Multi-view Clustering Methods Research Articles

Information bottleneck fusion for deep multi-view clustering

Multi-view clustering aims to employ semantic information from multiple perspectives to accomplish the clustering task. However, a crucial concern in this domain is the selection of distinctive features. Most existing methods map data into a single feature space and then construct a similarity matrix, which often leads to an insufficient utilisation of intrinsic information in the data, meanwhile neglecting the impact of noise in the data, resulting in poor representation learning performance. Information bottleneck (IB) is a theoretical model based on information theory, the core idea of which is to extract information that is useful for a given task by selecting an appropriate representation and discarding redundant and irrelevant information. In this study, we propose an innovative IB fusion model for deep multi-view clustering (IBFDMVC), which operates on two distinct feature spaces and reconstructs semantic information in a parallel manner. IBFDMVC consists of three modules. The encoder module uses two linear encoding layers to learn and obtain embeddings with different dimensions. The fusion module adopts a collaborative training learning concept, where contrastive learning is first employed to enhance representation and IB theory is further used to reduce representation noise. Finally, clustering is performed using k-means in the clustering module. Compared with state-of-the-art multi-view clustering methods, IBFDMVC achieves better results, verifying the significant role of IB theory in providing a robust framework for feature selection and semantic information extraction in multi-view data analysis.

Accurate multi-view clustering to seek the cross-viewed yet uniform sample assignment via tensor feature matching

Multi-view clustering has become one of the popular clustering branches with data accumulation from multiple domains. Unfortunately, a large heterogeneity gap exists due to cross-view discrepancy, resulting in inaccurate sample-wise similarity estimation. Furthermore, the popular multi-view clustering methods heavily rely on sample-wise similarity measurements, which often lead to suboptimal clustering performance due to inaccurate similarity estimation across views. To tackle these challenges, this paper presents an accurate multi-view clustering method from a standpoint of inter-view feature-wise matching to bypass the inaccurate sample-wise similarity that leverages tensor feature matching for cross-viewed yet uniform sample assignment, named by multi-view clustering via tensor feature matching (MC-TFM). Specifically, our approach begins with exploring a comprehensive feature matching tensor by exploiting both intra-view and inter-view correlations among multi-view features. Subsequently, a feature matching matrix, which preserves the correlations and importance of multi-view features for guiding the cross-viewed yet uniform sample assignment, is estimated based on this tensor. Furthermore, these correlations and importance are maintained into two coded feature bases by decomposing the feature matching matrix. Finally, a sample assignment matrix is learned via jointly reconstructing the samples using the two bases further cooperating with spectral clustering. In this way, the heterogeneity gap is bridged by tensor feature matching, and the inaccurate sample-wise similarity estimation is omitted by using feature-wise matching to guide sample-wise assignment. Extensive experiments conducted on seven real-world datasets highlight the effectiveness of the cross-viewed yet uniform sample assignment, demonstrating the potential of our approach in accurate multi-view clustering tasks.

A Tensor Approach for Uncoupled Multiview Clustering.

Multiview clustering plays an important part in unsupervised learning. Although the existing methods have shown promising clustering performances, most of them assume that the data is completely coupled between different views, which is unfortunately not always ensured in real-world applications. The clustering performance of these methods drops dramatically when handling the uncoupled data. The main reason is that: 1) cross-view correlation of uncoupled data is unclear, which limits the existing multiview clustering methods to explore the complementary information between views and 2) features from different views are uncoupled with each other, which may mislead the multiview clustering methods to partition data into wrong clusters. To address these limitations, we propose a tensor approach for uncoupled multiview clustering (T-UMC) in this article. Instead of pairwise correlation, T-UMC chooses a most reliable view by view-specific silhouette coefficient (VSSC) at first, and then couples the self-representation matrix of each view with it by pairwise cross-view coupling learning. After that, by integrating recoupled self-representation matrices into a third-order tensor, the high-order correlations of all views are explored with tensor singular value decomposition (t-SVD)-based tensor nuclear norm (TNN). And the view-specific local structures of each individual view are also preserved with the local structure learning scheme with manifold learning. Besides, the physical meaning of view-specific coupling matrix is also discussed in this article. Extensive experiments on six commonly used benchmark datasets have demonstrated the superiority of the proposed method compared with the state-of-the-art multiview clustering methods.

A Similarity Matrix Low-Rank Approximation and Inconsistency Separation Fusion Approach for Multiview Clustering

In recent years, multi-view clustering algorithms have achieved promising performance by exploiting the com-plementarity and consistency of different views. However, many multi-view spectral clustering methods only focus on the con-sistent information of views, and the time cost of feature decomposition is expensive. Moreover, these methods also require post-processing (e.g., k-means) to obtain the final clustering results. To overcome these limitations simultaneously, we propose a novel multi-view clustering algorithm. Firstly, the method removes the inconsistent information of the views through cross-view measurement to maintain consistent information. These inconsistencies may be caused by noise, corruptions, or view-specific properties and will affect the quality of the similarity matrix. Then, we learn a consensus embedding matrix with non-negative constraints by performing a low-rank decomposition of the consistency information. In this way, we can replace the eigendecomposition of the n × n Laplacian matrix in spectral clustering with the singular value decomposition of a n × c low-rank matrix to reduce the computational burden, where c ≪ n. Furthermore, due to the non-negative constraint, we can directly obtain the clustering results. Also, to consider the diversity of views, adaptive weighting is applied to different view data. Compared to state-of-the-art multi-view clustering methods on five benchmark multi-view datasets, we demonstrate the superiority and effectiveness of our approach. We release the source code at <uri xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">https://github.com/hulu88/FAMvC</uri> .

One-Step Multiview Clustering via Adaptive Graph Learning and Spectral Rotation.

In graph based multiview clustering methods, the ultimate partition result is usually achieved by spectral embedding of the consistent graph using some traditional clustering methods, such as k -means. However, optimal performance will be reduced by this multistep procedure since it cannot unify graph learning with partition generation closely. In this article, we propose a one-step multiview clustering method through adaptive graph learning and spectral rotation (AGLSR). For every view, AGLSR adaptively learns affinity graphs to capture similar relationships of samples. Then, a spectral embedding is designed to take advantage of the potential feature space shared by different views. In addition, AGLSR utilizes a spectral rotation strategy to obtain the discrete clustering labels from the learned spectral embeddings directly. An effective updating algorithm with proven convergence is derived to optimize the optimization problem. Sufficient experiments on benchmark datasets have clearly demonstrated the effectiveness of the proposed method in six metrics. The code of AGLSR is uploaded at https://github.com/tangchuan2000/AGLSR.

Pick-and-Place Transform Learning for Fast Multi-View Clustering.

To manipulate large-scale data, anchor-based multi-view clustering methods have grown in popularity owing to their linear complexity in terms of the number of samples. However, these existing approaches pay less attention to two aspects. 1) They target at learning a shared affinity matrix by using the local information from every single view, yet ignoring the global information from all views, which may weaken the ability to capture complementary information. 2) They do not consider the removal of feature redundancy, which may affect the ability to depict the real sample relationships. To this end, we propose a novel fast multi-view clustering method via pick-and-place transform learning named PPTL, which could capture insightful global features to characterize the sample relationships quickly. Specifically, PPTL first concatenates all the views along the feature direction to produce a global matrix. Considering the redundancy of the global matrix, we design a pick-and-place transform with ℓ2,p-norm regularization to abandon the poor features and consequently construct a compact global representation matrix. Thus, by conducting anchor-based subspace clustering on the compact global representation matrix, PPTL can learn a consensus skinny affinity matrix with a discriminative clustering structure. Numerous experiments performed on small-scale to large-scale datasets demonstrate that our method is not only faster but also achieves superior clustering performance over state-of-the-art methods across a majority of the datasets.

LSVC: A Lifelong Learning Approach for Stream-View Clustering.

Multiview clustering (MVC) can achieve more accurate results by utilizing complementary information from multiple perspectives, compared to traditional single-view methods. However, current multiview techniques require all views to be available upfront, making them inadequate for dealing with prevalent data sources that arrive as streams, such as stem cell analysis and multicamera surveillance. To address this problem, in this article, we propose a method called lifelong stream-view clustering (LSVC), which comprises an embedding anchor knowledge library and three key components, enabling the capability to perform asynchronous clustering on stream views. These three components are specifically: 1) the knowledge extraction module that extracts the abstract knowledge of the newcome view over time and updates the shared knowledge library; 2) the knowledge transfer module that aligns the newcome view with the historical knowledge library, enabling the transfer of structure information to the knowledge library; and 3) the knowledge rule module that constraints the knowledge library to enjoy a fair amount of anchors for each cluster, improving the discrimination of knowledge. The experimental results show that LSVC outperforms traditional single-view clustering (SVC) and MVC methods as it gradually improves with the accumulation of stream views and tends to be stable over time.

Regularized Instance Weighting Multiview Clustering via Late Fusion Alignment.

Multiview clustering has become a prominent research topic in data analysis, with wide-ranging applications across various fields. However, the existing late fusion multiview clustering (LFMVC) methods still exhibit some limitations, including variable importance and contributions and a heightened sensitivity to noise and outliers during the alignment process. To tackle these challenges, we propose a novel regularized instance weighting multiview clustering via late fusion alignment (R-IWLF-MVC), which considers the instance importance from various views, enabling information integration to be more effective. Specifically, we assign each sample an importance attribute to enable the learning process to focus more on the key sample nodes and avoid being influenced by noise or outliers, while laying the groundwork for the fusion of different views. In addition, we continue to employ late fusion alignment to integrate base clustering from various views and introduce a new regularization term with prior knowledge to ensure that the learning process does not deviate too much from the expected results. After that, we design a three-step alternating optimization strategy with proven convergence for the resultant problem. Our proposed approach has been extensively evaluated on multiple real-world datasets, demonstrating its superiority to state-of-the-art methods.

Deep Adversarial Inconsistent Cognitive Sampling for Multiview Progressive Subspace Clustering.

Deep multiview clustering methods have achieved remarkable performance. However, all of them failed to consider the difficulty labels (uncertainty of ground truth for training samples) over multiview samples, which may result in a nonideal clustering network for getting stuck into poor local optima during the training process; worse still, the difficulty labels from the multiview samples are always inconsistent, and such a fact makes it even more challenging to handle. In this article, we propose a novel deep adversarial inconsistent cognitive sampling (DAICS) method for multiview progressive subspace clustering. A multiview binary classification (easy or difficult) loss and a feature similarity loss are proposed to jointly learn a binary classifier and a deep consistent feature embedding network, throughout an adversarial minimax game over difficulty labels of multiview consistent samples. We develop a multiview cognitive sampling strategy to select the input samples from easy to difficult for multiview clustering network training. However, the distributions of easy and difficult samples are mixed together, hence not trivial to achieve the goal. To resolve it, we define a sampling probability with a theoretical guarantee. Based on that, a golden section mechanism is further designed to generate a sample set boundary to progressively select the samples with varied difficulty labels via a gate unit, which is utilized to jointly learn a multiview common progressive subspace and clustering network for more efficient clustering. Experimental results on four real-world datasets demonstrate the superiority of DAICS over state-of-the-art methods.

Deep Incomplete Multiview Clustering via Local and Global Pseudo-Label Propagation.

Since the rapid progress in multimedia and sensor technologies, multiview clustering (MVC) has become a prominent research area within machine learning and data mining, experiencing significant advancements over recent decades. MVC is distinguished from single-view clustering by its ability to integrate complementary information from multiple distinct data perspectives and enhance clustering performance. However, the efficacy of MVC methods is predicated on the availability of complete views for all samples-an assumption that frequently fails in practical scenarios where data views are often incomplete. To surmount this challenge, various approaches to incomplete MVC (IMVC) have been proposed, with deep neural networks emerging as a favored technique for their representation learning ability. Despite their promise, previous methods commonly adopt sample-level (e.g., features) or affinity-level (e.g., graphs) guidance, neglecting the discriminative label-level guidance (i.e., pseudo-labels). In this work, we propose a novel deep IMVC method termed pseudo-label propagation for deep IMVC (PLP-IMVC), which integrates high-quality pseudo-labels from the complete subset of incomplete data with deep label propagation networks to obtain improved clustering results. In particular, we first design a local model (PLP-L) that leverages pseudo-labels to their fullest extent. Then, we propose a global model (PLP-G) that exploits manifold regularization to mitigate the label noises, promote view-level information fusion, and learn discriminative unified representations. Experimental results across eight public benchmark datasets and three evaluation metrics prove our method's efficacy, demonstrating superior performance compared to 18 advanced baseline methods.

Unpaired Multi-View Graph Clustering With Cross-View Structure Matching.

Multi-view clustering (MVC), which effectively fuses information from multiple views for better performance, has received increasing attention. Most existing MVC methods assume that multi-view data are fully paired, which means that the mappings of all corresponding samples between views are predefined or given in advance. However, the data correspondence is often incomplete in real-world applications due to data corruption or sensor differences, referred to as the data-unpaired problem (DUP) in multi-view literature. Although several attempts have been made to address the DUP issue, they suffer from the following drawbacks: 1) most methods focus on the feature representation while ignoring the structural information of multi-view data, which is essential for clustering tasks; 2) existing methods for partially unpaired problems rely on pregiven cross-view alignment information, resulting in their inability to handle fully unpaired problems; and 3) their inevitable parameters degrade the efficiency and applicability of the models. To tackle these issues, we propose a novel parameter-free graph clustering framework termed unpaired multi-view graph clustering framework with cross-view structure matching (UPMGC-SM). Specifically, unlike the existing methods, UPMGC-SM effectively utilizes the structural information from each view to refine cross-view correspondences. Besides, our UPMGC-SM is a unified framework for both the fully and partially unpaired multi-view graph clustering. Moreover, existing graph clustering methods can adopt our UPMGC-SM to enhance their ability for unpaired scenarios. Extensive experiments demonstrate the effectiveness and generalization of our proposed framework for both paired and unpaired datasets.

One-step Multi-view Clustering with Consensus Graph and Data Representation Convolution

Multi-view clustering aims to partition unlabeled patterns into disjoint clusters using consistent and complementary information derived from features of patterns in multiple views. Downstream methods perform this clustering sequentially: estimation of individual or consistent similarity matrices, spectral embedding, and clustering. In this article, we present an approach that can address some of the shortcomings of previous multiview clustering methods. We propose a single objective function whose optimization can jointly provide the consistent graph matrix for all views, the unified spectral data representation, the cluster assignments, and the view weights. We propose a new constraint term that sets the cluster index matrix to the convolution of the consistent spectral projection matrix over the consistent graph. Our proposed scheme has two interesting properties that the recent works do not have simultaneously. First, the cluster assignments can be estimated directly without the need for an additional clustering phase, which depends heavily on initialization. Second, the soft cluster assignments are directly linked to the kernel representation of the features of the views. Moreover, our method automatically computes the weights of each view, requiring fewer hyperparameters. We have conducted a series of experiments on real datasets. These demonstrate the effectiveness of the proposed approach, which compares favorably to many competing multi-view clustering methods.

Multi-View Discrete Clustering: A Concise Model.

In most existing graph-based multi-view clustering methods, the eigen-decomposition of the graph Laplacian matrix followed by a post-processing step is a standard configuration to obtain the target discrete cluster indicator matrix. However, we can naturally realize that the results obtained by the two-stage process will deviate from that obtained by directly solving the primal clustering problem. In addition, it is essential to properly integrate the information from different views for the enhancement of the performance of multi-view clustering. To this end, we propose a concise model referred to as Multi-view Discrete Clustering (MDC), aiming at directly solving the primal problem of multi-view graph clustering. We automatically weigh the view-specific similarity matrix, and the discrete indicator matrix is directly obtained by performing clustering on the aggregated similarity matrix without any post-processing to best serve graph clustering. More importantly, our model does not introduce an additive, nor does it has any hyper-parameters to be tuned. An efficient optimization algorithm is designed to solve the resultant objective problem. Extensive experimental results on both synthetic and real benchmark datasets verify the superiority of the proposed model.

Multi-view clustering using a flexible and optimal multi-graph fusion method

Recently, many multi-view clustering (MVC) methods based on graphs have been proposed to address prevalent multi-view data. For these methods, the multi-graph fusion step, aim of which is to obtain a consensus graph is vital for obtaining good clustering performance. However, these methods still have two problems. First, the column sum of the consensus graph is restricted to one, which is not flexible enough for practical applications. Affected by the sum-to-one constraint, the similarity between some noisy points may be large, which may cause these abnormal points to be grouped into a separate cluster. Second, the cluster structure of the consensus graph is often not considered. To address these problems, in this paper, we propose a novel multi-view clustering using a flexible and optimal multi-graph fusion method (MVC/FOMF). Specifically, we first obtain the similarity graph of each view by using red the self-expressive method. Second, we fuse these graphs into a consensus graph whose column sum is constrained to s(0<s≤1), and we can adjust s to look for the best clustering performance. Third, we impose a rank constraint on the Laplacian matrix of the consensus graph to learn the best clustering structure. Finally, all these steps are unified into a framework and the corresponding optimization procedure, which is based on the alternating multiplier method, is also designed. More importantly, the complexity of our algorithm is also lower than those of many representative algorithms. Compared with that of the state-of-the-art algorithms, our algorithm shows very encouraging performance on some datasets. The code can be found at https://github.com/wulala2233/MVCFOMF.

Geometric-inspired graph-based Incomplete Multi-view Clustering

Multi-view clustering methods group data into different clusters by discovering the consensus in heterogeneous sources, which however becomes difficult when partial views of real-world data are missing. Consequently, reducing the impact of missing views and leveraging available views are the key concerns for the Incomplete Multi-view Clustering (IMvC) problem. In this research, we take an innovative, geometry-based perspective to investigate the IMvC problem under a commonly-used weight aggregation framework. We conduct a geometric analysis to understand how missing views shift the aggregation solution from the one achieved with full views, subsequently impacting the clustering result. Drawing from our analysis, we introduce a weight reallocation approach that minimizes the shift and approximates the full-view solution by reallocating the factual weight of each available view. Furthermore, we address the IMvC problem by using our reallocation method on a graph aggregation algorithm to obtain reliable clusters. Our extensive experiments demonstrate that our proposed approach outperforms previous IMvC methods, reporting superior results on four datasets with three metrics. Especially, on the Caltech101-7 dataset with 40 percent missing data, our method achieves an accuracy of 0.686, which significantly outperforms the results of other comparison methods that are no larger than 0.662. Further, our method can be used as a flexible plugin to improve other weight aggregation algorithms. The source code of this work is publicly available at https://github.com/bjlfzs/Geometric-Inspired-Graph-based-Incomplete-Multi-view-Clustering.

Deep graph reconstruction for multi-view clustering

Graph-based multi-view clustering methods have achieved impressive success by exploring a complemental or independent graph embedding with low-dimension among multiple views. The majority of them, however, are shallow models with limited ability to learn the nonlinear information in multi-view data. To this end, we propose a novel deep graph reconstruction (DGR) framework for multi-view clustering, which contains three modules. Specifically, a Multi-graph Fusion Module (MFM) is employed to obtain the consensus graph. Then node representation is learned by the Graph Embedding Network (GEN). To assign clusters directly, the Clustering Assignment Module (CAM) is devised to obtain the final low-dimensional graph embedding, which can serve as the indicator matrix. In addition, a simple and powerful loss function is designed in the proposed DGR. Extensive experiments on seven real-world datasets have been conducted to verify the superior clustering performance and efficiency of DGR compared with the state-of-the-art methods.

Multiview Deep Matrix Factorization for Shared Compact Representation

Multiview learning aims to learn beneficial patterns from heterogeneous data sources and has captured growing attention in recent years. Most of the previous research studies focused on searching for an effective feature embedding of downstream tasks using diverse optimization algorithms, however, very limited work has been conducted to explore the connection between multiview learning and deep neural networks of structure sharing hidden layers. In this article, we propose a multiview deep matrix factorization model to learn a shared compact representation from multiview data. First, the proposed model constructs a multiview auto-encoder architecture with one shared encoder and multiple decoders, where each view corresponds to a factorization and the shared encoder leads to a common hidden layer. Accordingly, matrix factorizations from multiview data share the last hidden layer for a high-level semantic representation. Second, the nonnegativity constraint of the learned representation is transformed to the projection operation, which can be easily achieved by activating weights of the shared encoder network. Third, this network is trained with a joint loss of the reconstruction error and the compactness loss. By employing the clustering layer, the proposed method serves as an end-to-end multiview clustering method. Finally, comprehensive experiments on nine real-world datasets demonstrate the superiority of the proposed method against state-of-the-art multiview clustering methods.

Multiview Clustering via Hypergraph Induced Semi-Supervised Symmetric Nonnegative Matrix Factorization

Nonnegative matrix factorization (NMF) based multiview technique has been commonly used in multiview data clustering tasks. However, previous NMF based multiview clustering approaches fail to take advantage of a small amount of supervisory information to effectively improve the clustering performance, and are easily affected by the additional post-processing method in clustering tasks. To cope with these issues, a novel framework named multiview clustering via hypergraph induced semi-supervised symmetric NMF (MVCHSS) is proposed in this paper for multiview data clustering applications. Specifically, the proposed method has the following features: 1) a new multiview based hypergraph pairwise constraints propagation (MHPCP) algorithm is developed in MVCHSS to construct a set of informative similarity matrices, revealing the high-order relationships effectively and fully utilizing the limited pairwise constraint supervisory information among samples of each view data; 2) the obtained similarity matrices with much supervisory information are not only enforced into the symmetric NMF (SNMF) model, but also incorporated into the graph regularization for each view data; 3) the optimization problem of MVCHSS is formulated for multiview data clustering tasks to acquire a more discriminative clustering indicator matrix (or called consensus assignment matrix) without additional post-processing method. Moreover, the proof of convergence and the computational complexity for MVCHSS are presented. Extensive experiments on five multiview datasets demonstrate that the proposed MVCHSS framework outperforms several state-of-the-art multiview clustering methods.

Adversarial Multiview Clustering Networks With Adaptive Fusion.

The existing deep multiview clustering (MVC) methods are mainly based on autoencoder networks, which seek common latent variables to reconstruct the original input of each view individually. However, due to the view-specific reconstruction loss, it is challenging to extract consistent latent representations over multiple views for clustering. To address this challenge, we propose adversarial MVC (AMvC) networks in this article. The proposed AMvC generates each view's samples conditioning on the fused latent representations among different views to encourage a more consistent clustering structure. Specifically, multiview encoders are used to extract latent descriptions from all the views, and the corresponding generators are used to generate the reconstructed samples. The discriminative networks and the mean squared loss are jointly utilized for training the multiview encoders and generators to balance the distinctness and consistency of each view's latent representation. Moreover, an adaptive fusion layer is developed to obtain a shared latent representation, on which a clustering loss and the l1,2 -norm constraint are further imposed to improve clustering performance and distinguish the latent space. Experimental results on video, image, and text datasets demonstrate that the effectiveness of our AMvC is over several state-of-the-art deep MVC methods.

Hypergraph Learning-Based Semi-Supervised Multi-View Spectral Clustering

Graph-based semi-supervised multi-view clustering has demonstrated promising performance and gained significant attention due to its capability to handle sample spaces with arbitrary shapes. Nevertheless, the ordinary graph employed by most existing semi-supervised multi-view clustering methods only captures the pairwise relationships between samples, and cannot fully explore the higher-order information and complex structure among multiple sample points. Additionally, most existing methods do not make full use of the complementary information and spatial structure contained in multi-view data, which is crucial to clustering results. We propose a novel hypergraph learning-based semi-supervised multi-view spectral clustering approach to overcome these limitations. Specifically, the proposed method fully considers the relationship between multiple sample points and utilizes hypergraph-induced hyper-Laplacian matrices to preserve the high-order geometrical structure in data. Based on the principle of complementarity and consistency between views, this method simultaneously learns indicator matrices of all views and harnesses the tensor Schatten p-norm to extract both complementary information and low-rank spatial structure within these views. Furthermore, we introduce an auto-weighted strategy to address the discrepancy between singular values, enhancing the robustness and stability of the algorithm. Detailed experimental results on various datasets demonstrate that our approach surpasses existing state-of-the-art semi-supervised multi-view clustering methods.