Multiview Subspace Dual Clustering

Dynamic Graph Guided Progressive Partial View-Aligned Clustering

In recent years, there has been a growing focus on multiview data, driven by its rich complementary and consistent information, which has the potential to significantly enhance the performance of downstream tasks. Although many multiview clustering (MVC) methods have achieved promising results by integrating the information of multiple views to learn the consistent representation or consistent graph, these methods typically require complete and entirely accurate correspondences between multiview data, which is challenging to fulfill in practice leading to the problem of partially view-aligned clustering (PVC). To tackle it, we propose a novel method, called dynamic graph guided progressive partial view-aligned clustering (DGPPVC) in this article. To the best of our knowledge, this could be the first work to employ graph convolutional network (GCN) to address the problem of PVC, which explores GCN with dynamic adjacency matrix to reduce unreliable alignments and locate the feature representation with consistent graph structure. In particular, DGPPVC develops an end-to-end framework that encompasses graph construction, feature representation learning, and alignment relationships learning, in which the three parts mutually influence and benefit each other. Moreover, DGPPVC adopts a novel alignment learning strategy that progresses from simplicity to complexity, enabling the step-by-step acquisition of unknown correspondences between different modalities. By giving priority to simple instance pairs, a variant of Jaccard similarities is designed to identify more reliable and complex alignments progressively. During the gradual learning process of alignment relationships, the graph structure matrix is continually and dynamically optimized, thus acquiring a greater variety of graph information between different views. Experiments on several real-world datasets show our promising performance compared with the state-of-the-art methods in partially view-aligned clustering.

Sparse Low-Rank Multi-View Subspace Clustering With Consensus Anchors and Unified Bipartite Graph

Anchor technology is popularly employed in multi-view subspace clustering (MVSC) to reduce the complexity cost. However, due to the sampling operation being performed on each individual view independently and not considering the distribution of samples in all views, the produced anchors are usually slightly distinguishable, failing to characterize the whole data. Moreover, it is necessary to fuse multiple separated graphs into one, which leads to the final clustering performance heavily subject to the fusion algorithm adopted. What is worse, existing MVSC methods generate dense bipartite graphs, where each sample is associated with all anchor candidates. We argue that this dense-connected mechanism will fail to capture the essential local structures and degrade the discrimination of samples belonging to the respective near anchor clusters. To alleviate these issues, we devise a clustering framework named SL-CAUBG. Specifically, we do not utilize sampling strategy but optimize to generate the consensus anchors within all views so as to explore the information between different views. Based on the consensus anchors, we skip the fusion stage and directly construct the unified bipartite graph across views. Most importantly, norm and Laplacian-rank constraints employed on the unified bipartite graph make it capture both local and global structures simultaneously. norm helps eliminate the scatters between anchors and samples by constructing sparse links and guarantees our graph to be with clear anchor-sample affinity relationship. Laplacian-rank helps extract the global characteristics by measuring the connectivity of unified bipartite graph. To deal with the nondifferentiable objective function caused by norm, we adopt an iterative re-weighted method and the Newton's method. To handle the nonconvex Laplacian-rank, we equivalently transform it as a convex trace constraint. We also devise a four-step alternate method with linear complexity to solve the resultant problem. Substantial experiments show the superiority of our SL-CAUBG.

Multiview Spectral Clustering Based on Consensus Neighbor Strategy

Multiview spectral clustering, renowned for its spatial learning capability, has garnered significant attention in the data mining field. However, existing methods assume that the optimal consensus adjacency matrix is confined within the space spanned by each view's adjacency matrix. This constraint restricts the feasible domain of the algorithm and hinders the exploration of the optimal consensus adjacency matrix. To address this limitation, we propose a novel and convex strategy, termed the consensus neighbor strategy, for learning the optimal consensus adjacency matrix. This approach constructs the optimal consensus adjacency matrix by capturing the consensus local structure of each sample across all views, thereby expanding the search space and facilitating the discovery of the optimal consensus adjacency matrix. Furthermore, we introduce the concept of a correlation measuring matrix to prevent trivial solution. We develop an efficient iterative algorithm to solve the resulting optimization problem, benefitting from the convex nature of our model, which ensures convergence to a global optimum. Experimental results on 16 multiview datasets demonstrate that our proposed algorithm surpasses state-of-the-art methods in terms of its robust consensus representation learning capability. The code of this article is uploaded to https://github.com/PhdJiayiTang/Consensus-Neighbor-Strategy.git.

Multiview Clustering by Consensus Spectral Rotation Fusion

Multiview clustering (MVC) aims to partition data into different groups by taking full advantage of the complementary information from multiple views. Most existing MVC methods fuse information of multiple views at the raw data level. They may suffer from performance degradation due to the redundant information contained in the raw data. Graph learning-based methods often heavily depend on one specific graph construction, which limits their practical applications. Moreover, they often require a computational complexity of O(n3 ) because of matrix inversion or eigenvalue decomposition for each iterative computation. In this paper, we propose a consensus spectral rotation fusion (CSRF) method to learn a fused affinity matrix for MVC at the spectral embedding feature level. Specifically, we first introduce a CSRF model to learn a consensus low-dimensional embedding, which explores the complementary and consistent information across multiple views. We develop an alternating iterative optimization algorithm to solve the CSRF optimization problem, where a computational complexity of O(n2 ) is required during each iterative computation. Then, the sparsity policy is introduced to design two different graph construction schemes, which are effectively integrated with the CSRF model. Finally, a multiview fused affinity matrix is constructed from the consensus low-dimensional embedding in spectral embedding space. We analyze the convergence of the alternating iterative optimization algorithm and provide an extension of CSRF for incomplete MVC. Extensive experiments on multiview datasets demonstrate the effectiveness and efficiency of the proposed CSRF method.

Recursive integration of synergised graph representations of multi-omics data for cancer subtypes identification

Cancer subtypes identification is one of the critical steps toward advancing personalized anti-cancerous therapies. Accumulation of a massive amount of multi-platform omics data measured across the same set of samples provides an opportunity to look into this deadly disease from several views simultaneously. Few integrative clustering approaches are developed to capture shared information from all the views to identify cancer subtypes. However, they have certain limitations. The challenge here is identifying the most relevant feature space from each omic view and systematically integrating them. Both the steps should lead toward a global clustering solution with biological significance. In this respect, a novel multi-omics clustering algorithm named RISynG (Recursive Integration of Synergised Graph-representations) is presented in this study. RISynG represents each omic view as two representation matrices that are Gramian and Laplacian. A parameterised combination function is defined to obtain a synergy matrix from these representation matrices. Then a recursive multi-kernel approach is applied to integrate the most relevant, shared, and complementary information captured via the respective synergy matrices. At last, clustering is applied to the integrated subspace. RISynG is benchmarked on five multi-omics cancer datasets taken from The Cancer Genome Atlas. The experimental results demonstrate RISynG’s efficiency over the other approaches in this domain.