Low-Rank Tensor Based Proximity Learning for Multi-View Clustering

An increasing amount of attention have been attracted in multi-view subspace clustering, whose impressive performance can be achieved by means of the self-expressive property, under the assumption of linear relations between multi-view data samples. However, most of them fail to recover the nonlinear relations between multi-view data for deeper study, and additionally they are incapable of discovering the comprehensiveness and higher-order correlations among multiple views. To deal with these challenges, we propose a novel model termed Coupled Learning for Kernel Representation and Graph Tensor (CLKT) in Multi-view Subspace Clustering, where both nonlinear relations and higher-order correlations among multiple affinity graphs are jointly learned in a unified framework. Optimal solutions of the proposed method can be obtained by an alternative minimizing optimization strategy. Extensive experiments on six real-world datasets indicate the superiority of CLKT compared with the state-of-the-art methods.KeywordsMulti-view clusteringKernel learningLow-rank tensor representation

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.

The existing multiview clustering models learn a consistent low-dimensional embedding either from multiple feature matrices or multiple similarity matrices, which ignores the interaction between the two procedures and limits the improvement of clustering performance on multiview data. To address this issue, a bidirectional probabilistic subspaces approximation (BPSA) model is developed in this article to learn a consistently orthogonal embedding from multiple feature matrices and multiple similarity matrices simultaneously via the disturbed probabilistic subspace modeling and approximation. A skillful bidirectional fusion strategy is designed to guarantee the parameter-free property of the BPSA model. Two adaptively weighted learning mechanisms are introduced to ensure the inconsistencies among multiple views and the inconsistencies between bidirectional learning processes. To solve the optimization problem involved in the BPSA model, an iterative solver is derived, and a rigorous convergence guarantee is provided. Extensive experimental results on both toy and real-world datasets demonstrate that our BPSA model achieves state-of-the-art performance even if it is parameter-free.

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.

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.

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.

Graph-based multi-view clustering can effectively reveal the latent cluster structure of multi-view data, however, it remains challenging to construct high-quality graphs by exploring the discriminant information from data. Most of the existing graph-based methods usually construct the graph in the original space or subspace, which may not take the differences of semantic information in different spaces into considerations. Moreover, existing approaches generally measure the relevance of the pair-wise views, which may result in insufficient information exploitation and limited graph representation. To remedy these issues, we proposed an innovative multi-view clustering algorithm called reciprocal consistency graph learning (RCGL), which learns consistency representation by aligning the semantic information from three spaces simultaneously to uncover latent complementarity and consistency among different views. Specifically, we construct the low-dimensional space based on linear projection to preserve essential semantic information. Furthermore, RCGL maps the low-dimension representation from linear space into nonlinear space via Hilbert–Schmidt independence criterion, to explore the nonlinear information hidden in data. Moreover, multiple graphs in kernel space are extended to tensor space for learning a high-order graph, which is helpful to better measure the correlation between multiple views. Finally, the objective function is solved by an alternating optimization scheme. Extensive experiments on five benchmark multi-view datasets demonstrate that RCGL outperforms state-of-the-art baselines markedly.

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.

Multiple perspectives can be used to explore rich and complex datasets that are widely used in many applications. However, in real-world applications, the multi-view data are often noisy because of various environmental factors. The key challenge of graph-based multi-view clustering is obtaining a consistent clustering structure. Most graph-based methods learn independently in one view how similar the data points in each view are to one another. However, the consistency of information in a multi-view dataset is easily overlooked, causing an unsatisfactory unified graph matrix. To address this problem, this study proposes a novel self-weighted graph-based framework for multi-view clustering (SGMF). This framework integrates these initial similar graph matrices into a unified graph matrix by assigning different weights to the initial graphs of each view. This algorithm’s goal is to effectively learn a unified graph matrix and eliminate noise or irrelevant information from the dataset. This is the first time a generalized multi-view framework based on the L1-norm has been proposed. L1-norm can be used to improve the robustness of the algorithm. Particularly, SGMF can automatically weigh each view’s initial similar graph matrix to solve the noise problem and obtain a consistent data structure. Simultaneously, a rank constraint is imposed on the graph Laplacian matrix of the final unified matrix, which helps to automatically divide the data points into the appropriate number of clusters. The experimental results on synthetic and real datasets verify the effectiveness and superiority of the proposed method over the latest baseline.

Multi-view data are becoming common in real-world modeling tasks and many multi-view data clustering algorithms have thus been proposed. The existing algorithms usually focus on the cooperation of different views in the original space but neglect the influence of the hidden information among these different visible views, or they only consider the hidden information between the views. The algorithms are therefore not efficient since the available information is not fully excavated, particularly the otherness information in different views and the consistency information between them. In practice, the otherness and consistency information in multi-view data are both very useful for effective clustering analyses. In this study, a Multi-View clustering algorithm developed with the Cooperation of Visible and Hidden views, i.e., MV-Co-VH, is proposed. The MV-Co-VH algorithm first projects the multiple views from different visible spaces to the common hidden space by using the non-negative matrix factorization (NMF) strategy to obtain the common hidden view data. Collaborative learning is then implemented in the clustering procedure based on the visible views and the shared hidden view. The results of extensive experiments on UCI multi-view datasets and real-world image multi-view datasets show that the clustering performance of the proposed algorithm is competitive with or even better than that of the existing algorithms.

The low-rank tensor could characterize inner structure and explore high-order correlation among multi-view representations, which has been widely used in multi-view clustering. Existing approaches adopt the tensor nuclear norm (TNN) as a convex approximation of non-convex tensor rank function. However, TNN treats the different singular values equally and over-penalizes the main rank components, leading to sub-optimal tensor representation. In this paper, we devise a better surrogate of tensor rank, namely the tensor logarithmic Schatten- p norm ([Formula: see text]N), which fully considers the physical difference between singular values by the non-convex and non-linear penalty function. Further, a tensor logarithmic Schatten- p norm minimization ([Formula: see text]NM)-based multi-view subspace clustering ([Formula: see text]NM-MSC) model is proposed. Specially, the proposed [Formula: see text]NM can not only protect the larger singular values encoded with useful structural information, but also remove the smaller ones encoded with redundant information. Thus, the learned tensor representation with compact low-rank structure will well explore the complementary information and accurately characterize the high-order correlation among multi-views. The alternating direction method of multipliers (ADMM) is used to solve the non-convex multi-block [Formula: see text]NM-MSC model where the challenging [Formula: see text]NM problem is carefully handled. Importantly, the algorithm convergence analysis is mathematically established by showing that the sequence generated by the algorithm is of Cauchy and converges to a Karush-Kuhn-Tucker (KKT) point. Experimental results on nine benchmark databases reveal the superiority of the [Formula: see text]NM-MSC model.

Multiview data, characterized by rich features, are crucial in many machine learning applications. However, effectively extracting intraview features and integrating interview information present significant challenges in multiview learning (MVL). Traditional deep network-based approaches often involve learning multiple layers to derive latent. In these methods, the features of different classes are typically implicitly embedded rather than systematically organized. This lack of structure makes it challenging to explicitly map classes to independent principal subspaces in the feature space, potentially causing class overlap and confusion. Consequently, the capability of these representations to accurately capture the intrinsic structure of the data remains uncertain. In this article, we introduce an innovative multiview representation learning (MVRL) by maximizing two information-theoretic metrics: intraview coding rate reduction and interview mutual information. Specifically, in the intraview representation learning, we aim to optimize feature representations by maximizing the coding rate difference between the entire dataset and individual classes. This process expands the feature representation space while compressing the representations within each class, resulting in more compact feature representations within each viewpoint. Subsequently, we align and fuse these view-specific features through space transformation and cross-sample fusion to achieve consistent representation across multiple views. Finally, we maximize information transmission to maintain consistency and correlation among data representations across views. By maximizing mutual information between the consensus representations and view-specific representations, our method ensures that the learned representations capture more concise intrinsic features and correlations among different views, thereby enhancing the performance and generalization ability of MVL. Experiments show that the proposed methods have achieved excellent performance.

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.