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.

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 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.