Error-robust multi-view clustering

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.

A number of opportunistic content sharing services were developed that exploit device-to-device contacts for infrastructure-less operation. All of them depend, like geo-based ad-hoc routing protocols, on mobile devices knowing their respective positions to accurately perform data replication. In this paper, we explore the impact of different types of location errors on the performance of such a service. We use a GPS error distribution for mobiles derived from real-world measurements, consider different frequencies for GPS readings, and account for only subsets of mobile devices actively using GPS. We carry out extensive simulation studies using synthetic mobility models as well as real-world traces to assess the impact of different types of errors. We find that, overall, opportunistic content sharing is quite robust provided that a sufficient number of nodes support GPS and allow the others to have a rough estimate of where they are. Whether or not the GPS position is prone to errors affects some scenarios and is almost negligible in others.

Error matrices in gas-electron diffraction: II. Influence of weight matrix

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.

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 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.

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.

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.

The availability of many heterogeneous but related views of data has arisen in numerous clustering problems. Different views encode distinct representations of the same data, which often admit the same underlying cluster structure. The goal of multi-view clustering is to properly combine information from multiple views so as to generate high quality clustering results that are consistent across different views. Based on max-product belief propagation, we propose a novel multi-view clustering algorithm termed multi-view affinity propagation (MVAP). The basic idea is to establish a multi-view clustering model consisting of two components, which measure the within-view clustering quality and the explicit clustering consistency across different views, respectively. Solving this model is NP-hard, and a multi-view affinity propagation is proposed, which works by passing messages both within individual views and across different views. However, the exemplar consistency constraint makes the optimization almost impossible. To this end, by using some previously designed mathematical techniques, the messages as well as the cluster assignment vector computations are simplified to get simple yet functionally equivalent computations. Experimental results on several real-world multi-view datasets show that MVAP outperforms existing multi-view clustering algorithms. It is especially suitable for clustering more than two views.

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.

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.

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.

In the era of big data, it is becoming common to have data with multiple modalities or coming from multiple sources, known as "multi-view data". Multi-view data are usually unlabeled and come from high-dimensional spaces (such as language vocabularies), unsupervised multi-view feature selection is crucial to many applications. However, it is nontrivial due to the following challenges. First, there are too many instances or the feature dimensionality is too large. Thus, the data may not fit in memory. How to select useful features with limited memory space? Second, how to select features from streaming data and handles the concept drift? Third, how to leverage the consistent and complementary information from different views to improve the feature selection in the situation when the data are too big or come in as streams? To the best of our knowledge, none of the previous works can solve all the challenges simultaneously. In this paper, we propose an Online unsupervised Multi-View Feature Selection, OMVFS, which deals with large-scale/streaming multi-view data in an online fashion. OMVFS embeds unsupervised feature selection into a clustering algorithm via NMF with sparse learning. It further incorporates the graph regularization to preserve the local structure information and help select discriminative features. Instead of storing all the historical data, OMVFS processes the multi-view data chunk by chunk and aggregates all the necessary information into several small matrices. By using the buffering technique, the proposed OMVFS can reduce the computational and storage cost while taking advantage of the structure information. Furthermore, OMVFS can capture the concept drifts in the data streams. Extensive experiments on four real-world datasets show the effectiveness and efficiency of the proposed OMVFS method. More importantly, OMVFS is about 100 times faster than the off-line methods.

Multi-view clustering via pairwise sparse subspace representation