Multi-view clustering with adaptive anchor and bipartite graph learning

Multi-view subspace clustering has been an important and powerful tool for partitioning multi-view data, especially multi-view high-dimensional data. Despite great success, most of the existing multi-view subspace clustering methods still suffer from three limitations. First, they often recover the subspace structure in the original space, which can not guarantee the robustness when handling multi-view data with nonlinear structure. Second, these methods mostly regard subspace clustering and affinity matrix learning as two independent steps, which may not well discover the latent relationships among data samples. Third, many of them ignore the different importance of multiple views, whose performance may be badly affected by the low-quality views in multi-view data. To overcome these three limitations, this paper develops a novel subspace clustering method for multi-view data, termed Kernelized Multi-view Subspace Clustering via Auto-weighted Graph Learning (KMSC-AGL). Specifically, the proposed method implicitly maps the multi-view data from linear space into nonlinear space via kernel-induced functions, so as to exploit the nonlinear structure hidden in data. Furthermore, our method aims to enhance the clustering performance by learning a set of view-specific representations and their affinity matrix in a general framework. By integrating the view weighting strategy into this framework, our method can automatically assign the weights to different views, while learning an optimal affinity matrix that is well-adapted to the subsequent spectral clustering. Extensive experiments are conducted on a variety of multi-view data sets, which have demonstrated the superiority of the proposed method.

Multiview clustering (MVC), which aims to explore the underlying cluster structure shared by multiview data, has drawn more research efforts in recent years. To exploit the complementary information among multiple views, existing methods mainly learn a common latent subspace or develop a certain loss across different views, while ignoring the higher level information such as basic partitions (BPs) generated by the single-view clustering algorithm. In light of this, we propose a novel marginalized multiview ensemble clustering (M2VEC) method in this paper. Specifically, we solve MVC in an EC way, which generates BPs for each view individually and seeks for a consensus one. By this means, we naturally leverage the complementary information of multiview data upon the same partition space. In order to boost the robustness of our approach, the marginalized denoising process is adopted to mimic the data corruptions and noises, which provides robust partition-level representations for each view by training a single-layer autoencoder. A low-rank and sparse decomposition is seamlessly incorporated into the denoising process to explicitly capture the consistency information and meanwhile compensate the distinctness between heterogeneous features. Spectral consensus graph partitioning is also involved by our model to make M2VEC as a unified optimization framework. Moreover, a multilayer M2VEC is eventually delivered in a stacked fashion to encapsulate nonlinearity into partition-level representations for handling complex data. Experimental results on eight real-world data sets show the efficacy of our approach compared with several state-of-the-art multiview and EC methods. We also showcase our method performs well with partial multiview data.

Multi-view clustering can mine the underlying structure of multi-view data and has attracted increasing attention. Most existing multi-view clustering methods either construct the similarity matrix from the global level through self-representation learning or construct the similarity matrix from the local level through graph learning. Spectral clustering method can be used to yield the clustering results based on the similarity matrix. However, the similarity matrix that only considers global information or local information is not robust. Moreover, separating the similarity matrix learning and clustering as two steps may lead to sub-optimal clustering results. To address these issues, we propose in this paper, a multi-view subspace clustering with local and global information (MVSCLG) method. Our method combines the self-representation learning and graph learning to learn a similarity matrix with global and local information, and simultaneously utilizes the spectral decomposition and the spectral rotation techniques to yield the clustering results. We also develop an effective optimization algorithm to solve the resulting optimization problem. The effectiveness and superiority of this method are verified on four multi-view benchmark data sets.

Multi-view clustering via high-order bipartite graph fusion

Advances in single-cell biotechnologies have generated the single-cell RNA sequencing (scRNA-seq) of gene expression profiles at cell levels, providing an opportunity to study cellular distribution. Although significant efforts developed in their analysis, many problems remain in studying cell types distribution because of the heterogeneity, high dimensionality, and noise of scRNA-seq. In this study, a multi-view clustering with graph learning algorithm (MCGL) for scRNA-seq data is proposed, which consists of multi-view learning, graph learning, and cell type clustering. In order to avoid a single feature space of scRNA-seq being inadequate to comprehensively characterize the functions of cells, MCGL constructs the multiple feature spaces and utilizes multi-view learning to comprehensively characterize scRNA-seq data from different perspectives. MCGL adaptively learns the similarity graphs of cells that overcome the dependence on fixed similarity, transforming scRNA-seq analysis into the analysis of multi-view clustering. MCGL decomposes the networks of cells into view-specific and common networks in multi-view learning, which better characterizes the topological relationship of cells. MCGL simultaneously utilizes multiple types of cell-cell networks and fully exploits the connection relationship between cells through the complementarity between networks to improve clustering performance. The graph learning, graph factorization, and cell-type clustering processes are accomplished simultaneously under one optimization framework. The performance of the MCGL algorithm is validated with ten scRNA-seq datasets from different scales, and experimental results imply that the proposed algorithm significantly outperforms fourteen state-of-the-art scRNA-seq algorithms.

Multi-view clustering (MVC) can fuse the information of multiple views for robust clustering result, among it two fusion strategies, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">early-fusion</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">late-fusion</i> are widely adopted. Although they have derived many MVC methods, there are still two crucial questions: (1) <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">early-fusion</i> forces multiple views to share a consensus latent representation, which compounds the challenge of excavating view-specific diverse local information; (2) <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">late-fusion</i> generates view-partitions independently and then integrates them in the following clustering procedure, where the two procedures cannot guide each other and lack necessary negotiation. In view of this, we propose a novel Graph Proxy Fusion (GPF) method to preserve and fuse view-specific local information concertedly in one unified framework. Specifically, we first propose anchor-based local information learning to capture view-specific local structural information in bipartite graphs; meanwhile, a view-consensus graph learned through self-expressiveness-based proxy graph learning module is deemed as a higher-order proxy; following, the novel graph proxy fusion module integrally embeds all lower-order bipartite graphs in the higher-order proxy via higher-order correlation theory. As a novel fusion strategy, the proposed GPF efficiently investigates the valuable consensus and diverse information of multiple views. Experiments on various multi-view datasets demonstrate the superiority of our method.

For graph-based multi-view clustering, a critical issue is to capture consensus cluster structures via a two-stage learning scheme. Most current methods learn pairwise similarities between objects for each view independently, which is widely used in single view. However, the consensus information contained in multiple views are ignored, and the involved biases lead to an undesirable unified graph matrix. To this end, we propose a bipartite graph based multi-view clustering (BIGMC) approach. The consensus information can be represented by a small number of representative uniform anchor points for different views. A bipartite graph is constructed between data points and anchor points. The unified bipartite graph matrix in turn improves the bipartite graph similarity matrix of each view and the anchor set. The final unified graph matrix forms the final clusters directly. In BIGMC, an adaptive weight is added for each view to avoid outlier views. A low-rank constraint is imposed on the Laplacian matrix of the unified matrix to construct a multi-component unified bipartite graph, where the component number corresponds to the cluster number. The objective function is optimized in an alternating optimization fashion. Experimental results on synthetic and real-world data sets demonstrate its effectiveness and superiority than the state-of-the-art baselines.

In the era of Industry 4.0, single‐view clustering algorithm is difficult to play a role in the face of complex data, i.e., multiview data. In recent years, an extension of the traditional single‐view clustering is multiview clustering technology, which is becoming more and more popular. Although the multiview clustering algorithm has better effectiveness than the single‐view clustering algorithm, almost all the current multiview clustering algorithms usually have two weaknesses as follows. (1) The current multiview collaborative clustering strategy lacks theoretical support. (2) The weight of each view is averaged. To solve the above‐mentioned problems, we used the Havrda‐Charvat entropy and fuzzy index to construct a new collaborative multiview fuzzy c‐means clustering algorithm using fuzzy weighting called Co‐MVFCM. The corresponding results show that the Co‐MVFCM has the best clustering performance among all the comparison clustering algorithms.

Multi-view clustering has become a widely studied problem in the area of unsupervised learning. It aims to integrate multiple views by taking advantages of the consensus and complimentary information from multiple views. Most of the existing works in multi-view clustering utilize the vector-based representation for features in each view. However, in many real-world applications, instances are represented by graphs, where those vector-based models cannot fully capture the structure of the graphs from each view. To solve this problem, in this paper we propose a Multi-view Clustering framework on graph instances with Graph Embedding (MCGE). Specifically, we model the multi-view graph data as tensors and apply tensor factorization to learn the multi-view graph embeddings, thereby capturing the local structure of graphs. We build an iterative framework by incorporating multi-view graph embedding into the multi-view clustering task on graph instances, jointly performing multi-view clustering and multi-view graph embedding simultaneously. The multi-view clustering results are used for refining the multi-view graph embedding, and the updated multi-view graph embedding results further improve the multi-view clustering. Extensive experiments on two real brain network datasets (i.e., HIV and Bipolar) demonstrate the superior performance of the proposed MCGE approach in multi-view connectome analysis for clinical investigation and application.

Subspace clustering by directly solving Discriminative K-means

Despite significant progress, there remain three limitations to the previous multi-view clustering algorithms. First, they often suffer from high computational complexity, restricting their feasibility for large-scale datasets. Second, they typically fuse multi-view information via one-stage fusion, neglecting the possibilities in multi-stage fusions. Third, dataset-specific hyperparameter-tuning is frequently required, further undermining their practicability. In light of this, we propose a fast multi-view clustering via ensembles (FastMICE) approach. Particularly, the concept of random view groups is presented to capture the versatile view-wise relationships, through which the hybrid early-late fusion strategy is designed to enable efficient multi-stage fusions. With multiple views extended to many view groups, three levels of diversity (w.r.t. features, anchors, and neighbors, respectively) are jointly leveraged for constructing the view-sharing bipartite graphs in the early-stage fusion. Then, a set of diversified base clusterings for different view groups are obtained via fast graph partitioning, which are further formulated into a unified bipartite graph for final clustering in the late-stage fusion. Notably, FastMICE has almost linear time and space complexity, and is free of dataset-specific tuning. Experiments on 22 multi-view datasets demonstrate its advantages in scalability (for extremely large datasets), superiority (in clustering performance), and simplicity (to be applied) over the state-of-the-art. Code available: https://github.com/huangdonghere/FastMICE.

To improve the performance and adaptability of multi-view clustering and address issues such as the neglect of view consistency information in graph construction, sensitivity to initial values, and the inability to adaptively learn view weights in existing algorithms, this paper proposes a Multi-View Clustering method based on Bipartite Graph Matrix Consistency (BGMC). The method learns consistency information represented by consistent anchor points across multiple views, jointly optimizes the similarity bipartite graphs of each view, and uses an alternating iterative strategy to solve for the optimal bipartite graph matrix. The model integrates view weights, a unified matrix, anchor matrices, and similarity matrices into a single optimization framework and introduces an anchor point mechanism to reduce computational complexity.Experiments on five real-world datasets including 3sources and YouTube Faces show that BGMC achieves an ACC 3-8 percent higher than the optimal method, an NMI 5-10 percent higher, and a convergence speed improved by over 20 percent.

Recently, numerous multi-view clustering (MVC) and multi-view graph clustering (MVGC) methods have been proposed. Despite significant progress, they still face two issues: I) MVC and MVGC are often developed independently for multi-view and multi-graph data. They have redundancy but lack a unified methodology to combine their strengths. II) Contrastive learning is usually adopted to explore the associations across multiple views. However, traditional contrastive losses ignore the neighbor relationship in multi-view scenarios and easily lead to false associations in sample pairs. To address these issues, we propose Graph Embedded Contrastive Learning for Multi-View Clustering. Concretely, we propose a process of view-specific pre-training with adaptive graph convolution to make our method compatible with both multi-view and multi-graph data, which aggregates the graph information into data and leverages autoencoders to learn view-specific representations. Furthermore, to explore the view-cross associations, we introduce the process of view-cross contrastive learning and clustering, where we propose the graph-guided contrastive learning that can generate global graph to mitigate the false association issue as well as the cluster-guided contrastive clustering for improving the model robustness. Finally, extensive experiments demonstrate that our method achieves superior performance on both MVC and MVGC tasks.

Multi-view clustering (MVC) seeks to uncover the intrinsic group structures embedded in multi-view data, which has attracted considerable attention in recent years. Existing approaches predominantly concentrate on incorporating suitable model priors to capture consistency across views. However, these explicit constraints often fail to hold in scenarios involving significant modal differences between views or the presence of noise, thereby limiting the efficacy of these methods in more complex contexts. To address these issues, this paper introduces BONE, a lightweight and interpretable MVC framework that Bridges Optimization and Neural networks for Efficient MVC. By leveraging learnable parameters to extract high-level features from low-level features derived through classical optimization, BONE integrates the consistency information across views without the need for explicit prior constraints, while eliminating the necessity for pre-training or post-processing. Extensive experiments show that BONE achieves clustering performance comparable to or even better than existing deep MVC methods, while using only 1% of the parameters, offering a new perspective for designing efficient MVC algorithms.

Graph clustering plays an important role in data mining. Based on an input data graph, data points are partitioned into clusters. However, most existing methods keep the data graph fixed during the clustering procedure, so they are limited to exploit the implied data manifold and highly dependent on the initial graph construction. Inspired by the recent development on manifold learning, this paper proposes an Adaptive Consistency Propagation (ACP) method for graph clustering. In order to utilize the features captured from different perspectives, we further put forward the Multi-view version of the ACP model (MACP). The main contributions are threefold: (1) the manifold structure of input data is sufficiently exploited by propagating the topological connectivities between data points from near to far; (2) the optimal graph for clustering is learned by taking graph learning as a part of the optimization procedure; and (3) the negotiation among the heterogeneous features is captured by the multi-view clustering model. Extensive experiments on real-world datasets validate the effectiveness of the proposed methods on both single- and multi-view clustering, and show their superior performance over the state-of-the-arts.