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 Graph Clustering (DMGC) aims to partition instances into different groups using the graph information extracted from multi-view data. The mainstream framework of DMGC methods applies graph neural networks to embed structure information into the view-specific representations and fuse them for the consensus representation. However, on one hand, we find that the graph learned in advance is not ideal for clustering as it is constructed by original multi-view data and localized connecting. On the other hand, most existing methods learn the consensus representation in a late fusion manner, which fails to propagate the structure relations across multiple views. Inspired by the observations, we propose a Structure-adaptive Unified gRaph nEural network for multi-view clusteRing (SURER), which can jointly learn a heterogeneous multi-view unified graph and robust graph neural networks for multi-view clustering. Specifically, we first design a graph structure learning module to refine the original view-specific attribute graphs, which removes false edges and discovers the potential connection. According to the view-specific refined attribute graphs, we integrate them into a unified heterogeneous graph by linking the representations of the same sample from different views. Furthermore, we use the unified heterogeneous graph as the input of the graph neural network to learn the consensus representation for each instance, effectively integrating complementary information from various views. Extensive experiments on diverse datasets demonstrate the superior effectiveness of our method compared to other state-of-the-art approaches.

Incomplete Multiple Kernel Clustering algorithms, which aim to learn a common latent representation from pre-constructed incomplete multiple kernels from the original data, followed by k-means for clustering. They have attracted intensive attention due to their high computational efficiency. However, our observation reveals that the imputation of these approaches for each kernel ignores the influence of other incomplete kernels. In light of this, we present a novel method called Low-Rank Kernel Tensor Learning for Incomplete Multiple Views Clustering (LRKT-IMVC) to address the above issue. Specifically, LRKT-IMVC first introduces the concept of kernel tensor to explore the inter-view correlations, and then the low-rank kernel tensor constraint is used to further capture the consistency information to impute missing kernel elements, thereby improving the quality of clustering. Moreover, we carefully design an alternative optimization method with promising convergence to solve the resulting optimization problem. The proposed method is compared with recent advances in experiments with different missing ratios on seven well-known datasets, demonstrating its effectiveness and the advantages of the proposed interpolation method.

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.

In this study, we reported the analysis of Arabidopsis thaliana microarray gene expression profile of root tissues after the plant was challenged with fungal pathogen Fusarium solani f. sp. glycines (Fsg). Our microarray analysis showed that the infection caused 130 transcript abundances (TAs) to increase by more than 2 fold and 32 out of 130 TAs were increased by more than 3 fold in the root tissues. However, only nineteen ESTs were observed with a decrease in TAs by more than 2 fold and 13 of them went down more than 3 fold due to the pathogen infection. In addition, the number of the up-regulated genes was nearly seven times more than that of downregulated genes. The coordinate regulation of adjacent genes was detected and the distance distribution of the nearest neighbor genes was less likely to be randomly scattered in genome. The results of this study enabled us to decipher the resistance mechanism to Fsg through an integrated computational approach.