Bidirectional Probabilistic Subspaces Approximation for Multiview Clustering.

Graph-oriented multi-view clustering methods have achieved impressive performances by employing relationships and complex structures hidden in multi-view data. However, most of them still suffer from the following two common problems. (1) They target at studying a common representation or pairwise correlations between views, neglecting the comprehensiveness and deeper higher-order correlations among multiple views. (2) The prior knowledge of view-specific representation can not be taken into account to obtain the consensus indicator graph in a unified graph construction and clustering framework. To deal with these problems, we propose a novel Low-rank Tensor Based Proximity Learning (LTBPL) approach for multi-view clustering, where multiple low-rank probability affinity matrices and consensus indicator graph reflecting the final performances are jointly studied in a unified framework. Specifically, multiple affinity representations are stacked in a low-rank constrained tensor to recover their comprehensiveness and higher-order correlations. Meanwhile, view-specific representation carrying different adaptive confidences is jointly linked with the consensus indicator graph. Extensive experiments on nine real-world datasets indicate the superiority of LTBPL compared with the state-of-the-art methods.

Multi-view clustering aims at simultaneously obtaining a consensus underlying subspace across multiple views and conducting clustering on the learned consensus subspace, which has gained a variety of interest in image processing. In this paper, we propose the Semi-supervised Structured Subspace Learning algorithm for clustering data points from Multiple sources (SSSL-M). We explicitly extend the traditional multi-view clustering with a semi-supervised manner and then build an anti-block-diagonal indicator matrix with small amount of supervisory information to pursue the block-diagonal structure of the shared affinity matrix. SSSL-M regularizes multiple view-specific affinity matrices into a shared affinity matrix based on reconstruction through a unified framework consisting of backward encoding networks and the self-expressive mapping. The shared affinity matrix is comprehensive and can flexibly encode complementary information from multiple view-specific affinity matrices. An enhanced structural consistency of affinity matrices from different views can be achieved and the intrinsic relationships among affinity matrices from multiple views can be effectively reflected in this manner. Technically, we formulate the proposed model as an optimization problem, which can be solved by an alternating optimization scheme. Experimental results over seven different benchmark datasets demonstrate that better clustering results can be obtained by our method compared with the state-of-the-art approaches.

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.

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.

In the era of big data, data may come from multiple sources, known as multi-view data. Multi-view clustering aims at generating better clusters by exploiting complementary and consistent information from multiple views rather than relying on the individual view. Due to inevitable system errors caused by data-captured sensors or others, the data in each view may be erroneous. Various types of errors behave differently and inconsistently in each view. More precisely, error could exhibit as noise and corruptions in reality. Unfortunately, none of the existing multi-view clustering approaches handle all of these error types. Consequently, their clustering performance is dramatically degraded. In this paper, we propose a novel Markov chain method for Error-Robust Multi-View Clustering (EMVC). By decomposing each view into a shared transition probability matrix and error matrix and imposing structured sparsity-inducing norms on error matrices, we characterize and handle typical types of errors explicitly. To solve the challenging optimization problem, we propose a new efficient algorithm based on Augmented Lagrangian Multipliers and prove its convergence rigorously. Experimental results on various synthetic and real-world datasets show the superiority of the proposed EMVC method over the baseline methods and its robustness against different types of errors.

Nowadays, multi-view dataset have become ubiquitous along with more and more data are gathered from different measuring technologies or various sources, in which various aspects of dataset are formalized as multiple views. Although a variety of multi-view clustering analysis approaches have been put forward to uncover the cluster structure hidden in the data, most of these existing methods are based on such a hypothesis: the relationship between objects and clusters are definite. However, most of the data in our real life may have no clear cluster boundaries but have indistinct or overlapping boundaries. How to effectively reveal the uncertain cluster structure under multiview data is still a big challenge for multi-view clustering analysis. Inspired by the powerful uncertain information modeling and analysis capabilities of rough and fuzzy sets, this paper proposes a new multi-view clustering method to discover the uncertain cluster information. A rough set concept based cluster centroid updating strategy is designed to efficiently describe the uncertain construction of clusters. A view weight is introduced to capture the different importance of various views. A fuzzy-based iterative optimization objective function is developed to fuse different view information. Finally, an efficient iterative optimization algorithm is devised to solve the proposed rough fuzzy objective function. Experiments on widely used benchmark datasets prove that our proposed method is always superior to several latest clustering approaches.

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.

In recent years, anchor and hash-based multi-view clustering methods have gained attention for their efficiency and simplicity in handling large-scale data. However, existing methods often overlook the interactions among multi-view data and higher-order cooperative relationships during projection, negatively impacting the quality of hash representation in low-dimensional spaces, clustering performance, and sensitivity to noise. To address this issue, we propose a novel approach named Tensor-Interacted Projection and Cooperative Hashing for Multi-View Clustering(TPCH). TPCH stacks multiple projection matrices into a tensor, taking into account the synergies and communications during the projection process. By capturing higher-order multi-view information through dual projection and Hamming space, TPCH employs an enhanced tensor nuclear norm to learn more compact and distinguishable hash representations, promoting communication within and between views. Experimental results demonstrate that this refined method significantly outperforms state-of-the-art methods in clustering on five large-scale multi-view datasets. Moreover, in terms of CPU time, TPCH achieves substantial acceleration compared to the most advanced current methods.

Information in multiple views is typically symmetrical and distinctive. Multi-view clustering generally attempts to address two key issues: (1) how to mine/leverage additional useful information between different views for current view clustering, and (2) how to combine multiple clustering results from multiple views by using compatible and complementary information hidden in multiple views. In order to achieve this, we propose a multi-view clustering method, namely the multi-view utility-based clustering method (MUC), from the novel perspective of utility-based mutual supervision between different views. The proposed method, MUC, has notable merits: (1) It moves multi-view clustering from the level of feature and/or sample side to partition side information. That is, in order to handle the first issue, MUC considers how to use utility-based partition-level side information from all the other views for current view clustering. Such partition-level side information is consistent with human thinking; it is high-caliber and instructional for clustering. (2) The utility-based partition-level side information provided by other views complements current view information in a mutually supervised way. Then, we conduct multi-view clustering via a mutual supervision mode to circumvent the second issue. As a result, using an alternating optimization strategy, the objective function of MUC can be solved in a K-means-like way. Moreover, we leverage multi-view weight learning based on maximum entropy to integrate multi-view clustering results and further improve performance. The extensive experimental results on various multi-view datasets indicate that the proposed method is better than—or at least comparable to—the existing commonly used single- and multi-view clustering methods, in terms of both clustering performance and running speed.

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.

Adaptive multi-view subspace learning based on distributed optimization

Clustering with multiview data is becoming a hot topic in data mining, pattern recognition, and machine learning. In order to realize an effective multiview clustering, two issues must be addressed, namely, how to combine the clustering result from each view and how to identify the importance of each view. In this paper, based on a newly proposed objective function which explicitly incorporates two penalty terms, a basic multiview fuzzy clustering algorithm, called collaborative fuzzy c-means (Co-FCM), is firstly proposed. It is then extended into its weighted view version, called weighted view collaborative fuzzy c-means (WV-Co-FCM), by identifying the importance of each view. The WV-Co-FCM algorithm indeed tackles the above two issues simultaneously. Its relationship with the latest multiview fuzzy clustering algorithm Collaborative Fuzzy K-Means (Co-FKM) is also revealed. Extensive experimental results on various multiview datasets indicate that the proposed WV-Co-FCM algorithm outperforms or is at least comparable to the existing state-of-the-art multitask and multiview clustering algorithms and the importance of different views of the datasets can be effectively identified.

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.

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.

Recent researches on multiview learning have received widespread attention due to the increasing generalization of multiview data. As an effective probabilistic model, random walk has also shown encouraging performance in various fields. To further exploit the potential of utilizing random walk schemes to address multiview learning problems, this article proposes a simple yet efficient multigraph random walk scheme for both multiview clustering and semisupervised classification tasks. The proposed model integrates random walk with multiview learning, and recursively learns a globally stable probability distribution matrix from multiple views, on the basis of which the label indicator is obtained in the scene of clustering or semisupervised classification. Furthermore, an adaptive weight vector is learned to incorporate the diversity and complementarity of multiview data. Besides, the relationships between the proposed scheme and spectral clustering, neighborhood embedding and manifold embedding are analyzed theoretically. Finally, comprehensive comparative experiments are conducted with several state-of-the-art multiview clustering and semisupervised classification methods on eight real-world datasets. The experimental results demonstrate the superiority of the proposed method in terms of both clustering and classification performance.