Multi-view data containing complementary and consensus information can facilitate representation learning by exploiting the intact integration of multi-view features. Because most objects in the real world often have underlying connections, organizing multi-view data as heterogeneous graphs is beneficial to extracting latent information among different objects. Due to the powerful capability to gather information of neighborhood nodes, in this article, we apply Graph Convolutional Network (GCN) to cope with heterogeneous graph data originating from multi-view data, which is still under-explored in the field of GCN. In order to improve the quality of network topology and alleviate the interference of noises yielded by graph fusion, some methods undertake sorting operations before the graph convolution procedure. These GCN-based methods generally sort and select the most confident neighborhood nodes for each vertex, such as picking the top- k nodes according to pre-defined confidence values. Nonetheless, this is problematic due to the non-differentiable sorting operators and inflexible graph embedding learning, which may result in blocked gradient computations and undesired performance. To cope with these issues, we propose a joint framework dubbed Multi-view Graph Convolutional Network with Differentiable Node Selection (MGCN-DNS), which is constituted of an adaptive graph fusion layer, a graph learning module, and a differentiable node selection schema. MGCN-DNS accepts multi-channel graph-structural data as inputs and aims to learn more robust graph fusion through a differentiable neural network. The effectiveness of the proposed method is verified by rigorous comparisons with considerable state-of-the-art approaches in terms of multi-view semi-supervised classification tasks, and the experimental results indicate that MGCN-DNS achieves pleasurable performance on several benchmark multi-view datasets.

Most multi-view clustering methods based on shallow models are limited in sound nonlinear information perception capability, or fail to effectively exploit complementary information hidden in different views. To tackle these issues, we propose a novel Subspace-Contrastive Multi-View Clustering (SCMC) approach. Specifically, SCMC utilizes a set of view-specific auto-encoders to map the original multi-view data into compact features capturing its nonlinear structures. Considering the large semantic gap of data from different modalities, we project multiple heterogeneous features into a joint semantic space, namely the embedded compact features are passed through the self-expression layers to learn the subspace representations, respectively. In order to enhance the discriminability and efficiently excavate the complementarity of various subspace representations, we use the contrastive strategy to maximize the similarity between positive pairs while differentiate negative pairs. Thus, the graph regularization is employed to encode the local geometric structure within varying subspaces for optimizing the consistent affinity matrix. Furthermore, to endow the proposed SCMC with the ability of handling the multi-view out-of-samples, we develop a consistent sparse representation (CSR) learning mechanism over the in-samples. To demonstrate the effectiveness of the proposed model, we conduct a large number of comparative experiments on ten challenging datasets, and the experimental results show that SCMC outperforms existing shallow and deep multi-view clustering methods. In addition, the experimental results on out-of-samples illustrate the effectiveness of the proposed CSR.

Federated Learning (FL) provides a novel paradigm for privacy-preserving machine learning, enabling multiple clients to collaborate on model training without sharing private data. To handle multi-source heterogeneous data, Vertical Federated Learning (VFL) has been extensively investigated. However, in the context of VFL, the label information tends to be kept in one authoritative client and is very limited. This poses two challenges for model training in the VFL scenario. On the one hand, a small number of labels cannot guarantee to train a well VFL model with informative network parameters, resulting in unclear boundaries for classification decisions. On the other hand, the large amount of unlabeled data is dominant and should not be discounted, and it is worthwhile to focus on how to leverage them to improve representation modeling capabilities. To address the preceding two challenges, we first introduce supervised contrastive loss to enhance the intra-class aggregation and inter-class estrangement, which is to deeply explore label information and improve the effectiveness of downstream classification tasks. Then, for unlabeled data, we introduce a pseudo-label-guided consistency mechanism to induce the classification results coherent across clients, which allows the representations learned by local networks to absorb the knowledge from other clients, and alleviates the disagreement between different clients for classification tasks. We conduct sufficient experiments on four commonly used datasets, and the experimental results demonstrate that our method is superior to the state-of-the-art methods, especially in the low-label rate scenario, and the improvement becomes more significant.

In deep multi-view clustering, three intractable problems are posed ahead of researchers, namely, the complementarity exploration problem, the information preservation problem, and the cluster structure discovery problem. In this paper, we consider the deep multi-view clustering from the perspective of mutual information (MI), and attempt to address the three important concerns with a Mutual Information-Driven Multi-View Clustering (MIMC) method, which extracts the common and view-specific information hidden in multi-view data and constructs a clustering-oriented comprehensive representation. Specifically, three constraints based on MI are devised in response to three issues. Correspondingly, we minimize the MI between the common representation and view-specific representations to exploit the inter-view complementary information. Further, we maximize the MI between the refined data representations and original data representations to preserve the principal information. Moreover, to learn a clustering-friendly comprehensive representation, the MI between the comprehensive embedding space and cluster structure is maximized. Finally, we conduct extensive experiments on six benchmark datasets, and the experimental results indicate that the proposed MIMC outperforms other clustering methods.

With the rapidly growing attention to multi-view data in recent years, multi-view outlier detection has become a rising field with intense research. These researches have made some success, but still exist some issues that need to be solved. First, many multi-view outlier detection methods can only handle datasets that conform to the cluster structure but are powerless for complex data distributions such as manifold structures. This overly restrictive data assumption limits the applicability of these methods. In addition, almost the majority of multi-view outlier detection algorithms cannot solve the online detection problem of multi-view outliers. To address these issues, we propose a new detection method based on the local similarity relation and data reconstruction, i.e., the Self-Representation Method with Local Similarity Preserving for fast multi-view outlier detection (SRLSP). By using the local similarity structure, the proposed method fully utilizes the characteristics of outliers and detects outliers with an applicable objective function. Besides, a well-designed optimization algorithm is proposed, which completes each iteration with linear time complexity and can calculate each instance parallelly. Also, the optimization algorithm can be easily extended to the online version, which is more suitable for practical production environments. Extensive experiments on both synthetic and real-world datasets demonstrate the superiority of the proposed method on both performance and time complexity.

Multi-view clustering (MVC) aims at exploiting the consistent features within different views to divide samples into different clusters. Existing subspace-based MVC algorithms usually assume linear subspace structures and two-stage similarity matrix construction strategies, thereby posing challenges in imprecise low-dimensional subspace representation and inadequacy of exploring consistency. This paper presents a novel hierarchical representation for MVC method via the integration of intra-sample, intra-view, and inter-view representation learning models. In particular, we first adopt the deep autoencoder to adaptively map the original high-dimensional data into the latent low-dimensional representation of each sample. Second, we use the self-expression of the latent representation to explore the global similarity between samples of each view and obtain the subspace representation coefficients. Third, we construct the third-order tensor by arranging multiple subspace representation matrices and impose the tensor low-rank constraint to sufficiently explore the consistency among views. Being incorporated into a unified framework, these three models boost each other to achieve a satisfactory clustering result. Moreover, an alternating direction method of multipliers algorithm is developed to solve the challenging optimization problem. Extensive experiments on both simulated and real-world multi-view datasets show the superiority of the proposed method over eight state-of-the-art baselines.