In incomplete multi-view multi-label learning scenarios, it is crucial to use the incomplete multi-view data to extract consistent and specific representations from different data sources and to fully exploit the missing label information. However, most previous approaches ignore the separation problem between view-shared and specific information. To address this problem, in this paper, we propose a method that can separate view-consistent features from view-specific features under the Variational Autoen-coder (VAE) framework. Specifically, we first introduce cross-view reconstruction to capture view-consistent features and extract shared information from different views through unsupervised pre-training. Subsequently, we develop a disentangling module to learn specific features by minimizing the variational upper bound of mutual information between consistent and specific features. Finally, we utilize prior label relevance information derived from training data to guide the learning of the distribution of label semantic embeddings, aggregating relevant semantic embeddings and maintaining the label relevance topology in the semantic space. In extensive experiments, our model outperforms existing state-of-the-art algorithms on several real-world datasets, which fully validates its strong adaptability to missing views and labels.

In recent years, deep multi-view clustering methods based on contrastive learning have gained significant attention. Most existing approaches treat the anchor and its cross-view representations as positive pairs, while the anchor and other samples are considered negative pairs. However, this pairwise assignment does not account for the higher similarity between the anchor and samples that are close, which should also be treated as positive pairs. To address this issue, we introduce topology-aware positive sampling: for each anchor, both its intra-view neighbors and cross-view consistent neighbors are selected as additional positive samples, which aligns contrastive learning with the homophily principle of clustering. Additionally, to obtain reliable neighbor relationships, most existing methods construct graphs from the original data or extracted features and average them to form a consensus graph. However, this approach overlooks the fact that views of varying quality should be assigned different weights, and unreliable connections within a view should be discarded. To overcome this, we design a global-guided weak connections suppression mechanism to weaken unreliable connections in the initial graph of each view, then apply weighted graph fusion to obtain a more accurate consensus graph. We also combine the view weights from graph fusion with the corresponding view's neighbor contrastive loss to enhance consistency between the two processes. Extensive experimental results demonstrate the superiority of our proposed method.

Although significant progress has been made in multi-view learning over the past few decades, it remains challenging, especially in the context of incomplete multi-view clustering, where modeling complex correlations among different views and handling missing data are key difficulties. In this paper, we propose a novel incomplete multi-view clustering network to address the aforementioned issue, named Incomplete Multi-view Clustering via Multi-level Contrastive Learning (IMC-MCL). Specifically, the proposed model aims to minimize the conditional entropy between views to recover missing data by dual prediction strategy. Moreover, the approach learns multi-level features, including latent, high-level and semantic features, with the goal of satisfying both reconstruction and consistency objectives in distinct feature spaces. Specifically, latent features are utilized to accomplish the reconstruction objective, while high-level features and semantic labels are employed to achieve the two consistency goals through contrastive learning. This framework enables the exploration of shared semantics within high-level features and achieves clustering assignment using semantic features. Extensive experiments have shown that the proposed approach outperforms other state-of-the-art incomplete multi-view clustering methods on seven challenging datasets.

Multi-view K-means clustering successfully generalizes K-means from single-view to multi-view, and obtains excellent clustering performance. In every view, it makes each data point close to the center of the corresponding cluster. However, multi-view K-means only considers the compactness of each cluster, but ignores the separability of different clusters, which is of great importance to producing a good clustering result. In this paper, we propose Discriminatively Fuzzy Multi-view K-means clustering with Local Structure Preserving (DFMKLS). On the basis of minimizing the distance between each data point and the center of the corresponding cluster, DFMKLS separates clusters by maximizing the distance between the centers of pairwise clusters. DFMKLS also relaxes its objective by introducing the idea of fuzzy clustering, which calculates the probability that a data point belongs to each cluster. Considering multi-view K-means mainly focuses on the global information of the data, to efficiently use the local information, we integrate the local structure preserving into the framework of DFMKLS. The effectiveness of DFMKLS is evaluated on benchmark multi-view datasets. It obtains superior performances than state-of-the-art multi-view clustering methods, including multi-view K-means.

Multi-View Clustering (MVC) aims to mine complementary information across different views to partition multi-view data more effectively and has attracted considerable interest. However, existing deep multi-view clustering methods frequently neglect the exploration of structural information within individual view and lack the learning of structural consistency among views, which results in limitations in the clustering performance. In this paper, we introduce a novel multi-view clustering framework based on graph consistency learning to address this issue. Specifically, we design intra-view graph contrastive learning to uncover structural information within each view and achieve structural conscistency objectives through cross-view graph consistency learning. Additionally, to address the conflict between different learning objectives when trained in the same space, we introduce two new feature spaces, one for cluster-levcel contrastive learning and the other for instance-level contrastive learning. Subsequently, to make the most of discriminative information from all views, we concatenate high-level features from all views to form global features and employ self-supervision to promote clustering consistency across different views. Experimental results on several challenging datasets demonstrate the outstanding performance of our proposed method.

Traditional multi-view algorithms typically require data to be complete, and these algorithms may not be suitable or effective when dealing with incomplete data. As a result, the research field has witnessed the emergence of methods specifically designed for addressing incomplete multi-view clustering. In contrast, most of existing incomplete multi-view algorithms primarily emphasize capturing global information while neglecting the importance of local information. To overcome these challenges, we put forward a novel approach, named tensor low-rank graph embedding and learning for one-step incomplete multi-view clustering. We combine the beneficial aspects of graph embedding and tensor low-rank in this method, which not only focuses on local relationships but also provides insights into the global structure. Firstly, the initial similarity graph matrix is constructed using the inter-dependency between views. Secondly, the similarity graph matrix is structured as a third-order tensor and constrained by the tensor nuclear norm. This constraint enables the capturing of higher-order correlations across multiple views. Thirdly, graph embedding is added to obtain a common feature representation. Finally, the algorithm incorporates clustering to determine the optimal clustering labels. We conducted experiments comparing our algorithm with seven different incomplete multi-view methods using four different evaluation metrics. The experimental results indicate that our algorithm achieved the best clustering performance across five datasets under various missing rates. Especially when faced with a 50% missing rate in the Extended YaleB dataset, the clustering accuracy and normalized mutual information of our method are improved by 28.23% and 28.11%, respectively, compared to the second-best algorithm.

Spectral-type subspace clustering algorithms have shown excellent performance in many subspace clustering applications. The existing spectral-type subspace clustering algorithms either focus on designing constraints for the reconstruction coefficient matrix or feature extraction methods for finding latent features of original data samples. In this paper, inspired by graph convolutional networks, we use the graph convolution technique to develop a feature extraction method and a coefficient matrix constraint simultaneously. And the graph-convolutional operator is updated iteratively and adaptively in our proposed algorithm. Hence, we call the proposed method adaptive graph convolutional subspace clustering (AGCSC). We claim that, by using AGCSC, the aggregated feature representation of original data samples is suitable for subspace clustering, and the coefficient matrix could reveal the subspace structure of the original data set more faithfully. Finally, plenty of subspace clustering experiments prove our conclusions and show that AGCSC11We present the codes of AGCSC and the evaluated algorithms on https://github.com/weilyshmtu/AGCSC. outperforms some related methods as well as some deep models.

As one category of important incomplete multi-view clustering methods, subspace based methods seek the common latent representation of incomplete multi-view data by matrix factorization and then partition the latent representation to get clustering results. However, these methods ignore missing views in the process of matrix factorization, which makes the connection of different views be exploited inadequately. This paper proposes Incomplete Multi-view Clustering with Reconstructed Views (IMCRV), which utilizes the incomplete examples sufficiently. In IMCRV, the missing views of incomplete examples are reconstructed and the reconstructed views are also used to seek the common latent representation. IMCRV also involves the Laplacian regularization to preserve the global property of the latent representation. A novel gradient descent method with the multiplicative update rule is designed to solve the objective function of IMCRV. The corresponding iterative algorithm is developed and the convergence of the algorithm is proved. IMCRV is compared with many state-of-the-art incomplete multi-view clustering methods under different Incomplete Example Rates (IER) on public multi-view datasets. The experimental results demonstrate the superior effectiveness of IMCRV.

Canonical Correlation Analysis (CCA) is a popular multiview dimension reduction method, which aims to maximize the correlation between two views to find the common subspace shared by these two views. However, it can only deal with two-view data, while the number of views frequently exceeds two in many real applications. To handle data with more than two views, in the previous studies, either the pairwise correlation or the high-order correlation was employed. These two types of correlation define the relation of multiview data from different viewpoints, and both have special effects for view consistency. To obtain flexible view consistency, in this article, we propose multiview uncorrelated locality preserving projection (MULPP), which considers two types of correlation simultaneously. The MULPP also considers the complementary property of different views by preserving the local structures of all the views. To obtain multiple projections and minimize the redundancy of low-dimensional features, for each view, the MULPP makes the features extracted by different projections uncorrelated. The MULPP is solved by an iteration algorithm, and the convergence of the algorithm is proven. The experiments on Multiple Feature, Coil-100, 3Sources, and NUS-WIDE data sets demonstrate the effectiveness of MULPP.

Independent component analysis aiming at detecting the functional connectivity among discrete cortical brain regions has been extensively used to explore the functional magnetic resonance imaging data. Although the independent components (ICs) were with relatively high quality, the noise embedding in ICs has a great impact on the true active/inactive region inference and the reproducibility, in postprocessing stage, e.g., the extraction of statistical parametrical maps (SPMs). In this paper, a novel brain network enhancement model (BNEM) is proposed, which mainly consists of two key techniques: 1) 3-D wavelet noise filter (3DWNF) for the meaningful ICs, which greatly suppresses noise and enforces the real activation inference of SPMs; and 2) a spatial reproducibility enhancement algorithm (SREA), aiming to improve the reproducibility of SPMs. The simulated experiment demonstrated that the postfiltering signals by 3DWNF were with higher correlation and less normalized mean square error to the ground truths than the prefiltering ones; SREA could further enhance the quality of most postfiltering ones, preserving the consistency with 3DWNF. The real data experiments also revealed that 1) 3DWNF could lead to more accurate preservation of the true positive voxels by correctly identifying the high proportionally misclassified voxels of the nonenhanced SPMs; 2) SREA could further improve the classification accuracy of the active/inactive voxels of SPMs corresponding to the 3DWNF denoised ICs; and 3) both 3DWNF and SREA contribute to the reproducibility enhancement of the reproduced SPMs by BNEM. Thus, BNEM is expected to have wide applicability in the neuroscience and clinical domain.

Null space linear discriminant analysis (NLDA) and linear discriminant analysis based on generalized singular value decomposition (LDA/GSVD) are two popular linear discriminant analysis (LDA) methods that can solve Small Sample Size (SSS) problem. In this paper we present the relation between NLDA and LDA/GSVD under a mild condition, and propose a modified NLDA (MNLDA) algorithm. By both theoretical analysis and experimental results on ORL and FERET face databases, the proposed MNLDA has been proved to have the same discriminating power as LDA/GSVD and to be more efficient than LDA/GSVD.