Multiview Subspace Clustering via Co-Training Robust Data Representation

Anchors Crash Tensor: Efficient and Scalable Tensorial Multi-View Subspace Clustering

Tensorial Multi-view Clustering (TMC), a prominent approach in multi-view clustering, leverages low-rank tensor learning to capture high-order correlation among views for consistent clustering structure identification. Despite its promising performance, the TMC algorithms face three key challenges: 1). The severe computational burden makes it difficult for TMC methods to handle large-scale datasets. 2). Estimation bias problem caused by the convex surrogate of the tensor rank. 3). Lack of explicit balance of consistency and complementarity. Being aware of these, we propose a basic framework Efficient and Scalable Tensorial Multi-View Subspace Clustering (ESTMC) for large-scale multi-view clustering. ESTMC integrates anchor representation learning and non-convex function-based low-rank tensor learning with a Generalized Non-convex Tensor Rank (GNTR) into a unified objective function, which enhances the efficiency of the existing subspace-based TMC framework. Furthermore, a novel model ESTMC-C with the proposed Enhanced Tensor Rank (ETR), Consistent Geometric Regularization (CGR), and Tensorial Exclusive Regularization (TER) is extended to balance the learning of consistency and complementarity among views, delivering divisible representations for the clustering task. Efficient iterative optimization algorithms are designed to solve the proposed ESTMC and ESTMC-C, which enjoy time-economical complexity and exhibit theoretical convergence. Extensive experimental results on various datasets demonstrate the superiority of the proposed algorithms as compared to state-of-the-art methods.

One-Step Multi-View Clustering With Diverse Representation

Multi-View clustering has attracted broad attention due to its capacity to utilize consistent and complementary information among views. Although tremendous progress has been made recently, most existing methods undergo high complexity, preventing them from being applied to large-scale tasks. Multi-View clustering via matrix factorization is a representative to address this issue. However, most of them map the data matrices into a fixed dimension, limiting the model's expressiveness. Moreover, a range of methods suffers from a two-step process, i.e., multimodal learning and the subsequent k-means, inevitably causing a suboptimal clustering result. In light of this, we propose a one-step multi-view clustering with diverse representation (OMVCDR) method, which incorporates multi-view learning and k-means into a unified framework. Specifically, we first project original data matrices into various latent spaces to attain comprehensive information and auto-weight them in a self-supervised manner. Then, we directly use the information matrices under diverse dimensions to obtain consensus discrete clustering labels. The unified work of representation learning and clustering boosts the quality of the final results. Furthermore, we develop an efficient optimization algorithm with proven convergence to solve the resultant problem. Comprehensive experiments on various datasets demonstrate the promising clustering performance of our proposed method. The code is publicly available at https://github.com/wanxinhang/OMVCDR.

Subgraph Propagation and Contrastive Calibration for Incomplete Multiview Data Clustering

The success of multiview raw data mining relies on the integrity of attributes. However, each view faces various noises and collection failures, which leads to a condition that attributes are only partially available. To make matters worse, the attributes in multiview raw data are composed of multiple forms, which makes it more difficult to explore the structure of the data especially in multiview clustering task. Due to the missing data in some views, the clustering task on incomplete multiview data confronts the following challenges, namely: 1) mining the topology of missing data in multiview is an urgent problem to be solved; 2) most approaches do not calibrate the complemented representations with common information of multiple views; and 3) we discover that the cluster distributions obtained from incomplete views have a cluster distribution unaligned problem (CDUP) in the latent space. To solve the above issues, we propose a deep clustering framework based on subgraph propagation and contrastive calibration (SPCC) for incomplete multiview raw data. First, the global structural graph is reconstructed by propagating the subgraphs generated by the complete data of each view. Then, the missing views are completed and calibrated under the guidance of the global structural graph and contrast learning between views. In the latent space, we assume that different views have a common cluster representation in the same dimension. However, in the unsupervised condition, the fact that the cluster distributions of different views do not correspond affects the information completion process to use information from other views. Finally, the complemented cluster distributions for different views are aligned by contrastive learning (CL), thus solving the CDUP in the latent space. Our method achieves advanced performance on six benchmarks, which validates the effectiveness and superiority of our SPCC.

Anchor-Sharing and Cluster-Wise Contrastive Network for Multiview Representation Learning

Multiview clustering (MVC) has gained significant attention as it enables the partitioning of samples into their respective categories through unsupervised learning. However, there are a few issues as follows: 1) many existing deep clustering methods use the same latent features to achieve the conflict objectives, namely, reconstruction and view consistency. The reconstruction objective aims to preserve view-specific features for each individual view, while the view-consistency objective strives to obtain common features across all views; 2) some deep embedded clustering (DEC) approaches adopt view-wise fusion to obtain consensus feature representation. However, these approaches overlook the correlation between samples, making it challenging to derive discriminative consensus representations; and 3) many methods use contrastive learning (CL) to align the view's representations; however, they do not take into account cluster information during the construction of sample pairs, which can lead to the presence of false negative pairs. To address these issues, we propose a novel multiview representation learning network, called anchor-sharing and clusterwise CL (CwCL) network for multiview representation learning. Specifically, we separate view-specific learning and view-common learning into different network branches, which addresses the conflict between reconstruction and consistency. Second, we design an anchor-sharing feature aggregation (ASFA) module, which learns the sharing anchors from different batch data samples, establishes the bipartite relationship between anchors and samples, and further leverages it to improve the samples' representations. This module enhances the discriminative power of the common representation from different samples. Third, we design CwCL module, which incorporates the learned transition probability into CL, allowing us to focus on minimizing the similarity between representations from negative pairs with a low transition probability. It alleviates the conflict in previous sample-level contrastive alignment. Experimental results demonstrate that our method outperforms the state-of-the-art performance.

Partially multi-view clustering via re-alignment

Multi-view clustering learns consistent information from multi-view data, aiming to achieve more significant clustering characteristics. However, data in real-world scenarios often exhibit temporal or spatial asynchrony, leading to views with unaligned instances. Existing methods primarily address this issue by learning transformation matrices to align unaligned instances, but this process of learning differentiable transformation matrices is cumbersome. To address the challenge of partially unaligned instances, we propose Partially Multi-view Clustering via Re-alignment (PMVCR). Our approach integrates representation learning and data alignment through a two-stage training and a re-alignment process. Specifically, our training process consists of three stages: (i) In the coarse-grained alignment stage, we construct negative instance pairs for unaligned instances and utilize contrastive learning to preliminarily learn the view representations of the instances. (ii) In the re-alignment stage, we match unaligned instances based on the similarity of their view representations, aligning them with the primary view. (iii) In the fine-grained alignment stage, we further enhance the discriminative power of the view representations and the model's ability to differentiate between clusters. Compared to existing models, our method effectively leverages information between unaligned samples and enhances model generalization by constructing negative instance pairs. Clustering experiments on several popular multi-view datasets demonstrate the effectiveness and superiority of our method. Our code is publicly available at https://github.com/WenB777/PMVCR.git.

Clustering Enhanced Multiplex Graph Contrastive Representation Learning

Multiplex graph representation learning has attracted considerable attention due to its powerful capacity to depict multiple relation types between nodes. Previous methods generally learn representations of each relation-based subgraph and then aggregate them into final representations. Despite the enormous success, they commonly encounter two challenges: 1) the latent community structure is overlooked and 2) consistent and complementary information across relation types remains largely unexplored. To address these issues, we propose a clustering-enhanced multiplex graph contrastive representation learning model (CEMR). In CEMR, by formulating each relation type as a view, we propose a multiview graph clustering framework to discover the potential community structure, which promotes representations to incorporate global semantic correlations. Moreover, under the proposed multiview clustering framework, we develop cross-view contrastive learning and cross-view cosupervision modules to explore consistent and complementary information in different views, respectively. Specifically, the cross-view contrastive learning module equipped with a novel negative pairs selecting mechanism enables the view-specific representations to extract common knowledge across views. The cross-view cosupervision module exploits the high-confidence complementary information in one view to guide low-confidence clustering in other views by contrastive learning. Comprehensive experiments on four datasets confirm the superiority of our CEMR when compared to the state-of-the-art rivals.

Multi-kernel clustering with tensor fusion on Grassmann manifold for high-dimensional genomic data

The high dimensionality and noise challenges in genomic data make it difficult for traditional clustering methods. Existing multi-kernel clustering methods aim to improve the quality of the affinity matrix by learning a set of base kernels, thereby enhancing clustering performance. However, directly learning from the original base kernels presents challenges in handling errors and redundancies when dealing with high-dimensional data, and there is still a lack of feasible multi-kernel fusion strategies. To address these issues, we propose a Multi-Kernel Clustering method with Tensor fusion on Grassmann manifolds, called MKCTM. Specifically, we maximize the clustering consensus among base kernels by imposing tensor low-rank constraints to eliminate noise and redundancy. Unlike traditional kernel fusion approaches, our method fuses learned base kernels on the Grassmann manifold, resulting in a final consensus matrix for clustering. We integrate tensor learning and fusion processes into a unified optimization model and propose an effective iterative optimization algorithm for solving it. Experimental results on ten datasets, comparing against 12 popular baseline clustering methods, confirm the superiority of our approach. Our code is available at https://github.com/foureverfei/MKCTM.git.

Deep Double Incomplete Multi-View Multi-Label Learning With Incomplete Labels and Missing Views

View missing and label missing are two challenging problems in the applications of multi-view multi-label classification scenery. In the past years, many efforts have been made to address the incomplete multi-view learning or incomplete multi-label learning problem. However, few works can simultaneously handle the challenging case with both the incomplete issues. In this article, we propose a new incomplete multi-view multi-label learning network to address this challenging issue. The proposed method is composed of four major parts: view-specific deep feature extraction network, weighted representation fusion module, classification module, and view-specific deep decoder network. By, respectively, integrating the view missing information and label missing information into the weighted fusion module and classification module, the proposed method can effectively reduce the negative influence caused by two such incomplete issues and sufficiently explore the available data and label information to obtain the most discriminative feature extractor and classifier. Furthermore, our method can be trained in both supervised and semi-supervised manners, which has important implications for flexible deployment. Experimental results on five benchmarks in supervised and semi-supervised cases demonstrate that the proposed method can greatly enhance the classification performance on the difficult incomplete multi-view multi-label classification tasks with missing labels and missing views.

Multiview Subspace Clustering via Low-Rank Symmetric Affinity Graph

Multiview subspace clustering (MVSC) has been used to explore the internal structure of multiview datasets by revealing unique information from different views. Most existing methods ignore the consistent information and angular information of different views. In this article, we propose a novel MVSC via low-rank symmetric affinity graph (LSGMC) to tackle these problems. Specifically, considering the consistent information, we pursue a consistent low-rank structure across views by decomposing the coefficient matrix into three factors. Then, the symmetry constraint is utilized to guarantee weight consistency for each pair of data samples. In addition, considering the angular information, we utilize the fusion mechanism to capture the inherent structure of data. Furthermore, to alleviate the effect brought by the noise and the high redundant data, the Schatten p-norm is employed to obtain a low-rank coefficient matrix. Finally, an adaptive information reduction strategy is designed to generate a high-quality similarity matrix for spectral clustering. Experimental results on 11 datasets demonstrate the superiority of LSGMC in clustering performance compared with ten state-of-the-art multiview clustering methods.

Multiview Clustering With Propagating Information Bottleneck

In many practical applications, massive data are observed from multiple sources, each of which contains multiple cohesive views, called hierarchical multiview (HMV) data, such as image-text objects with different types of visual and textual features. Naturally, the inclusion of source and view relationships offers a comprehensive view of the input HMV data and achieves an informative and correct clustering result. However, most existing multiview clustering (MVC) methods can only process single-source data with multiple views or multisource data with single type of feature, failing to consider all the views across multiple sources. Observing the rich closely related multivariate (i.e., source and view) information and the potential dynamic information flow interacting among them, in this article, a general hierarchical information propagation model is first built to address the above challenging problem. It describes the process from optimal feature subspace learning (OFSL) of each source to final clustering structure learning (CSL). Then, a novel self-guided method named propagating information bottleneck (PIB) is proposed to realize the model. It works in a circulating propagation fashion, so that the resulting clustering structure obtained from the last iteration can "self-guide" the OFSL of each source, and the learned subspaces are in turn used to conduct the subsequent CSL. We theoretically analyze the relationship between the cluster structures learned in the CSL phase and the preservation of relevant information propagated from the OFSL phase. Finally, a two-step alternating optimization method is carefully designed for optimization. Experimental results on various datasets show the superiority of the proposed PIB method over several state-of-the-art methods.

Low-Rank Graph Completion-Based Incomplete Multiview Clustering

In order to reduce the negative effect of missing data on clustering, incomplete multiview clustering (IMVC) has become an important research content in machine learning. At present, graph-based methods are widely used in IMVC, but these methods still have some defects. First, some of the methods overlook potential relationships across views. Second, most of the methods depend on local structure information and ignore the global structure information. Third, most of the methods cannot use both global structure information and potential information across views to adaptively recover the incomplete relationship structure. To address the above issues, we propose a unified optimization framework to learn reasonable affinity relationships, called low-rank graph completion-based IMVC (LRGR_IMVC). 1) Our method introduces adaptive graph embedding to effectively explore the potential relationship among views; 2) we append a low-rank constraint to adequately exploit the global structure information among views; and 3) this method unites related information within views, potential information across views, and global structure information to adaptively recover the incomplete graph structure and obtain complete affinity relationships. Experimental results on several commonly used datasets show that the proposed method achieves better clustering performance significantly than some of the most advanced methods.

Fast Continual Multi-View Clustering With Incomplete Views

Multi-view clustering (MVC) has attracted broad attention due to its capacity to exploit consistent and complementary information across views. This paper focuses on a challenging issue in MVC called the incomplete continual data problem (ICDP). Specifically, most existing algorithms assume that views are available in advance and overlook the scenarios where data observations of views are accumulated over time. Due to privacy considerations or memory limitations, previous views cannot be stored in these situations. Some works have proposed ways to handle this problem, but all of them fail to address incomplete views. Such an incomplete continual data problem (ICDP) in MVC is difficult to solve since incomplete information with continual data increases the difficulty of extracting consistent and complementary knowledge among views. We propose Fast Continual Multi-View Clustering with Incomplete Views (FCMVC-IV) to address this issue. Specifically, the method maintains a scalable consensus coefficient matrix and updates its knowledge with the incoming incomplete view rather than storing and recomputing all the data matrices. Considering that the given views are incomplete, the newly collected view might contain samples that have yet to appear; two indicator matrices and a rotation matrix are developed to match matrices with different dimensions. In addition, we design a three-step iterative algorithm to solve the resultant problem with linear complexity and proven convergence. Comprehensive experiments conducted on various datasets demonstrate the superiority of FCMVC-IV over the competing approaches. The code is publicly available at https://github.com/wanxinhang/FCMVC-IV.

M3W: Multistep Three-Way Clustering

Three-way clustering has been an active research topic in the field of cluster analysis in recent years. Some efforts are focused on the technique due to its feasibility and rationality. We observe, however, that the existing three-way clustering algorithms struggle to obtain more information and limit the fault tolerance excessively. Moreover, although the one-step three-way allocation based on a pair of fixed, global thresholds is the most straightforward way to generate the three-way cluster representations, the clusters derived from a pair of global thresholds cannot exactly reveal the inherent clustering structure of the dataset, and the threshold values are often difficult to determine beforehand. Inspired by sequential three-way decisions, we propose an algorithm, called multistep three-way clustering (M3W), to address these issues. Specifically, we first use a progressive erosion strategy to construct a multilevel structure of data, so that lower levels (or external layers) can gather more available information from higher levels (or internal layers). Then, we further propose a multistep three-way allocation strategy, which sufficiently considers the neighborhood information of every eroded instance. We use the allocation strategy in combination with the multilevel structure to ensure that more information is gradually obtained to increase the probability of being assigned correctly, capturing adaptively the inherent clustering structure of the dataset. The proposed algorithm is compared with eight competitors using 18 benchmark datasets. Experimental results show that M3W achieves superior performance, verifying its advantages and effectiveness.

Multiview Deep Anomaly Detection: A Systematic Exploration

Anomaly detection (AD), which models a given normal class and distinguishes it from the rest of abnormal classes, has been a long-standing topic with ubiquitous applications. As modern scenarios often deal with massive high-dimensional complex data spawned by multiple sources, it is natural to consider AD from the perspective of multiview deep learning. However, it has not been formally discussed by the literature and remains underexplored. Motivated by this blank, this article makes fourfold contributions: First, to the best of our knowledge, this is the first work that formally identifies and formulates the multiview deep AD problem. Second, we take recent advances in relevant areas into account and systematically devise various baseline solutions, which lays the foundation for multiview deep AD research. Third, to remedy the problem that limited benchmark datasets are available for multiview deep AD, we extensively collect the existing public data and process them into more than 30 multiview benchmark datasets via multiple means, so as to provide a better evaluation platform for multiview deep AD. Finally, by comprehensively evaluating the devised solutions on different types of multiview deep AD benchmark datasets, we conduct a thorough analysis on the effectiveness of the designed baselines and hopefully provide other researchers with beneficial guidance and insight into the new multiview deep AD topic.

A New Graph Autoencoder-Based Consensus-Guided Model for scRNA-seq Cell Type Detection

Single-cell RNA sequencing (scRNA-seq) technology is famous for providing a microscopic view to help capture cellular heterogeneity. This characteristic has advanced the field of genomics by enabling the delicate differentiation of cell types. However, the properties of single-cell datasets, such as high dropout events, noise, and high dimensionality, are still a research challenge in the single-cell field. To utilize single-cell data more efficiently and to better explore the heterogeneity among cells, a new graph autoencoder (GAE)-based consensus-guided model (scGAC) is proposed in this article. The data are preprocessed into multiple top-level feature datasets. Then, feature learning is performed by using GAEs to generate new feature matrices, followed by similarity learning based on distance fusion methods. The learned similarity matrices are fed back to the GAEs to guide their feature learning process. Finally, the abovementioned steps are iterated continuously to integrate the final consistent similarity matrix and perform other related downstream analyses. The scGAC model can accurately identify critical features and effectively preserve the internal structure of the data. This can further improve the accuracy of cell type identification.

Multi-View Clustering for Integration of Gene Expression and Methylation Data With Tensor Decomposition and Self-Representation Learning

The accumulated DNA methylation and gene expression provide a great opportunity to exploit the epigenetic patterns of genes, which is the foundation for revealing the underlying mechanisms of biological systems. Current integrative algorithms are criticized for undesirable performance because they fail to address the heterogeneity of expression and methylation data, and the intrinsic relations among them. To solve this issue, a novel multi-view clustering with self-representation learning and low-rank tensor constraint (MCSL-LTC) is proposed for the integration of gene expression and DNA methylation data, which are treated as complementary views. Specifically, MCSL-LTC first learns the low-dimensional features for each view with the linear projection, and then these features are fused in a unified tensor space with low-rank constraints. In this case, the complementary information of various views is precisely captured, where the heterogeneity of omic data is avoided, thereby enhancing the consistency of different views. Finally, MCSL-LTC obtains a consensus cluster of genes reflecting the structure and features of various views. Experimental results demonstrate that the proposed approach outperforms state-of-the-art baselines in terms of accuracy on both the social and cancer data, which provides an effective and efficient method for the integration of heterogeneous genomic data.

Multi-View Graph Clustering by Adaptive Manifold Learning

Graph-oriented methods have been widely adopted in multi-view clustering because of their efficiency in learning heterogeneous relationships and complex structures hidden in data. However, existing methods are typically investigated based on a Euclidean structure instead of a more suitable manifold topological structure. Hence, it is expected that a more suitable manifold topological structure will be adopted to carry out intrinsic similarity learning. In this paper, we explore the implied adaptive manifold for multi-view graph clustering. Specifically, our model seamlessly integrates multiple adaptive graphs into a consensus graph with the manifold topological structure considered. We further manipulate the consensus graph with a useful rank constraint so that its connected components precisely correspond to distinct clusters. As a result, our model is able to directly achieve a discrete clustering result without any post-processing. In terms of the clustering results, our method achieves the best performance in 22 out of 24 cases in terms of four evaluation metrics on six datasets, which demonstrates the effectiveness of the proposed model. In terms of computational performance, our optimization algorithm is generally faster or in line with other state-of-the-art algorithms, which validates the efficiency of the proposed algorithm.

Multiview Clustering of Adaptive Sparse Representation Based on Coupled P Systems

A multiview clustering (MVC) has been a significant technique to dispose data mining issues. Most of the existing studies on this topic adopt a fixed number of neighbors when constructing the similarity matrix of each view, like single-view clustering. However, this may reduce the clustering effect due to the diversity of multiview data sources. Moreover, most MVC utilizes iterative optimization to obtain clustering results, which consumes a significant amount of time. Therefore, this paper proposes a multiview clustering of adaptive sparse representation based on coupled P system (MVCS-CP) without iteration. The whole algorithm flow runs in the coupled P system. Firstly, the natural neighbor search algorithm without parameters automatically determines the number of neighbors of each view. In turn, manifold learning and sparse representation are employed to construct the similarity matrix, which preserves the internal geometry of the views. Next, a soft thresholding operator is introduced to form the unified graph to gain the clustering results. The experimental results on nine real datasets indicate that the MVCS-CP outperforms other state-of-the-art comparison algorithms.

View-Wise Versus Cluster-Wise Weight: Which Is Better for Multi-View Clustering?

Weighted multi-view clustering (MVC) aims to combine the complementary information of multi-view data (such as image data with different types of features) in a weighted manner to obtain a consistent clustering result. However, when the cluster-wise weights across views are vastly different, most existing weighted MVC methods may fail to fully utilize the complementary information, because they are based on view-wise weight learning and can not learn the fine-grained cluster-wise weights. Additionally, extra parameters are needed for most of them to control the weight distribution sparsity or smoothness, which are hard to tune without prior knowledge. To address these issues, in this paper we propose a novel and effective Cluster-weighted mUlti-view infoRmation bottlEneck (CURE) clustering algorithm, which can automatically learn the cluster-wise weights to discover the discriminative clusters across multiple views and thus can enhance the clustering performance by properly exploiting the cluster-level complementary information. To learn the cluster-wise weights, we design a new weight learning scheme by exploring the relation between the mutual information of the joint distribution of a specific cluster (containing a group of data samples) and the weight of this cluster. Finally, a novel draw-and-merge method is presented to solve the optimization problem. Experimental results on various multi-view datasets show the superiority and effectiveness of our cluster-wise weighted CURE over several state-of-the-art methods.