Due to the efficiency of discovering the high-order correlations of multiple views, tensorized multi-view clustering (TMVC) has been extensively investigated and achieve impressive performance. However, previous TMVC studies merely emphasize on exploring the multi-view consistency, but rarely consider the cross-view inconsistency that may be caused by noise, corruptions or view-specific properties, rendering the abundant information contained in multiple features cannot be comprehensively detected. To this end, this paper proposes aTwin tensOrized affinity learning framewOrk for mulTi-view cluStering (TOOTS), which seamlessly integrates multi-view consistency and cross-view inconsistency into a unified framework. Specifically, the TOOTS model employs the self-representation mechanism to learn two sets of affinity matrices, which are reorganized into twin tensors (i.e., consistent tensor and diverse tensor). Meanwhile, tensor low-rank constraint and exclusive lasso with$\ell _{21}$regularization are imposed on consistent part and diverse part respectively, leading to the intra-view spatial structure and the inter-view inconsistency be exploited simultaneously. Furthermore, the multiple consistent factors are manipulated by a connectivity constraint and fused into a consensus graph with different weights, making the explicit clusters structural and the salient difference between views effectively leveraged. Substantial experimental results demonstrate that the proposed TOOTS model outperforms state-of-the-arts.

Incomplete Multi-View Clustering (IMVC) has made significant progress by optimally merging multiple pre-specified incomplete views. Most existing IMVC algorithms operate under the assumption that view alignment is known, but in practice, the coupling information between views may be absent, thereby limiting the practical applicability of these methods. Being aware of this, we propose a novel IMVC method named Kernel cOupling And eLement imputAtion induced Multi-View Clustering (KOALA), which sufficiently explores the nonlinear relationship among features and optimally processes a group of kernels with missing and unaligned elements to simultaneously resolve multi-view clustering problem under both uncoupled and incomplete scenarios. Specifically, we first introduce a cross-kernel alignment learning strategy to reconstruct the coupling relationships among multiple kernels, which effectively captures high-order nonlinear relationships among samples and enhances alignment accuracy. Additionally, a low-rank tensor constraint is imposed on the optimizable alignment kernel tensor, facilitating the effective imputation of missing kernel elements by leveraging consistency information across views. Subsequently, we develop an alternative optimization approach with promising convergence to solve the resultant optimization problem. Extensive experimental results on various multi-view datasets demonstrate that the KOALA method achieves remarkable clustering performance.

Deep multi-view clustering (DMVC) has emerged as a promising paradigm for integrating information from multiple views by leveraging the representation power of deep neural networks. However, most existing DMVC methods primarily focus on modeling pairwise relationships between samples, while neglecting higher-order structural dependencies among multiple samples, which may hinder further improvements in clustering performance. To address this limitation, we propose a hypergraph neural network (HGNN)-driven multi-view clustering framework, termed Hypergraph-enhanced cOntrastive learning with hyPEr-Laplacian regulaRization (HOPER), a novel model that jointly captures high-order correlations and preserves local manifold structures across views. Specifically, we first construct view-specific hypergraph structures and employ the HGNN to learn node representations, thereby capturing high-order relationships among samples. Furthermore, we design a hypergraph-driven dual contrastive learning mechanism that integrates inter-view contrastive learning with intra-hyperedge contrastive learning, promoting cross-view consistency while maintaining discriminability within hyperedges. Finally, a hyper-Laplacian manifold regularization is introduced to preserve the local geometric structure within each view, thereby enhancing the structural fidelity and discriminative power of the learned representations. Extensive experiments on diverse datasets demonstrate the effectiveness of our approach.

Tensorized Incomplete Multi-View Clustering (TIMVC) algorithms have attracted growing attention for their ability to capture high-order correlations across multiple views. However, most existing TIMVC methods rely on simplistic noise assumptions using specific norms (e.g., $\ell_1$ or $\ell_{2,1}$), which fail to reflect the complex noise patterns encountered in real-world scenarios. Moreover, they primarily focus on modeling the global Euclidean structure of the tensor representation, while overlooking the preservation of local manifold structures. To address these limitations, we propose a novel approach, GaUssian regressIon-driven TIMVC with dual mAnifold Regularization (GUITAR). Specifically, we employ a Gaussian regression model to characterize complex noise distributions in a more realistic and flexible manner. Meanwhile, a dual manifold regularization is introduced in tensor representation learning, simultaneously modeling manifold information at both the view-specific and cross-view consensus levels, thereby promoting intra-view and inter-view consistency in the tensor representation. Furthermore, to better capture the intrinsic low-rank structure, we propose the high-preservation $\ell_{\delta}$-norm tensor rank constraint, which applies differentiated penalties to the singular values, thereby enhancing the robustness of the tensor representation. In addition, an efficient optimization algorithm is developed to solve the resulting non-convex problem with provable convergence. Extensive experiments on six datasets demonstrate that our method outperforms SOTA approaches.

This paper presents an efficient and scalable incomplete multi-view clustering method, referred to as Enhanced Dictionary-Induced tenSorized incomplete multi-view clustering with Gaussian errOr raNk minimization (EDISON). Specifically, EDISON employs an enhanced dictionary representation strategy as the foundation for inferring missing data and constructing anchor graphs, ensuring robustness to less-than-ideal data and maintaining high computational efficiency. Additionally, we introduce Gaussian error rank as a concise approximation of the true tensor rank, facilitating a comprehensive exploration of the diverse information encapsulated by various singular values in tensor data. Additionally, we integrate a hyper-anchor graph Laplacian manifold regularization into the tensor representation, allowing for the simultaneous utilization of inter-view high-order correlations and intra-view local correlations. Extensive experiments demonstrate the superiority of the EDISON model in both effectiveness and efficiency compared to SOTA methods.

Benefiting from the effective exploitation of the high-order correlations across multiple views, tensor-based multi-view clustering (TMVC) has garnered considerable attention in recent years. Nevertheless, prior TMVC techniques commonly involve assembling multiple view-specific spatial similarity graphs into a three-dimensional tensor, overlooking the intrinsic topological structure essential for precise clustering of data within a manifold. Additionally, mainstream techniques are constrained by equally shrinking all singular values to recover a low-rank tensor, limiting their capacity to distinguish significant variations among different singular values. In this investigation, we present an innovative TMVC framework termed toPology-driven multi-view clustering viA refined teNsorial sigmoiD rAnk minimization (PANDA ). Specifically, PANDA extracts view-specific topological structures from Euclidean graphs and intricately integrates them into a low-rank three-dimensional tensor, facilitating the concurrent utilization of intra-view topological connectivity and inter-view high-order correlations. Moreover, we develop a refined sigmoid function as the tighter surrogate to tensor rank, enabling the exploration of significant information of heterogeneous singular values. Meanwhile, the topological structures are merged into a unified structure with varying weights, associated with a connectivity constraint, empowering the significant divergence among views and the explicit cluster structure of the target graph are simultaneously leveraged. Extensive experiments demonstrate the superiority of PANDA, outperforming SOTA methods.

While Tensor-based Multi-view Subspace Clustering (TMSC) has garnered significant attention for its capacity to effectively capture high-order correlations among multiple views, three notable limitations in current TMSC methods necessitate consideration: 1) high computational complexity and reliance on dictionary completeness resulting from using observed data as the dictionary, 2) inaccurate subspace representation stemming from the oversight of local geometric information and 3) under-penalization of noise-related singular values within tensor data caused by treating all singular values equally. To address these limitations, this paper presents a \textbf{S}calable TMSC framework with \textbf{T}riple inf\textbf{O}rmatio\textbf{N} \textbf{E}nhancement (\textbf{STONE}). Notably, an enhanced anchor dictionary learning mechanism has been utilized to recover the low-rank anchor structure, resulting in reduced computational complexity and increased resilience, especially in scenarios with inadequate dictionaries. Additionally, we introduce an anchor hypergraph Laplacian regularizer to preserve the inherent geometry of the data within the subspace representation. Simultaneously, an improved hyperbolic tangent function has been employed as a precise approximation for tensor rank, effectively capturing the significant variations in singular values. Extensive experimentation on a variety of datasets demonstrates that our approach surpasses SOTA methods in both effectiveness and efficiency.

Benefiting from the effective exploration of the valuable topological pair-wise relationship of data points across multiple views, multi-view subspace clustering (MVSC) has received increasing attention in recent years. However, we observe that existing MVSC approaches still suffer from two limitations that need to be further improved to enhance the clustering effectiveness. Firstly, previous MVSC approaches mainly prioritize extracting multi-view consistency, often neglecting the cross-view discrepancy that may arise from noise, outliers, and view-inherent properties. Secondly, existing techniques are constrained by their reliance on pair-wise sample correlation and pair-wise view correlation, failing to capture the high-order correlations that are enclosed within multiple views. To address these issues, we propose a novel MVSC framework via joiNt crOss-view discrepancy discOvery anDhigh-order correLation dEtection (NOODLE), seeking an informative target subspace representation compatible across multiple features to facilitate the downstream clustering task. Specifically, we first exploit the self-representation mechanism to learn multiple view-specific affinity matrices, which are further decomposed into cohesive factors and incongruous factors to fit the multi-view consistency and discrepancy, respectively. Additionally, an explicit cross-view sparse regularization is applied to incoherent parts, ensuring the consistency and discrepancy to be precisely separated from the initial subspace representations. Meanwhile, the multiple cohesive parts are stacked into a three-dimensional tensor associated with a tensor-Singular Value Decomposition (t-SVD) based weighted tensor nuclear norm constraint, enabling effective detection of the high-order correlations implicit in multi-view data. Our proposed method outperforms state-of-the-art methods for multi-view clustering on six benchmark datasets, demonstrating its effectiveness.

Multi-view subspace clustering (MVSC), which leverages comprehensive information from multiple views to effectively reveal the intrinsic relationships among instances, has garnered significant research interest. However, previous MVSC research focuses on exploring the cross-view consistent information only in the instance representation hierarchy or affinity relationship hierarchy, which prevents a joint investigation of the multi-view consistency in multiple hierarchies. To this end, we propose a Triple-gRanularity contrastive learning framework for deep mUlti-view Subspace clusTering (TRUST), which benefits from the comprehensive discovery of valuable information from three hierarchies, including the instance, specific-affinity relationship, and consensus-affinity relationship. Specifically, we first use multiple view-specific autoencoders to extract noise-robust instance representations, which are then respectively input into the MLP model and self-representation model to obtain high-level instance representations and view-specific affinity matrices. Then, the instance and specific-affinity relationship contrastive regularization terms are separately imposed on the high-level instance representations and view specific-affinity matrices, ensuring the cross-view consistency can be found from the instance representations to the view-specific affinity matrices. Furthermore, multiple view-specific affinity matrices are fused into a consensus one associated with the consensus-affinity relationship contrastive constraint, which embeds the local structural relationship of high-level instance representations into the consensus affinity matrix. Extensive experiments on various datasets demonstrate that our method is more effective when compared with other state-of-art methods.

Multi-view clustering, which aims at boosting the clustering performance by leveraging the individual information and the common information of multi-view data, has gained extensive consideration in recent years. However, most existing multi-view clustering algorithms either focus on extracting the multi-view individuality or emphasize on exploring the multi-view commonality, neither of which can fully utilize the comprehensive information from multiple views. To this end, we propose a novel algorithm named V iew-specific and C onsensus G raph A lignment (VCGA) for multi-view clustering, which simultaneously formulates the multi-view individuality and the multi-view commonality into a unified framework to effectively partition data points. To be specific, the VCGA model constructs the view-specific graphs and the shared graph from original multi-view data and hidden latent representation, respectively. Furthermore, the view-specific graphs of different views and the consensus graph are aligned into an informative target graph, which is employed as a crucial input to the standard spectral clustering method for clustering. Extensive experimental results on six benchmark datasets demonstrate the superiority of our method against other state-of-the-art clustering algorithms.

Graph-based Multi-View Clustering (GMVC) has received extensive attention due to its ability to capture the neighborhood relationship among data points from diverse views. However, most existing approaches construct similarity graphs from the original multi-view data, the accuracy of which heavily and implicitly relies on the quality of the original multiple features. Moreover, previous methods either focus on mining the multi-view commonality or emphasize on exploring the multi-view individuality, making the rich information contained in multiple features cannot be effectively exploited. In this work, we design a novel GMVC framework via c O mmo N ality and I ndividuality disc O vering in late N t subspace ( ONION ), seeking for a robust and discriminative subspace representation compatible across multiple features for GMVC. To be specific, our method simultaneously formulates the unsupervised sparse feature selection and the robust subspace extraction, as well as the target graph learning in a unified optimization model, which can help the learning of the discriminative subspace representation and the target graph in a mutual reinforcement manner. Meanwhile, we manipulate the target graph by an explicit structural penalty, rendering the connected components in the graph directly reveal clusters. Experimental results on seven benchmark datasets demonstrate the effectiveness of our proposed method.