Multi-view clustering aims to group data by integrating complementary information from multiple views. However, the inherent heterogeneity among views often leads to feature entanglement, severely limiting clustering performance. To address this challenge, we propose DC-SPAN—a Dual Contrastive Attention Network—grounded in a disentangle-then-fuse paradigm. DC-SPAN employs a dual-path variational architecture to explicitly decompose each view into shared and private latent subspaces. These representations are then robustly integrated via a Product-of-Experts (PoE) mechanism. At the heart of our model is a novel dual contrastive learning objective that simultaneously encourages alignment of shared components across views and enforces separation of private ones, enabling structured and disentangled representations. A gated attention fusion module further adaptively aggregates these latent factors to yield a unified, discriminative embedding. The overall model is trained end-to-end using a composite loss function that incorporates reconstruction, orthogonality, and contrastive terms, along with a two-stage training scheme for improved stability. Extensive experiments on benchmark datasets demonstrate that DC-SPAN consistently outperforms existing state-of-the-art methods, highlighting its effectiveness and robustness in handling multi-view heterogeneity.

Multi-view clustering aims to uncover shared semantics and complementary information across different views. However, the inherent heterogeneity among views poses significant challenges to effective collaborative modeling and information integration. While recent studies have introduced distillation-based mechanisms to enhance cross-view consistency and alleviate heterogeneity, these approaches often rely on manually defined knowledge transfer paths or fixed fusion weights, which are inflexible in handling complex and dynamic view relationships in practice. To address this issue, we propose HOARD: a novel framework for Hierarchical crOss-view Alignment for multi-view clusteRing via Decoupled information distillation. HOARD structurally decouples multi-view representations into shared and specific components, and performs hierarchical alignment. Specifically, we introduce a granular-ball contrastive alignment to enhance the semantic consistency of shared features, and a prototype collaborative transmission alignment strategy to align specific features while preserving view-specific structural characteristics. Moreover, we design an information distillation unit to adaptively model cross-view knowledge transfer in both feature spaces. An attention mechanism is further employed to integrate shared and specific information. Extensive experiments on benchmark datasets demonstrate that HOARD significantly improves alignment quality and clustering performance, achieving state-of-the-art results.

Single-cell multi-view clustering enables the exploration of cellular heterogeneity within the same cell from different views. Despite the development of several multi-view clustering methods, two primary challenges persist. First, most existing methods treat the information from both single-cell RNA (scRNA) and single-cell Assay of Transposase Accessible Chromatin (scATAC) views as equally significant, overlooking the substantial disparity in data richness between the two views. This oversight frequently leads to a degradation in overall performance. Additionally, the majority of clustering methods necessitate manual specification of the number of clusters by users. However, for biologists dealing with cell data, precisely determining the number of distinct cell types poses a formidable challenge. To this end, we introduce scUNC, an innovative multi-view clustering approach tailored for single-cell data, which seamlessly integrates information from different views without the need for a predefined number of clusters. The scUNC method comprises several steps: initially, it employs a cross-view fusion network to create an effective embedding, which is then utilized to generate initial clusters via community detection. Subsequently, the clusters are automatically merged and optimized until no further clusters can be merged. We conducted a comprehensive evaluation of scUNC using six distinct single-cell datasets. The results underscored that scUNC outperforms the other baseline methods.

Multi-view clustering (MVC) leverages complementary information across heterogeneous views to improve unsupervised partitioning. Nevertheless, the majority of existing MVC methods critically assume that samples are fully aligned across views, an assumption frequently violated in practice when multi-view data are collected from independent sources without any correspondence. This gives rise to Completely Unaligned multi-view Clustering (CUC), where cross-view sample correspondences are entirely unknown, fundamentally impeding effective multi-view fusion. Prior CUC-oriented methods typically infer inter-view relations from distance/similarity matrices; however, severe cross-view heterogeneity often induces over-smoothing in such matrices, leading to unreliable matching signals and degraded clustering performance. To address these issues, we propose Cross-view Graph Matching for Completely Unaligned multi-view Clustering (CGM-CUC), a unified framework that couples structure-aware representation learning with progressive cross-view alignment. Specifically, CGM-CUC introduces a bipartite graph-based sample re-encoding mechanism to enhance discriminative structural cues, and an iterative cross-view matching network that progressively refines permutation matrices to recover latent correspondences. Moreover, we develop an alignment-guided optimization strategy that mitigates the over-smoothing effect in similarity estimation, thereby stabilizing the matching process and improving downstream clustering. Extensive experiments on multiple benchmark datasets demonstrate that CGM-CUC consistently achieves superior performance over state-of-the-art baselines, with particularly notable gains under fully unaligned view settings.

In incomplete multi-view clustering (IMVC), missing data induce prototype shifts within views and semantic inconsistencies across views. A feasible solution is to explore cross-view consistency in paired complete observations, further imputing and aligning the similarity relationships inherently shared across views. Nevertheless, existing methods are constrained by two-tiered limitations: (1) Neither instance- nor cluster-level consistency learning construct a semantic space shared across views to learn consensus semantics. The former enforces cross-view instances alignment, and wrongly regards unpaired observations with semantic consistency as negative pairs; the latter focuses on cross-view cluster counterparts while coarsely handling fine-grained intra-cluster relationships within views. (2) Excessive reliance on consistency results in unreliable imputation and alignment without incorporating view-specific cluster information. Thus, we propose an IMVC framework, imputation- and alignment-free for consensus semantics learning (FreeCSL). To bridge semantic gaps across all observations, we learn consensus prototypes from available data to discover a shared space, where semantically similar observations are pulled closer for consensus semantics learning. To capture semantic relationships within specific views, we design a heuristic graph clustering based on modularity to recover cluster structure with intra-cluster compactness and inter-cluster separation for cluster semantics enhancement. Extensive experiments demonstrate, compared to state-of-the-art competitors, FreeCSL achieves more confident and robust assignments on IMVC task.

Multi-view clustering aims to improve clustering accuracy by effectively integrating complementary information from multiple perspectives. However, existing methods often encounter challenges such as feature conflicts between views and insufficient enhancement of individual view features, which hinder clustering performance. To address these challenges, we propose a novel framework, EPFMVC, which integrates feature enhancement with progressive fusion to more effectively align multi-view data. Specifically, we introduce two key innovations: (1) a Feature Channel Attention Encoder (FCAencoder), which adaptively enhances the most discriminative features in each view, and (2) a View Graph-based Progressive Fusion Mechanism, which constructs a view graph using optimal transport (OT) distance to progressively fuse similar views while minimizing inter-view conflicts. By leveraging multi-head attention, the fusion process gradually integrates complementary information, ensuring more consistent and robust shared representations. These innovations enable superior representation learning and effective fusion across views. Extensive experiments demonstrate that our method significantly outperforms state-of-the-art techniques, achieving notable improvements in multi-view clustering tasks across various datasets and evaluation metrics.

Multi-view clustering (MVC) has emerged as a leading paradigm in unsupervised learning, gaining significant attention. Central to this framework is the concept of view-pair contrastive learning, which aims to maximize mutual information between pairs of views, thereby facilitating consistent latent representations. Nevertheless, two critical challenges remain: i) Identifying the most suitable pairs of views for contrastive learning becomes difficult when more than two views are available, especially in the absence of prior knowledge; ii)Including all available views in contrastive learning can degrade performance due to the presence of low-quality views. To address these issues, we propose a novel mechanism, EASEMVC(Efficient DuAl Selection MEchanism for Deep Multi-View Clustering). EASEMVC begins by constructing a view graph using the Optimal Transport (OT) distance between bipartite graphs of individual views. A view selection module is then designed to perform efficient view-level selection based on the topological relationships within the view graph. Additionally, a cross-view sample graph is built at the sample level, where the topological relationships among samples are used to generate reliable learning weights. Leveraging the selected view pairs and sample weights, contrastive learning is employed to obtain consistent representations across views. Extensive experiments across six benchmark datasets demonstrate that EASEMVC outperforms current state-of-the-art methods.

Multi-view clustering leverages complementary representations from diverse sources to enhance performance. However, real-world data often suffer incomplete cases due to factors like privacy concerns and device malfunctions. A key challenge is effectively utilizing available instances to recover missing views. Existing methods frequently overlook the heterogeneity among views during recovery, leading to significant distribution discrepancies between recovered and true data. Additionally, many approaches focus on cross-view correlations, neglecting insights from intra-view reliable structure and cross-view clustering structure. To address these issues, we propose BURG, a novel method for incomplete multi-view clustering with distriBution dUal-consistency Recovery Guidance. We treat each sample as a distinct category and perform cross-view distribution transfer to predict the distribution space of missing views. To compensate for the lack of reliable category information, we design a dual-consistency guided recovery strategy that includes intra-view alignment guided by neighbor-aware consistency and cross-view alignment guided by prototypical consistency. Extensive experiments on benchmarks demonstrate the superiority of BURG in the incomplete multi-view scenario.

Most of incomplete multi-view clustering (IMVC) methods typically choose to ignore the missing samples and only utilize observed unpaired samples to construct bipartite similarity. Moreover, they employ a single quantity of prototypes to extract the information of $\textbf{all}$ views. To eliminate these drawbacks, we present a simple yet effective IMVC approach, SIIHPC, in this work. It firstly transforms partial bipartition learning into original sample form by virtue of reconstruction concept to split out of observed similarity, and then loosens traditional non-negative constraints via regularizing samples to more freely characterize the similarity. Subsequently, it learns to recover the incomplete parts by utilizing the connection built between the similarity exclusive on respective view and the consensus graph shared for all views. On this foundation, it further introduces a group of hybrid prototype quantities for each individual view to flexibly extract the data features belonging to each view itself. Accordingly, the resulting graphs are with various scales and describe the overall similarity more comprehensively. It is worth mentioning that these all are optimized in one unified learning framework, which makes it possible for them to reciprocally promote. Then, to effectively solve the formulated optimization problem, we design an ingenious auxiliary function that is with theoretically proven monotonic-increasing properties. Finally, the clustering results are obtained by implementing spectral grouping action on the eigenvectors of stacked multi-scale consensus similarity. Experimental results confirm the effectiveness of SIIHPC.

Recent advancements in multiple kernel clustering (MKC) have highlighted the effectiveness of late fusion strategies, particularly in enhancing computational efficiency to near-linear complexity while achieving promising clustering performance. However, existing methods encounter three significant limitations: (1) reliance on fixed base partition matrices that do not adaptively optimize during the clustering process, thereby constraining their performance to the inherent representational capabilities of these matrices; (2) a focus on adjusting kernel weights to explore inter-view consistency and complementarity, which often neglects the intrinsic high-order correlations among views, thereby limiting the extraction of comprehensive multiple kernel information; (3) a lack of adaptive mechanisms to accommodate varying distributions within the data, which limits robustness and generalization. To address these challenges, this paper proposes a novel algorithm termed Dynamic Late Fusion Multiple Kernel Clustering with Robust {Tensor Learning via min-max optimization (DLEFT-MKC), which effectively overcomes the representational bottleneck of base partition matrices and facilitates the learning of meaningful high-order cross-view information. Specifically, it is the first to incorporate a min-max optimization paradigm into tensor-based MKC, enhancing algorithm robustness and generalization. Additionally, it dynamically reconstructs decision layers to enhance representation capabilities and subsequently stacks the reconstructed representations for tensor learning that promotes the capture of high-order associations and cluster structures across views, ultimately yielding consensus clustering partitions. To solve the resultant optimization problem, we innovatively design a strategy that combines reduced gradient descent with the alternating direction method of multipliers, ensuring convergence to local optima while maintaining high computational efficiency. Extensive experimental results across various benchmark datasets validate the superior effectiveness and efficiency of the proposed DLEFT-MKC.

Current multi-view clustering (MVC) techniques generally focus only on the relationship between anchors and samples, while overlooking that between anchors. Moreover, due to the lack of data labels, the cluster order is inconsistent across views and accordingly anchors encounter misalignment, which will confuse the graph structure and disorganize cluster representation. Even worse, it typically brings variance during forming spectral embedding, degenerating the stability of clustering results. In response to these concerns, in the paper we propose a MVC approach named DTP-SF-BVF. Concretely, we explicitly exploit the geometric properties between anchors via self-expression learning skill, and utilize topology learning strategy to feed captured anchor-anchor features into anchor-sample graph so as to explore the manifold structure hidden within samples more adequately. To reduce the misalignment risk, we introduce a permutation mechanism for each view to jointly rearrange anchors according to respective view characteristics. Besides not involving selecting the baseline view, it also can coordinate with anchors in the unified framework and thereby facilitate the learning of anchors. Further, rather than forming spectrum and then performing embedding partitioning, based on the criterion that samples and clusters should be hard assignment, we manage to construct the cluster labels directly from original samples using the binary strategy, not only preserving the data diversity but avoiding variance. Experiments on multiple publicly available datasets confirm the effectiveness of proposed DTP-SF-BVF method.

Multi-view clustering aims to effectively integrate data from multiple views to uncover the underlying clustering structure. However, existing methods typically adopt direct fusion strategies for multiview data, neglecting the issues of view gap-induced heterogeneity and the imbalance in view quality. Particularly, when there are significant differences between views, such direct fusion often leads to the loss of critical information and a decline in clustering performance. To address these challenges, we propose a novel Dynamic Progressive Fusion Multi-View Clustering (DPFMVC). DPFMVC employs a view-adaptive fusion mechanism that dynamically selects the most similar views, reducing conflicts between views while preserving complementary information. Additionally, DPFMVC introduces a dual contrastive loss module and a progressive fusion loss, which effectively align sample features with clustering centers, promoting efficient integration of multi-view information. Specifically, the dual contrastive loss compares the similarity between sample features and cluster centers, ensuring cross-view feature consistency and thus enhancing the discriminability of clustering. Meanwhile, the progressive fusion loss progressively adjusts the fusion order of views, effectively reducing the negative impact of low-quality views on the clustering results, strengthening the synergy between views, and facilitating more effective information fusion.Comprehensive experiments on multiple public benchmarks show that DPFMVC delivers superior clustering results and exhibits overall great effectiveness compared to state-of-the-art techniques.

Although receiving notable improvements, current multi-view clustering (MVC) techniques generally rely on feature library mechanisms to propagate accumulated knowledge from historical views to newly-arrived data, which overlooks the information pertaining to basis embedding within each view. Moreover, the mapping paradigm inevitably alters the values of learned landmarks and built affinities due to the uninterruption nature, accordingly disarraying the hierarchical cluster structures. To mitigate these two issues, we in the paper provide a named BSTM algorithm. Concretely, we firstly synchronize with the distinct dimensions by introducing a group of specialized projectors, and then establish unified anchors for all views collected so far to capture intrinsic patterns. Afterwards, departing from per-view architectures, we devise a shared bipartite graph construction via indicators to quantify similarity, which not only avoids redundant data-recalculations but alleviates the representation distortion caused by fusion. Crucially, there two components are optimized within an integrated framework, and collectively facilitate knowledge transfer upon encountering incoming views. Subsequently, to flexibly do transformation on anchors and meanwhile maintain numerical consistency, we develop a bit-swapping scheme operating exclusively on 0 and 1. It harmonizes anchors on current view and that on previous views through one-hot encoded row and column attributes, and the graph structures are correspondingly reordered to reach a matched configuration. Furthermore, a computationally efficient four-step updating strategy with linear complexity is designed to minimize the associated loss. Extensive experiments organized on publicly-available benchmark datasets with varying missing percentages confirm the superior effectiveness of our BSTM.

Incomplete multi-view clustering has gained significant attention due to the prevalence of incomplete multi-view data in real-world scenarios. However, existing methods often overlook the critical role of inter-view relationships. In unsupervised settings, selectively leveraging cross-view topological relationships can effectively guide view completion and representation learning. To address this challenge, we propose a novel framework called Selective Cross-View Topology Incomplete Multi-View Clustering (SCVT). Our approach constructs a view topology graph using the Optimal Transport (OT) distance between view. This graph helps identify neighboring views for those with missing data, enabling the inference of topological relationships and accurate completion of missing samples. Additionally, we introduce the Max View Graph Contrastive Alignment module to facilitate information transfer and alignment across neighboring views. Furthermore, we propose the View Graph Weighted Intra-View Contrastive Learning module, which enhances representation learning by pulling representations of samples within the same cluster closer, while applying varying degrees of enhancement across different views based on the view graph. Our method achieves state-of-the-art performance on seven benchmark datasets, significantly outperforming existing methods for incomplete multi-view clustering and demonstrating its effectiveness.

The success of multiview raw data mining relies on the integrity of attributes. However, each view faces various noises and collection failures, which leads to a condition that attributes are only partially available. To make matters worse, the attributes in multiview raw data are composed of multiple forms, which makes it more difficult to explore the structure of the data especially in multiview clustering task. Due to the missing data in some views, the clustering task on incomplete multiview data confronts the following challenges, namely: 1) mining the topology of missing data in multiview is an urgent problem to be solved; 2) most approaches do not calibrate the complemented representations with common information of multiple views; and 3) we discover that the cluster distributions obtained from incomplete views have a cluster distribution unaligned problem (CDUP) in the latent space. To solve the above issues, we propose a deep clustering framework based on subgraph propagation and contrastive calibration (SPCC) for incomplete multiview raw data. First, the global structural graph is reconstructed by propagating the subgraphs generated by the complete data of each view. Then, the missing views are completed and calibrated under the guidance of the global structural graph and contrast learning between views. In the latent space, we assume that different views have a common cluster representation in the same dimension. However, in the unsupervised condition, the fact that the cluster distributions of different views do not correspond affects the information completion process to use information from other views. Finally, the complemented cluster distributions for different views are aligned by contrastive learning (CL), thus solving the CDUP in the latent space. Our method achieves advanced performance on six benchmarks, which validates the effectiveness and superiority of our SPCC.

Multiview clustering thrives in applications where views are collected in advance by extracting consistent and complementary information among views. However, it overlooks scenarios where data views are collected sequentially, i.e., real-time data. Due to privacy issues or memory burden, previous views are not available with time in these situations. Some methods are proposed to handle it but are trapped in a stability-plasticity dilemma. In specific, these methods undergo a catastrophic forgetting of prior knowledge when a new view is attained. Such a catastrophic forgetting problem (CFP) would cause the consistent and complementary information hard to get and affect the clustering performance. To tackle this, we propose a novel method termed contrastive continual multiview clustering with filtered structural fusion (CCMVC-FSF). Precisely, considering that data correlations play a vital role in clustering and prior knowledge ought to guide the clustering process of a new view, we develop a data buffer to store filtered structural information and utilize it to guide the generation of a robust partition matrix via contrastive learning. Additionally, to address the high complexity involved in acquiring and storing structural information, we propose a sampling strategy called clustering then sample. Furthermore, we theoretically connect CCMVC-FSF with semisupervised learning and knowledge distillation. Extensive experiments exhibit the excellence of the proposed method. Our code is publicly available at https://github.com/wanxinhang/CCMVC-FSF/.

Multi-view graph clustering (MVGC) derives encouraging grouping results by seamlessly integrating abundant information inside heterogeneous data, and has captured surging focus recently. Nevertheless, the majority of current MVGC works involve at least one hyper-parameter, which not only requires additional efforts for tuning, but also leads to a complicated solving procedure, largely harming the flexibility and scalability of corresponding algorithms. To this end, in the article we are devoted to getting rid of hyper-parameters, and devise a non-parametric graph clustering (NpGC) framework to more practically partition multi-view data. To be specific, we hold that hyper-parameters play a role in balancing error item and regularization item so as to form high-quality clustering representations. Therefore, under without the assistance of hyper-parameters, how to acquire high-quality representations becomes the key. Inspired by this, we adopt two types of anchors, view-related and view-unrelated, to concurrently mine exclusive characteristics and common characteristics among views. Then, all anchors' information is gathered together via a consensus bipartite graph. By such ways, NpGC extracts both complementary and consistent multi-view features, thereby obtaining superior clustering results. Also, linear complexities enable it to handle datasets with over 120000 samples. Numerous experiments reveal NpGC's strong points compared to lots of classical approaches.

In recent years, anchor-based methods have achieved promising progress in multi-view clustering. The performances of these methods are significantly affected by the quality of the anchors. However, the anchors generated by previous works solely rely on single-view information, ig-noring the correlation among different views. In particular, we observe that similar patterns are more likely to exist between similar views so such correlation information can be leveraged to enhance the quality of the anchors, which is also omitted. To this end, we propose a novel plug-and-play anchor enhancement strategy through view correlation for multi-view clustering. Specifically, we construct a view graph based on aligned initial anchor graphs to explore inter-view correlations. By learning from view correlation, we enhance the anchors of the current view using the relationships between anchors and samples on neighboring views, thereby narrowing the spatial distribution of anchors on similar views. Experimental results on seven datasets demonstrate the superiority of our proposed method over other existing methods. Furthermore, extensive comparative experiments validate the effectiveness of the proposed anchor enhancement module when applied to various anchor-based methods.

Incomplete multi-view clustering (IMVC) methods typically encounter three drawbacks: (1) intense time and/or space overheads; (2) intractable hyper-parameters; (3) non-zero variance results. With these concerns in mind, we give a simple yet effective IMVC scheme, termed as ToRES. Concretely, instead of self-expression affinity, we manage to construct prototype-sample affinity for incomplete data so as to decrease the memory requirements. To eliminate hyper-parameters, besides mining complementary features among views by view-wise prototypes, we also attempt to devise cross-view prototypes to capture consensus features for jointly forming high-quality clustering representation. To avoid the variance, we successfully unify representation learning and clustering operation, and directly optimize the discrete cluster indicators from incomplete data. Then, for the resulting objective function, we provide two equivalent solutions from perspectives of feasible region partitioning and objective transformation. Many results suggest that ToRES exhibits advantages against 20 SOTA algorithms, even in scenarios with a higher ratio of incomplete data.

Multi-view clustering, a pivotal technology in multimedia research, aims to leverage complementary information from diverse perspectives to enhance clustering performance. The current multi-view clustering methods normally enforce the reduction of distances between any pair of views, overlooking the heterogeneity between views, thereby sacrificing the diverse and valuable insights inherent in multi-view data. In this paper, we propose a Tree-Based View-Gap Maintaining Multi-View Clustering (TGM-MVC) method. Our approach introduces a novel conceptualization of multiple views as a graph structure. In this structure, each view corresponds to a node, with the view gap, calculated by the cosine distance between views, acting as the edge. Through graph pruning, we derive the minimum spanning tree of the views, reflecting the neighbouring relationships among them. Specifically, we applied a share-specific learning framework, and generate view trees for both view-shared and view-specific information. Concerning shared information, we only narrow the distance between adjacent views, while for specific information, we maintain the view gap between neighboring views. Theoretical analysis highlights the risks of eliminating the view gap, and comprehensive experiments validate the efficacy of our proposed TGM-MVC method.

Incomplete multi-view clustering aims to learn complete correlations among samples by leveraging complementary information across multiple views for clustering. Anchor-based methods further establish sample-level similarities for representative anchor generation, effectively addressing scalability issues in large-scale scenarios. Despite efficiency improvements, existing methods overlook the misguidance in anchors learning induced by partial missing samples, i.e., the absence of samples results in shift of learned anchors, further leading to sub-optimal clustering performance. To conquer the challenges, our solution involves a cross-view reconstruction strategy that not only alleviate the anchor shift problem through a carefully designed cross-view learning process, but also reconstructs missing samples in a way that transcends the limitations imposed by convex combinations. By employing affine combinations, our method explores areas beyond the convex hull defined by anchors, thereby illuminating blind spots in the reconstruction of missing samples. Experimental results on four benchmark datasets and three large-scale datasets validate the effectiveness of our proposed method.

In recent years, there has been a growing trend in the realm of parallel clustering analysis for single-cell RNA-seq (scRNA) and single-cell Assay of Transposase Accessible Chromatin (scATAC) data. However, prevailing methods often treat these two data modalities as equals, neglecting the fact that the scRNA mode holds significantly richer information compared to the scATAC. This disregard hinders the model benefits from the insights derived from multiple modalities, compromising the overall clustering performance. To this end, we propose an effective multi-modal clustering model scEMC for parallel scRNA and Assay of Transposase Accessible Chromatin data. Concretely, we have devised a skip aggregation network to simultaneously learn global structural information among cells and integrate data from diverse modalities. To safeguard the quality of integrated cell representation against the influence stemming from sparse scATAC data, we connect the scRNA data with the aggregated representation via skip connection. Moreover, to effectively fit the real distribution of cells, we introduced a Zero Inflated Negative Binomial-based denoising autoencoder that accommodates corrupted data containing synthetic noise, concurrently integrating a joint optimization module that employs multiple losses. Extensive experiments serve to underscore the effectiveness of our model. This work contributes significantly to the ongoing exploration of cell subpopulations and tumor microenvironments, and the code of our work will be public at https://github.com/DayuHuu/scEMC.

Incomplete multiview clustering (IMVC) generally requires the number of anchors to be the same in all views. Also, this number needs to be tuned with extra manual efforts. This not only degenerates the diversity of multiview data but also limits the model's scalability. For generating differentiated numbers of anchors without tuning, in this article we devise a novel framework named DAQINT. To be specific, the most perfect solution is to jointly find the optimal number of anchors that belongs to respective view. Regretfully, it is extremely time consuming. In view of this, we choose to first offer a set of anchor numbers for each view, and then integrate their contributions by adaptive weighting to approximate the optimal number. In particular, these offered numbers are all predefined and do not require any tuning. Through adaptively weighting them, we hold that this equivalently makes each view enjoy a different number of anchors. Accordingly, the bipartite graphs generated on all views are with diverse scales. Besides exploring multiview features more deeply, they also balance the importance between views. Then, to fuse these multiscale bipartite graphs, we design a combination strategy that owns linear computation and storage overheads. Afterward, to solve the resulting optimization problem, we also carefully develop a three-step iterative algorithm with linear complexities and demonstrated convergence. Experiments on the multiple public datasets validate the superiority of DAQINT against several advanced IMVC methods, such as on Mfeat, DAQINT surpasses the competitors like MKC, EEIMVC, FLSD, DSIMVC, IMVC-CBG, and DCP by 36.65%, 6.33%, 48.53%, 22.46%, 15.06%, and 32.04%, respectively, in ACC.

Single-cell multi-view clustering is essential for analyzing the different cell subtypes of the same cell from different views. Some attempts have been made, but most of these models still struggle to handle single-cell sequencing data, primarily due to their non-specific design for cellular data. We observe that such data distinctively exhibits: (1) a profusion of high-order topological correlations, (2) a disparate distribution of information across different views, and (3) inherent fuzzy characteristics, indicating a cell's potential to associate with multiple cluster identities. Neglecting these key cellular patterns could significantly impair medical clustering. In response, we propose a specialized application of fuzzy clustering for single-cell sequencing data, namely the deep Single-cell Multi-view Fuzzy Clustering (scMFC) method. Concretely, we employ a random walk technique to capture high-order topological relationships on the cell graph and have developed a cross-view information aggregation mechanism that adaptively assigns weights to different views. Furthermore, to accurately reflect the dynamic insight in cellular development, we propose a deep fuzzy clustering strategy that allows cells to associate with diverse clusters. Extensive experiments conducted on three real-world single-cell multi-view datasets demonstrate our method's superior performance.

Multiview clustering has attracted increasing attention to automatically divide instances into various groups without manual annotations. Traditional shadow methods discover the internal structure of data, while deep multiview clustering (DMVC) utilizes neural networks with clustering-friendly data embeddings. Although both of them achieve impressive performance in practical applications, we find that the former heavily relies on the quality of raw features, while the latter ignores the structure information of data. To address the above issue, we propose a novel method termed iterative deep structural graph contrast clustering (IDSGCC) for multiview raw data consisting of topology learning (TL), representation learning (RL), and graph structure contrastive learning to achieve better performance. The TL module aims to obtain a structured global graph with constraint structural information and then guides the RL to preserve the structural information. In the RL module, graph convolutional network (GCN) takes the global structural graph and raw features as inputs to aggregate the samples of the same cluster and keep the samples of different clusters away. Unlike previous methods performing contrastive learning at the representation level of the samples, in the graph contrastive learning module, we conduct contrastive learning at the graph structure level by imposing a regularization term on the similarity matrix. The credible neighbors of the samples are constructed as positive pairs through the credible graph, and other samples are constructed as negative pairs. The three modules promote each other and finally obtain clustering-friendly embedding. Also, we set up an iterative update mechanism to update the topology to obtain a more credible topology. Impressive clustering results are obtained through the iterative mechanism. Comparative experiments on eight multiview datasets show that our model outperforms the state-of-the-art traditional and deep clustering competitors.

Graph anomaly detection (GAD) is a vital task in graph-based machine learning and has been widely applied in many real-world applications. The primary goal of GAD is to capture anomalous nodes from graph datasets, which evidently deviate from the majority of nodes. Recent methods have paid attention to various scales of contrastive strategies for GAD, i.e., node-subgraph and node-node contrasts. However, they neglect the subgraph-subgraph comparison information which the normal and abnormal subgraph pairs behave differently in terms of embeddings and structures in GAD, resulting in sub-optimal task performance. In this paper, we fulfill the above idea in the proposed multi-view multi-scale contrastive learning framework with subgraph-subgraph contrast for the first practice. To be specific, we regard the original input graph as the first view and generate the second view by graph augmentation with edge modifications. With the guidance of maximizing the similarity of the subgraph pairs, the proposed subgraph-subgraph contrast contributes to more robust subgraph embeddings despite of the structure variation. Moreover, the introduced subgraph-subgraph contrast cooperates well with the widely-adopted node-subgraph and node-node contrastive counterparts for mutual GAD performance promotions. Besides, we also conduct sufficient experiments to investigate the impact of different graph augmentation approaches on detection performance. The comprehensive experimental results well demonstrate the superiority of our method compared with the state-of-the-art approaches and the effectiveness of the multi-view subgraph pair contrastive strategy for the GAD task. The source code is released at https://github.com/FelixDJC/GRADATE.

The success of existing multi-view clustering relies on the assumption of sample integrity across multiple views. However, in real-world scenarios, samples of multi-view are partially available due to data corruption or sensor failure, which leads to incomplete multi-view clustering study (IMVC). Although several attempts have been proposed to address IMVC, they suffer from the following draw-backs: i) Existing methods mainly adopt cross-view contrastive learning forcing the representations of each sample across views to be exactly the same, which might ignore view discrepancy and flexibility in representations; ii) Due to the absence of non-observed samples across multiple views, the obtained prototypes of clusters might be unaligned and biased, leading to incorrect fusion. To address the above issues, we propose a Cross-view Partial Sample and Prototype Alignment Network (CPSPAN) for Deep Incomplete Multi-view Clustering. Firstly, unlike existing contrastive-based methods, we adopt pair-observed data alignment as 'proxy supervised signals' to guide instance-to-instance correspondence construction among views. Then, regarding of the shifted prototypes in IMVC, we further propose a prototype alignment module to achieve incomplete distribution calibration across views. Extensive experimental results showcase the effectiveness of our proposed modules, attaining noteworthy performance improvements when compared to existing IMVC competitors on benchmark datasets.

Multi-view clustering aims to extract valuable information from different sources or perspectives. Over the years, the deep neural network has demonstrated its superior representation learning capability in multi-view clustering and achieved impressive performance. However, most existing deep clustering approaches are dedicated to merging and exploring the consistent latent representation across multiple views while overlooking the abundant complementary information in each view. Furthermore, finding correlations between multiple views in an unsupervised setting is a significant challenge. To tackle these issues, we present a novel Cross-view Topology based Consistent and Complementary information extraction framework, termed CTCC. In detail, deep embedding can be obtained from the bipartite graph learning module for each view individually. CTCC then constructs the cross-view topological graph based on the OT distance between the bipartite graph of each view. Utilizing the above graph, we maximize the mutual information across views to learn consistent information and enhance the complementarity of each view by selectively isolating distributions from each other. Extensive experiments on five challenging datasets verify that CTCC outperforms existing methods significantly.

Anchor enhanced multi-view late fusion clustering has attracted numerous researchers' attention for its high clustering accuracy and promising efficiency. However, in the existing methods, the anchor points are usually generated through sampling or linearly combining the samples within the datasets, which could result in enormous time consumption and limited representation capability. To solve the problem, in our method, we learn the view-specific anchor points by learning them directly. Specifically, in our method, we first reconstruct the partition matrix of each view through multiplying a view-specific anchor matrix by a consensus reconstruction matrix. Then, by maximizing the weighted alignment between the base partition matrix and its estimated version in each view, we learn the optimal anchor points for each view. In particular, unlike previous late fusion algorithms, which define anchor points as linear combinations of existing samples, we define anchor points as a series of orthogonal vectors that are directly learned through optimization, which expands the learning space of the anchor points. Moreover, based on the above design, the resultant algorithm has only linear complexity and no hyper-parameter. Experiments on $12$ benchmark kernel datasets and 5 large-scale datasets illustrate that the proposed Efficient Anchor Learning-based Multi-view Clustering (AL-MVC) algorithm achieves the state-of-the-art performance in both clustering performance and efficiency.