Multi-view Clustering Research Articles

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.

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.

Latent information-guided one-step multi-view fuzzy clustering based on cross-view anchor graph

Although graph-inspired clustering methods have achieved impressive success in the area of multi-view data analysis, current methods still face several challenges. First, classical graph construction approaches are computationally expensive in terms of both time and space for large-scale data. Second, fusing graphs from different views remains a challenge. Third, most existing methods require additional post-processing steps to generate the label assignment matrix. To address the above challenges, this paper proposes a novel multi-view clustering algorithm, called latent information-guided one-step multi-view fuzzy clustering based on cross-view anchor graph. Specifically, we introduce an efficient cross-view anchor graph learning approach to construct the similarity matrix of multi-view data and extract latent information from the graph, which reduces the computational complexity of graph learning and inspires the optimization of the consensus membership matrix. Following that, our one-step multi-view fuzzy clustering algorithm can directly generate the final clustering result in an effective and straightforward manner. Furthermore, during the optimization process, the proposed method balances consensus matrix learning and view-specified membership exploration via a self-tuned weighting mechanism. The comprehensive experimental analysis demonstrates the superiority of our approach over the state-of-the-art approaches.

Self-filling evidential clustering for partial multi-view data

Partial multi-view clustering (PMVC) is a hot topic in data mining, where each view suffers from the absence of some data. Although many PMVC algorithms have been presented with appropriate performance, to the best of our knowledge, almost all of them need to be fed with the number of clusters as hyperparameters. Moreover, these existing algorithms only create hard partitions for objects with multiple views, which are often in highly overlapping areas. This ignores ambiguity and uncertainty in object assignment, which likely leads to performance degradation. To address these issues, we propose a novel self-filling evidential clustering algorithm (SFPMEC) for the PMVC problem. Based on the shared coefficient matrix learned from a self-filling process, SFPMEC provides a human-readable chart through which the number of clusters can be easily detected. SFPMEC then derives a credal partition under the framework of evidence theory, improving the fault tolerance of clustering and gaining deeper insight into the data structure. Extensive experiments are conducted to demonstrate the benefits of adopting the self-filling process and evidence theory. Besides, our algorithm shows better performance than other state-of-the-art methods on benchmark datasets11The source code can be found in https://drive.google.com/file/d/1KMi0N8cX85YhwiNjetBwA6QeolQP5TnC/view?usp=sharing..

Multi-view clustering via optimal transport algorithm

The surge in data with multiple views has propelled significant interest in the domain of multi-view clustering. Unlike conventional single-view data, multi-view data offers a more accurate representation of objects. However, the pivotal challenge remains in the effective categorization of data through feature extraction from multiple views within clustering tasks. Notably, prevailing multi-view clustering algorithms often emphasize the derivation of appropriate view weights, inadvertently sidestepping optimization intricacies. This approach frequently leads to protracted computational time due to the resource-intensive matrix multiplication operations involved in optimization, coupled with the necessity of weight allocation for diverse views. Addressing this, we propose an optimization framework founded on the optimal transport algorithm that operates independently of view weights. A paramount advantage of the optimal transport algorithm lies in its rapid convergence to a closed-form solution. This study diverges from the conventional focus on view weights and centers on the optimization process within clustering algorithms for resolving multi-view challenges. The introduced framework employing the optimal transport algorithm significantly mitigates computational complexity while handling multiple views. Rigorous experimentation duly substantiates the efficacy of the proposed framework in the realm of multi-view clustering. Across publicly available multi-view datasets, our framework exhibits superior performance over existing state-of-the-art algorithms.

Weakly supervised fine-grained semantic segmentation via spatial correlation-guided learning

Weakly supervised semantic segmentation (WSSS) mainly adopts class activation map (CAM) to recognize different categories with generated pseudo masks of only image-level labels. Recently, many advanced works focus on learning the semantic correlation to refine the conventional CAM, which only identify sparse and discriminative semantic regions, severely weakening the further learning ability of spatial features. To copy with the above problem, a spatial correlation-guided learning framework is proposed to exploit the spatial and semantic correlation between adjacent pixels for weakly supervised fine-grained semantic segmentation (WSFGSS). From the spatial perspective, self-supervised multi-view clustering (SMC) is designed to fully mine spatial correlation by clustering of multiple views including scale, angle and position. Moreover, a hybrid self-supervised (HS) loss function is used to further promote the optimized speed and accuracy of three spatial representations. From the semantic perspective, the affinity matrix is applied to describe the semantic similarity between different pixels by building a weighted graph, and combine above robust pseudo label into a probability transition matrix. Therefore, the initial CAM is gradually corrected during the iterative optimization by the random walk algorithm. Finally, the refined CAM is utilized as supervision information for training the standard segmentation network effectively. Sufficient experimental results on BSDS500, PASCAL VOC 2012 and MS COCO datasets show that the proposed SMC method obtains more accurate pseudo labels than the recent unsupervised segmentation models. Meantime, with these pseudo labels, the proposed fine-grained framework achieves the state-of-the-art performance for WSFGSS.

Multi-view clustering with Laplacian rank constraint based on symmetric and nonnegative low-rank representation

Multi-view spectral clustering has attracted more and more attention due to its promising advantages in data clustering, and many related methods have been proposed, among which the method based on low-rank representation have become increasingly popular. However, the similarity matrices learned by the existing methods inevitably contain some negative entries and are generally nonsymmetric. In order to guarantee weight consistency for each pair of data points and highly correlated data points to be together, we propose a new multi-view spectral clustering model based on the symmetric and nonnegative low-rank representation. This model can learn the view-specific consistent similarity matrix and also capture the local structure and discriminative information among data by imposing symmetric and nonnegative constraints on the representation matrix. By employing the compatible and complementary information from multi-view data points, it can also learn the consensus similarity matrix for all views and perform the spectral clustering simultaneously. By the augmented Lagrangian multiplier method, an alternating iterative optimization algorithm is designed for solving this model and its computational complexity and convergence is analyzed. Comprehensive experiments on multiple multi-view data sets also verify the effectiveness and superiority of the proposed approach.

Self-Supervised Graph Completion for Incomplete Multi-View Clustering

Incomplete multi-view clustering (IMVC) is challenging, as it requires adequately exploring complementary and consistency information under the incompleteness of data. Most existing approaches attempt to overcome the incompleteness at instance-level. In this work, we develop a new approach to facilitate IMVC from a new perspective. Specifically, we transfer the issue of missing instances to a similarity graph completion problem for incomplete views, and propose a self-supervised multi-view graph completion algorithm to infer the associated missing entries. Further, by incorporating constrained feature learning, the inferred graph can be naturally leveraged in representation learning. We theoretically show that our feature learning process performs an Auto-Regressive filter function by encoding the learned similarity graph, which could yield discriminative representation for a clustering task. Extensive experiments demonstrate the effectiveness of the proposed method in comparison with state-of-the-art methods. The source code of our method is available at the <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">GitHub</b> : <uri xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">https://github.com/CLiu272/SGC-IMVC</uri> .

Unbalanced incomplete multi-view clustering based on low-rank tensor graph learning

Unbalanced incomplete multi-view clustering based on low-rank tensor graph learning

Reading promotion mode of university libraries in the context of information development

Abstract This paper mainly proposes a technical route of user profiling based on multi-view clustering and constructs a multidimensional and multi-view reader feature system based on reader behavior data. According to the constructed reader feature system and the defects of the classical K-means algorithm in multi-view clustering, a multi-view dichotomous K-means algorithm based on Marxian distance is proposed. Using the proposed algorithm for multi-view clustering of readers, the user portrait features of readers can be obtained, and finally, a university library user portrait system is designed and implemented. By analyzing the behavior of college students through the user portrait technique, we get that the most preferred book genre of college students is literature accounting for 71.45%, followed by science and history with 57.64% and 51.37%, respectively. The most popular form of reading promotion among college students is classical film and television exhibitions, accounting for 63.73%, followed by lectures by celebrities and experts, accounting for 60.91%. The highest influence on college students going to the library is too many spare time activities, accounting for 64.38%, and not choosing books, accounting for 36.95%. These data can help libraries understand readers’ needs and provide help for reading accurate recommendations and services based on readers’ user profiles.

Binary multi-view clustering with spectral embedding

Techniques for large-scale multi-view clustering have attracted increasing attention in recent years. To explore complementary and consensus information across multiple views, mapping multi-view data into a hamming space for binary multi-view learning is highly effective. However, for binary multi-view clustering, it is difficult to adopt the local manifold structure of original data into the consensus representation. Therefore, a novel algorithm named Binary Multi-View Clustering With Spectral Embedding (BMVC_SE) is proposed in this study. This algorithm unifies binary consensus representation learning and multi-view spectral learning into a joint framework. Specifically, this algorithm exploits the shareable and individual information across multi-view data to learn a binary consensus representation. Furthermore, spectral rotation technique is employed to embed manifold information from original multi-view data into binary consensus representation. Note that a multi-view GPI algorithm is proposed in this study to obtain the better local manifold information. We also provide an effective optimization method to solve the existing method. Extensive experimental results show that our method outperforms some state-of-the-art methods.

SC[formula omitted]-Net: Self-supervised learning for multi-view complementarity representation and consistency fusion network

Multi-view clustering (MVC) seeks to improve the original single-view clustering by exploring the complementarity and consistency contained in multi-view data. While most subspace-based multi-view clustering methods now focus on exploring one of the consistency or complementarity features associated with multi-view datasets, rather than balancing the exploration of them. Meanwhile, the favored approach of combining deep learning tends to design the network structure to be relatively complex and then superimpose the constraints of multiple loss functions. Additionally, training results with unlabeled datasets are often unsatisfactory.To solve the aforementioned concerns, we present an innovative deep convolutional clustering network (SC2-Net) backed by self-supervised learning. SC2-Net learns multi-view complementarity representation and consistency fusion between views which adheres to the two principles of MVC. The clustering labels will be obtained by cooperating with k-means, the overall structure is simple but efficient. In addition, we supervise the network training by using two self-supervised loss functions, making the training process free from using data with annotations. We test the proposed network under multiple sets of experimental parameter combinations and prove its effectiveness and robustness.

Multi-view clustering via efficient representation learning with anchors

Multi-view spectral clustering has gained considerable attention due to its potential to enhance clustering performance. Although many methods have shown promising results, they often suffer from high time complexity and are not suitable for large-scale datasets. On the other hand, anchor-based methods are well-known for their efficiency. These methods typically learn the similarity relationship between instances and anchors and then convert it into the similarity relationship between instances, involving a considerable number of calculations. To address this issue, we propose a novel method called Multi-view clustering via Efficient Representation LearnIng with aNchors (MERLIN) in this paper. Instead of learning the instance–instance relationship, MERLIN approaches the clustering problem from the perspective of representation learning. Specifically, MERLIN selects the same anchors for different views and utilizes these anchors to learn a consensus representation that integrates information from all views. Additionally, MERLIN adaptively learns weights for different views to fully exploit the complementary information among multiple views. In comparison with seven state-of-the-art baseline methods across five datasets, MERLIN demonstrates both efficiency and effectiveness in handling multi-view datasets and is suitable for handling large-scale datasets.

Auto weighted robust dual graph nonnegative matrix factorization for multiview clustering

Recent multi-data fusion techniques have inspired multi-view clustering study, which has become a popular topic in machine learning. One successful way of solving multi-view clustering is nonnegative matrix factorization. This paper proposes an auto weighted robust dual graph nonnegative matrix factorization (ARDNMF), where ℓ2,1 norm is adopted to make ARDNMF robust as data contain noise and outliers. Through dual graphs, structure information in data space and feature space is considered. Moreover, an auto weighted assignment method is introduced in ARDNMF to assign appropriate weights to views. Effective updating rules are given. Experiments on real datasets show ARDNMF superiors to state-of-the-art algorithms in terms of clustering results.

Implicit Weight Learning for Multi-View Clustering.

Exploiting different representations, or views, of the same object for better clustering has become very popular these days, which is conventionally called multi-view clustering. In general, it is essential to measure the importance of each individual view, due to some noises, or inherent capacities in the description. Many previous works model the view importance as weight, which is simple but effective empirically. In this article, instead of following the traditional thoughts, we propose a new weight learning paradigm in the context of multi-view clustering in virtue of the idea of the reweighted approach, and we theoretically analyze its working mechanism. Meanwhile, as a carefully achieved example, all of the views are connected by exploring a unified Laplacian rank constrained graph, which will be a representative method to compare with other weight learning approaches in experiments. Furthermore, the proposed weight learning strategy is much suitable for multi-view data, and it can be naturally integrated with many existing clustering learners. According to the numerical experiments, the proposed implicit weight learning approach is proven effective and practical to use in multi-view clustering.

Incomplete Multiview Clustering Using Normalizing Alignment Strategy With Graph Regularization

Matrix factorization has demonstrated promising performance in the incomplete multiview clustering (IMC) tasks. However, many algorithms require feature normalization operations to ensure the stability of model results, so either the convergence is unstable, or the objective function cannot fit the data well. Addressing these issues, we propose a novel IMC algorithm using a normalizing alignment strategy (IMCNAS) based on nonnegative matrix factorization. Specifically, the columns of the basis matrices are constrained into unit vector space, which integrates the feature normalization and the optimizing process, and makes the model converge fast and stable. On the other hand, this enables the model to fit the data better and produce more reasonable factorization results. Further, we develop a novel pairwise co-regularization to align incomplete multiple views more directly, without introducing a common consensus matrix like traditional centroid-based co-regularization. Graph regularization is also incorporated in the proposed model to utilize the geometrical information of data. We implement IMCNAS with a centroid-based regularization and a pairwise co-regularization respectively, and leads to two variants, i.e., IMCNAS-1 and IMCNAS-2. Both variants are optimized with multiplicative updating rules. Extensive experiments conducted on various real-world datasets comparing several state-of-the-art IMC methods verified the effectiveness of the proposed methods. The source code is available at: <uri>https://github.com/GuoshengCui/IMCNAS</uri>.

Contrastive Multi-View Kernel Learning

Kernel method is a proven technique in multi-view learning. It implicitly defines a Hilbert space where samples can be linearly separated. Most kernel-based multi-view learning algorithms compute a kernel function aggregating and compressing the views into a single kernel. However, existing approaches compute the kernels independently for each view. This ignores complementary information across views and thus may result in a bad kernel choice. In contrast, we propose the Contrastive Multi-view Kernel - a novel kernel function based on the emerging contrastive learning framework. The Contrastive Multi-view Kernel implicitly embeds the views into a joint semantic space where all of them resemble each other while promoting to learn diverse views. We validate the method's effectiveness in a large empirical study. It is worth noting that the proposed kernel functions share the types and parameters with traditional ones, making them fully compatible with existing kernel theory and application. On this basis, we also propose a contrastive multi-view clustering framework and instantiate it with multiple kernel k-means, achieving a promising performance. To the best of our knowledge, this is the first attempt to explore kernel generation in multi-view setting and the first approach to use contrastive learning for a multi-view kernel learning.

Multi-View Adjacency-Constrained Hierarchical Clustering

This paper explores the problem of multi-view clustering, which aims to promote clustering performance with multi-view data. The majority of existing methods have problems with parameter adjustment and high computational complexity. Moreover, in the past, there have been few works based on hierarchical clustering to learn the granular information of multiple views. To overcome these limitations, we propose a simple but efficient framework: Multi-view adjacency-Constrained Hierarchical Clustering (MCHC). Specifically, MCHC mainly consists of three parts: including the Fusion Distance matrices with Extreme Weights (FDEW); adjacency-Constrained Nearest Neighbor Clustering (CNNC); and the internal evaluation Index based on Rawls' Max-Min criterion (MMI). FDEW aims to learn a fusion distance matrix set, which not only uses complementary information among multiple views, but exploits the information from each single view. CNNC is utilized to generate multiple partitions based on FDEW, and MMI is designed for choosing the best one from the multiple partitions. In addition, we propose a parameter-free version of MCHC (MCHC-PF). Without any parameter selection, MCHC-PF can give partitions at different granularity levels with a low time complexity. Comprehensive experiments tested on eight real-world datasets validate the superiority of the proposed methods compared with the 13 current state-of-the-art methods.

Deep Multi-View Clustering Based on Reconstructed Self-Expressive Matrix

Deep Multi-view Subspace Clustering is a powerful unsupervised learning technique for clustering multi-view data, which has achieved significant attention during recent decades. However, most current multi-view clustering methods rely on learning self-expressive layers to obtain the ultimate clustering results, where the size of the self-expressive matrix increases quadratically with the number of input data points, making it difficult to handle large-scale datasets. Moreover, since multiple views are rich in information, both consistency and specificity of the input images need to be considered. To solve these problems, we propose a novel deep multi-view clustering approach based on the reconstructed self-expressive matrix (DCRSM). We use a reconstruction module to approximate self-expressive coefficients using only a small number of training samples, while the conventional self-expressive model must train the network with entire datasets. We also use shared layers and specific layers to integrate consistent and specific information of features to fuse information between views. The proposed DCRSM is extensively evaluated on multiple datasets, including Fashion-MNIST, COIL-20, COIL-100, and YTF. The experimental results demonstrate its superiority over several existing multi-view clustering methods, achieving an improvement between 1.94% and 4.2% in accuracy and a maximum improvement of 4.5% in NMI across different datasets. Our DCRSM also yields competitive results even when trained by 50% samples of the whole datasets.

Shared and individual representation learning with Feature Diversity for Deep MultiView Clustering

Due to the remarkable representation ability of Nonnegative matrix factorization (NMF), its multiview variants have become a crucial kind of multiview representation learning methods. However, the majority of existing methods fail to effectively utilize complex higher-level hierarchical information, shared information, and individual information of multiview data. To address these challenges, we propose the Shared and individual representation learning with feature Diversity for Deep Multiview Clustering (SiDDMVC). Specifically, this method decomposes data of each view through nonnegative matrix factorization in a layer-wise fashion to exploit complex higher-level hierarchical information. The outputs of NMF are then divided into shared and individual representations with shared geometrical constraint and feature diversity constraint. Experimental results on six real-world datasets have shown that SiDDMVC not only achieves superior performance through the use of graph regularization and two diversity constraints, but also surpasses several state-of-the-art multiview clustering methods.