cluster assignments, which accomplishes the clustering consistency of multiple views while preserving their features’ diversity. Experiments on various types of multi-view datasets show that SDMVC outperforms 14 competitors including classic and state-of-the-art methods. The code is available athttps://github.com/SubmissionsIn/SDMVC.

In this work, we focus on the challenging task, neuro-disease classification, using functional magnetic resonance imaging (fMRI). In population graph-based disease analysis, graph convolutional neural networks (GCNs) have achieved remarkable success. However, these achievements are inseparable from abundant labeled data and sensitive to spurious signals. To improve fMRI representation learning and classification under a label-efficient setting, we propose a novel and theory-driven self-supervised learning (SSL) framework on GCNs, namely Graph CCA for Temporal sElf-supervised learning on fMRI analysis (GATE). Concretely, it is demanding to design a suitable and effective SSL strategy to extract formation and robust features for fMRI. To this end, we investigate several new graph augmentation strategies from fMRI dynamic functional connectives (FC) for SSL training. Further, we leverage canonical-correlation analysis (CCA) on different temporal embeddings and present the theoretical implications. Consequently, this yields a novel two-step GCN learning procedure comprised of (i) SSL on an unlabeled fMRI population graph and (ii) fine-tuning on a small labeled fMRI dataset for a classification task. Our method is tested on two independent fMRI datasets, demonstrating superior performance on autism and dementia diagnosis. Our code is available at https://github.com/LarryUESTC/GATE.

In this paper, we propose a simple unsupervised graph representation learning method to conduct effective and efficient contrastive learning. Specifically, the proposed multiplet loss explores the complementary information between the structural information and neighbor information to enlarge the inter-class variation, as well as adds an upper bound loss to achieve the finite distance between positive embeddings and anchor embeddings for reducing the intra-class variation. As a result, both enlarging inter-class variation and reducing intra-class variation result in small generalization error, thereby obtaining an effective model. Furthermore, our method removes widely used data augmentation and discriminator from previous graph contrastive learning methods, meanwhile available to output low-dimensional embeddings, leading to an efficient model. Experimental results on various real-world datasets demonstrate the effectiveness and efficiency of our method, compared to state-of-the-art methods. The source codes are released at https://github.com/YujieMo/SUGRL.

Incomplete multi-view clustering (IMVC) is an important unsupervised approach to group the multi-view data containing missing data in some views. Previous IMVC methods suffer from the following issues: (1) the inaccurate imputation or padding for missing data negatively affects the clustering performance, (2) the quality of features after fusion might be interfered by the low-quality views, especially the inaccurate imputed views. To avoid these issues, this work presents an imputation-free and fusion-free deep IMVC framework. First, the proposed method builds a deep embedding feature learning and clustering model for each view individually. Our method then nonlinearly maps the embedding features of complete data into a high-dimensional space to discover linear separability. Concretely, this paper provides an implementation of the high-dimensional mapping as well as shows the mechanism to mine the multi-view cluster complementarity. This complementary information is then transformed to the supervised information with high confidence, aiming to achieve the multi-view clustering consistency for the complete data and incomplete data. Furthermore, we design an EM-like optimization strategy to alternately promote feature learning and clustering. Extensive experiments on real-world multi-view datasets demonstrate that our method achieves superior clustering performance over state-of-the-art methods.

Multi-view clustering can explore common semantics from multiple views and has attracted increasing attention. However, existing works punish multiple objectives in the same feature space, where they ignore the conflict between learning consistent common semantics and reconstructing inconsistent view-private information. In this paper, we propose a new framework of multi-level feature learning for contrastive multi-view clustering to address the aforementioned issue. Our method learns different levels of features from the raw features, including low-level features, high-level features, and semantic labels/features in a fusion-free manner, so that it can effectively achieve the reconstruction objective and the consistency objectives in different feature spaces. Specifically, the reconstruction objective is conducted on the low-level features. Two consistency objectives based on contrastive learning are conducted on the high-level features and the semantic labels, respectively. They make the high-level features effectively explore the common semantics and the semantic labels achieve the multi-view clustering. As a result, the proposed framework can reduce the adverse influence of view-private information. Extensive experiments on public datasets demonstrate that our method achieves state-of-the-art clustering effectiveness.

Multi-view clustering, a long-standing and important research problem, focuses on mining complementary information from diverse views. However, existing works often fuse multiple views’ representations or handle clustering in a common feature space, which may result in their entanglement especially for visual representations. To address this issue, we present a novel VAE-based multi-view clustering framework (Multi-VAE) by learning disentangled visual representations. Concretely, we define a view-common variable and multiple view-peculiar variables in the generative model. The prior of view-common variable obeys approximately discrete Gumbel Softmax distribution, which is introduced to extract the common cluster factor of multiple views. Meanwhile, the prior of view-peculiar variable follows continuous Gaussian distribution, which is used to represent each view’s peculiar visual factors. By controlling the mutual information capacity to disentangle the view-common and view-peculiar representations, continuous visual information of multiple views can be separated so that their common discrete cluster information can be effectively mined. Experimental results demonstrate that Multi-VAE enjoys the disentangled and explainable visual representations, while obtaining superior clustering performance compared with state-of-the-art methods.