Multi-view clustering has been found useful to leverage diverse data sources for accurate and robust underlying data representations. It typically relies on effectively integrating the latent features from different views through allocating weights while simultaneously mining their specificity and consensus information. However, it remains open how to achieve a more fine-grained sample-level weight allocation for promoting view-specific information fusion and view-shared consensus. To address this problem, we propose a novel multi-expert learning framework named Gated Variational Graph AutoEncoder with Competition and Consensus (GVGAE-C2). In particular, it employs multiple view-specific Variational Graph AutoEncoders (VGAEs) as experts to capture the latent features from their own views. Furthermore, we design a fine-grained structure-aware gating network, which dynamically computes sample-level weights based on the proposed structure-aware quality evaluation on each expert, thus facilitating competition among experts. Meanwhile, each expert is trained not only to study its assigned view's specificity features, but also explicitly encouraged to learn consensus-aware features across views. Extensive multi-view clustering experiments on benchmark datasets reveal that GVGAE-C2 significantly outperforms state-of-the-art methods.

Multi-view learning aims to integrate multi-source information for a comprehensive data representation, which has gained widespread attention in image processing. Each view contains view-specific noise and joint features associated with other views, and thus exploring the specificity and consistency among views is a typical solution to deal with multi-view data for learning discriminative representations. In this paper, we present a theory-induced model, termed Adversarial Distribution Alignment Network (ADAN), which learns view-invariant features and alleviate the negative impact of view-specific noise. We first demonstrate the necessity of suppressing view-specific noise and capturing view-invariant features inspired by the theory of view generalization, and then derive two collaborative modules: a feature disentangler and an adversarial alignment module. In detail, the feature disentanglement separates view-specific noise and view-invariant features by minimizing the mutual information between them. Following this, a negative entropy is proposed to suppress the negative impact of view-specific noise. Meanwhile, the adversarial module uses the adversarial technique that can fit more complex data conformed to different distributions to adaptively align cross-view features so that features encoded in different views converge. Substantial experiments are constructed on multi-view datasets, demonstrating that ADAN can achieve more promising performance compared to other superior methods. Code is available at https://github.com/huangsuj/ADANet.

Graph Neural Networks (GNNs) have exhibited remarkable capabilities for dealing with graph-structured data. However, recent studies have revealed their fragility to adversarial attacks, where imperceptible perturbations to the graph structure can easily mislead predictions. To enhance adversarial robustness, some methods attempt to learn robust representation through improving GNN architectures. Subsequently, another approach suggests that these GNNs might taint feature information and have poor classifier performance, leading to the introduction of Graph Contrastive Learning (GCL) methods to build a refining-classifying pipeline. However, existing methods focus on global-local contrastive strategies, which fails to address the robustness issues inherent in the contexts of adversarial robustness. To address these challenges, we propose a novel paradigm named GRANCE to enhance the robustness of learned representations by shifting the focus to local neighborhoods. Specifically, a dual neighborhood contrastive learning strategy is designed to extract local topological and semantic information. Paired with a neighbor estimator, the strategy can learn robust representations that are resilient to adversarial edges. Additionally, we also provide an improved GNN as classifier. Theoretical analyses provide a stricter lower bound of mutual information, ensuring the convergence of GRANCE. Extensive experiments validate the effectiveness of GRANCE compared to state-of-the-art baselines against various adversarial attacks.

Time series anomaly detection has garnered significant research attention due to growing demands for temporal data monitoring across diverse domains. Despite the rapid advent of unsupervised anomaly detection models, existing approaches face two critical challenges in understanding the mechanisms of reconstruction-based models when handling diverse temporal dependencies: (1) the insufficient exploration of complex inter-timestamp relationships encompassing both short-term and long-term dependencies, and (2) the lack of integrated frameworks for jointly learning short-term patterns and long-term temporal characteristics. To address these challenges, we propose the novel Multi-Scale Hypergraph Transformer (MSHTrans), which leverages the capacity of hypergraphs for modeling multi-order temporal dependencies. Particularly, our method employs multi-scale downsampling to derive complementary fine-grained and coarse-grained representations, integrated with trainable hypergraph neural networks that can adaptively learn inter-timestamp relationships. The framework further integrates time series decomposition to systematically extract periodic and trend components from multi-granular features, thereby enhancing long-term dependency modeling. Through synergistic integration of learned short-term patterns and long-term temporal structures, the model achieves comprehensive time series reconstruction for effective anomaly detection. Extensive experiments demonstrate that MSHTrans outperforms state-of-the-art competitors with an average performance improvement of 8.21% (without point adjustment) and 3.52% (with point adjustment).

The convergence of graph learning and multi-view learning has propelled the emergence of multi-view graph neural networks (MGNNs), offering strong capabilities to address complex real-world data characterized by heterogeneous yet interconnected information. While existing MGNNs exploit the potential of multi-view graphs, the inherent conflict persists between the two critical inductive biases of multi-view learning, consistency and complementarity. Consequently, the challenge of defining and resolving this tension in the new context of multi-view graphs remains largely underexplored. To bridge this gap, we propose Multi-view Collaborative Graph Experts (MvCGE), a novel framework grounded in the Mixture-of-Experts (MoE) paradigm. MvCGE establishes architectural consistency through shared parameters while preserving complementarity via layer-wise collaborative graph experts, which are dynamically activated by a graph-aware routing mechanism that adapts to the structural nuances of each view. This dual-level design is further reinforced by two novel components: a load equilibrium loss to prevent expert collapse and ensure balanced specialization, and a graph discrepancy loss based on distributional divergence to enhance inter-view complementarity. Extensive experiments on diverse datasets demonstrate MvCGE’s superiority.

Although Graph Neural Networks (GNNs) have exhibited the powerful ability to gather graph-structured information from neighborhood nodes via various message-passing mechanisms, the performance of GNNs is limited by poor generalization and fragile robustness caused by noisy and redundant graph data. As a prominent solution, Graph Augmentation Learning (GAL) has recently received increasing attention in the literature. Among the existing GAL approaches, edge-dropping methods that randomly remove edges from a graph during training are effective techniques to improve the robustness of GNNs. However, randomly dropping edges often results in bypassing critical edges. Consequently, the effectiveness of message passing is weakened. In this paper, we propose a novel adversarial edge-dropping method (ADEdgeDrop) that leverages an adversarial edge predictor guiding the removal of edges, which can be flexibly incorporated into diverse GNN backbones. Employing an adversarial training framework, the edge predictor utilizes the line graph transformed from the original graph to estimate the edges to be dropped, which improves the interpretability of the edge-dropping method. The proposed ADEdgeDrop is optimized alternately by stochastic gradient descent and projected gradient descent. Comprehensive experiments on eight graph benchmark datasets demonstrate that the proposed ADEdgeDrop outperforms state-of-the-art baselines across various GNN backbones, demonstrating improved generalization and robustness.

Graph convolutional network (GCN) has gained widespread attention in semisupervised classification tasks. Recent studies show that GCN-based methods have achieved decent performance in numerous fields. However, most of the existing methods generally adopted a fixed graph that cannot dynamically capture both local and global relationships. This is because the hidden and important relationships may not be directed exhibited in the fixed structure, causing the degraded performance of semisupervised classification tasks. Moreover, the missing and noisy data yielded by the fixed graph may result in wrong connections, thereby disturbing the representation learning process. To cope with these issues, this article proposes a learnable GCN-based framework, aiming to obtain the optimal graph structures by jointly integrating graph learning and feature propagation in a unified network. Besides, to capture the optimal graph representations, this article designs dual-GCN-based meta-channels to simultaneously explore local and global relations during the training process. To minimize the interference of the noisy data, a semisupervised graph information bottleneck (SGIB) is introduced to conduct the graph structural learning (GSL) for acquiring the minimal sufficient representations. Concretely, SGIB aims to maximize the mutual information of both the same and different meta-channels by designing the constraints between them, thereby improving the node classification performance in the downstream tasks. Extensive experimental results on real-world datasets demonstrate the robustness of the proposed model, which outperforms state-of-the-art methods with fixed-structure graphs.

Facing the increasing heterogeneity of data in the real world, multi-view learning has become a crucial area of research. Graph Convolutional Networks (GCNs) are powerful for modeling both graph structures and features, making them a focal point in multi-view learning research. However, these methods typically only account for static data dependencies within each view separately when constructing the topology necessary for GCNs, overlooking potential relationships across views in multi-view data. Furthermore, there is a notable absence of theoretical guidance for constructing multi-view data topologies, leading to uncertainty regarding the progression of graph embeddings toward a consistent state. To tackle these challenges, we introduce a framework named energy-constrained multi-view graph diffusion. This approach establishes a mathematical correspondence between multi-view data and GCNs via graph diffusion. It treats multi-view data as a unified entity and devises a feature propagation process with inter-view awareness by considering both inter-view and intra-view feature flow across the entire system. Additionally, an energy function is introduced to guide the inter- and intra-view diffusion, ensuring that the representations converge towards global consistency. The empirical research on several benchmark datasets substantiates the benefits of the proposed method.

Graph Convolutional Network (GCN) has drawn widespread attention in data mining on graphs due to its outstanding performance and rigor theoretical guarantee. However, some recent studies have revealed that GCN-based methods may mine latent information insufficiently owing to the underutilization of the feature space . Besides, the unlearnable topology also significantly imperils the performance of GCN-based methods. In this paper, we conduct experiments to investigate these issues, finding that GCN does not fully consider the potential structure in the feature space, and a fixed topology deteriorates the robustness of GCN. Thus, it is desired to distill node features and establish a learnable graph. Motivated by this goal, we propose a framework dubbed G raph C onvolutional N etwork with e lastic t opology (GCNet 1 ). With the analysis of the optimization for the proposed flexible Laplacian embedding, GCNet is naturally constructed by alternative graph convolutional layers and adaptive topology learning layers. GCNet aims to deeply explore the feature space and employ the mined information to construct a learnable topology, which leads to a more robust graph representation. In addition, a set-level orthogonal loss is utilized to meet the orthogonal constraint required by the flexible Laplacian embedding and promote better class separability . Moreover, comprehensive experiments indicate that GCNet achieves remarkable performance and generalization on several real-world datasets.

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.

Multi-view learning is a promising research field that aims to enhance learning performance by integrating information from diverse data perspectives. Due to the increasing interest in graph neural networks, researchers have gradually incorporated various graph models into multi-view learning. Despite significant progress, current methods face challenges in extracting information from multiple graphs while simultaneously accommodating specific downstream tasks. Additionally, the lack of a subsequent refinement process for the learned graph leads to the incorporation of noise. To address the aforementioned issues, we propose a method named generative essential graph convolutional network for multi-view semi-supervised classification. Our approach integrates the extraction of multi-graph consistency and complementarity, graph refinement, and classification tasks within a comprehensive optimization framework. This is accomplished by extracting a consistent graph from the shared representation, taking into account the complementarity of the original topologies. The learned graph is then optimized through downstream-specific tasks. Finally, we employ a graph convolutional network with a learnable threshold shrinkage function to acquire the graph embedding. Experimental results on benchmark datasets demonstrate the effectiveness of our approach.

Graph convolutional network (GCN) with the powerful capacity to explore graph-structural data has gained noticeable success in recent years. Nonetheless, most of the existing GCN-based models suffer from the notorious over-smoothing issue, owing to which shallow networks are extensively adopted. This may be problematic for complex graph datasets because a deeper GCN should be beneficial to propagating information across remote neighbors. Recent works have devoted effort to addressing over-smoothing problems, including establishing residual connection structure or fusing predictions from multilayer models. Because of the indistinguishable embeddings from deep layers, it is reasonable to generate more reliable predictions before conducting the combination of outputs from various layers. In light of this, we propose an alternating graph-regularized neural network (AGNN) composed of graph convolutional layer (GCL) and graph embedding layer (GEL). GEL is derived from the graph-regularized optimization containing Laplacian embedding term, which can alleviate the over-smoothing problem by periodic projection from the low-order feature space onto the high-order space. With more distinguishable features of distinct layers, an improved Adaboost strategy is utilized to aggregate outputs from each layer, which explores integrated embeddings of multi-hop neighbors. The proposed model is evaluated via a large number of experiments including performance comparison with some multilayer or multi-order graph neural networks, which reveals the superior performance improvement of AGNN compared with the state-of-the-art models.

Due to the powerful capability to gather the information of neighborhood nodes, Graph Convolutional Network (GCN) has become a widely explored hotspot in recent years. As a well-established extension, Graph AutoEncoder (GAE) succeeds in mining underlying node representations via evaluating the quality of adjacency matrix reconstruction from learned features. However, limited works on GAE were devoted to leveraging both semantic and topological graphs, and they only indirectly extracted the relationships between graphs via weights shared by features. To better capture the connections between nodes from these two types of graphs, this paper proposes a graph neural network dubbed Dual Low-Rank Graph AutoEncoder (DLR-GAE), which takes both semantic and topological homophily into consideration. Differing from prior works that share common weights between GCNs, the presented DLR-GAE conducts sustained exploration of low-rank information between two distinct graphs, and reconstructs adjacency matrices from learned latent factors and embeddings. In order to obtain valid adjacency matrices that meet certain conditions, we design some surrogates and projections to restrict the learned factor matrix. We compare the proposed model with state-of-the-art methods on several datasets, which demonstrates the superior accuracy of DLR-GAE in semi-supervised classification.

The low-rank matrix completion has gained rapidly increasing attention from researchers in recent years for its efficient recovery of the matrix in various fields. Numerous studies have exploited the popular neural networks to yield low-rank outputs under the framework of low-rank matrix factorization. However, due to the discontinuity and nonconvexity of rank function, it is difficult to directly optimize the rank function via back propagation. Although a large number of studies have attempted to find relaxations of the rank function, e.g., Schatten-$p$norm, they still face the following issues when updating parameters via back propagation: 1) These methods or surrogate functions are still non-differentiable, bringing obstacles to deriving the gradients of trainable variables. 2) Most of these surrogate functions perform singular value decomposition upon the original matrix at each iteration, which is time-consuming and blocks the propagation of gradients. To address these problems, in this paper, we develop an efficient block-wise model dubbed differentiable low-rank learning (DLRL) framework that adopts back propagation to optimize the Multi-Schatten-$p$norm Surrogate (MSS) function. Distinct from the original optimization of this surrogate function, the proposed framework avoids singular value decomposition to admit the gradient propagation and builds a block-wise learning scheme to minimize values of Schatten-$p$norms. Accordingly, it speeds up the computation and makes all parameters in the proposed framework learnable according to a predefined loss function. Finally, we conduct substantial experiments in terms of image recovery and collaborative filtering. The experimental results verify the superiority of the proposed framework in terms of both runtimes and learning performance compared with other state-of-the-art low-rank optimization methods. Our codes are available athttps://github.com/chenzl23/DLRL.

Multi-view subspace clustering aims to utilize the comprehensive information of multi-source features to aggregate data into multiple subspaces. Recently, low-rank tensor learning has been applied to multi-view subspace clustering, which explores high-order correlations of multi-view data and has achieved remarkable results. However, these existing methods have certain limitations: 1) The learning processes of low-rank tensor and label indicator matrix are independent. 2) Variable contributions of different views to the consistent clustering results are not discriminated. To handle these issues, we propose a unified framework that integrates low-rank tensor learning and spectral embedding (ULTLSE) for multi-view subspace clustering. Specifically, the proposed model adopts the tensor singular value decomposition (t-SVD) based tensor nuclear norm to encode the low-rank property of the self-representation tensor, and a label indicator matrix via spectral embedding is simultaneously exploited. To distinguish the importance of various views, we learn a quantifiable weighting coefficient for each view. An effective recursion optimization algorithm is also developed to address the proposed model. Finally, we conduct comprehensive experiments on eight real-world datasets with three categories. The experimental results indicate that the proposed ULTLSE is advanced over existing state-of-the-art clustering methods.

As real-world data become increasingly heterogeneous, multi-view semi-supervised learning has garnered widespread attention. Although existing studies have made efforts towards this and achieved decent performance, they are restricted to shallow models and how to mine deeper information from multiple views remains to be investigated. As a recently emerged neural network, Graph Convolutional Network (GCN) exploits graph structure to propagate label signals and has achieved encouraging performance, and it has been widely employed in various fields. Nonetheless, research on solving multi-view learning problems via GCN is limited and lacks interpretability. To address this gap, in this paper we propose a framework termed Interpretable Multi-view Graph Convolutional Network (IMvGCN11Code is available athttps://github.com/ZhihaoWu99/IMvGCN.). We first combine the reconstruction error and Laplacian embedding to formulate a multi-view learning problem that explores the original space from feature and topology perspectives. In light of a series of derivations, we establish a potential connection between GCN and multi-view learning, which holds significance for both domains. Furthermore, we propose an orthogonal normalization method to guarantee the mathematical connection, which solves the intractable problem of orthogonal constraints in deep learning. In addition, the proposed framework is applied to the multi-view semi-supervised learning task. Comprehensive experiments demonstrate the superiority of our proposed method over other state-of-the-art methods.

Deep multi-view representation learning focuses on training a unified low-dimensional representation for data with multiple sources or modalities. With the rapidly growing attention of graph neural networks, more and more researchers have introduced various graph models into multi-view learning. Although considerable achievements have been made, most existing methods usually propagate information in a single view and fuse multiple information only from the perspective of attributes or relationships. To solve the aforementioned problems, we propose an efficient model termed Dual Fusion-Propagation Graph Neural Network (DFP-GNN) and apply it to deep multi-view clustering tasks. The proposed method is designed with three submodules and has the following merits: a) The proposed view-specific and cross-view propagation modules can capture the consistency and complementarity information among multiple views; b) The designed fusion module performs multi-view information fusion with the attributes of nodes and the relationships among them simultaneously. Experiments on popular databases show that DFP-GNN achieves significant results compared with several state-of-the-art algorithms.

Sparsity-constrained optimization problems are common in machine learning, such as sparse coding, low-rank minimization and compressive sensing. However, most of previous studies focused on constructing various hand-crafted sparse regularizers, while little work was devoted to learning adaptive sparse regularizers from given input data for specific tasks. In this paper, we propose a deep sparse regularizer learning model that learns data-driven sparse regularizers adaptively. Via the proximal gradient algorithm, we find that the sparse regularizer learning is equivalent to learning a parameterized activation function. This encourages us to learn sparse regularizers in the deep learning framework. Therefore, we build a neural network composed of multiple blocks, each being differentiable and reusable. All blocks contain learnable piecewise linear activation functions which correspond to the sparse regularizer to be learned. Furthermore, the proposed model is trained with back propagation, and all parameters in this model are learned end-to-end. We apply our framework to multi-view clustering and semi-supervised classification tasks to learn a latent compact representation. Experimental results demonstrate the superiority of the proposed framework over state-of-the-art multi-view learning models.

In tensor-based multi-view learning methods, the self-representation based subspace clustering is widely researched, which is effective but heavy in high computational complexity. Furthermore, most of approaches learn the low-rank tensor representation and the final affinity matrix separately and ignore the difference between views. In this paper, we construct the target tensor composed of multiple normalized similarity matrices based on the Gaussian kernel function, which is constrained with the t-SVD based tensor nuclear norm to recover the low-rank part. The final affinity matrix is simultaneously learned via weighted multi-view fusion while optimizing the low-rank tensor, which suggests that each view is distributed to an adaptive weight. Moreover, the proposed method can be extended to semi-supervised classification through the collaborative optimization of the similarity tensor and the label indicator matrix. Extensive experiments conducted on four real-world datasets demonstrate the superiority of the proposed method compared with other state-of-the-art methods.