Graph-level anomaly detection (GLAD) aims to identify graphs that significantly deviate from the norm. Despite remarkable advancements in recent years, existing GLAD approaches struggle with the scarcity of labeled anomalies. Although some semi-supervised approaches leverage a small fraction of anomalous graphs during training, the limited diversity of these anomalies poses challenges in learning robust decision boundaries. Additionally, the detection of multi-task graph anomalies, a prevalent challenge in real-world scenarios, remains largely unexplored. To bridge these gaps, we propose MoEGAD, a novel framework leveraging a mixture of experts (MoE) architecture for GLAD. MoEGAD introduces an iterative anomalous graph generation module to produce pseudo-anomalous graphs, which facilitates the subsequent decision boundary learning. An early stopping mechanism is incorporated to ensure that the generated anomalies preserve sufficient dissimilarity from normal graphs. More importantly, we also propose a latent MoE module comprising multiple expert networks alongside a specialized gating network, which promotes cross-task adaptability for diverse GLAD problems. To the best of our knowledge, this is the first work exploring the potential of MoE architecture in the context of GLAD. Extensive experiments across single-task, large-scale, and multi-task scenarios demonstrate that MoEGAD significantly outperforms state-of-the-art GLAD baselines.

Multi-view clustering (MVC) aims to integrate information from diverse data sources to facilitate the clustering process, which has achieved considerable success in various real-world applications. However, previous MVC methods typically employ one of two strategies: (1) designing separate feature extraction pipelines for each view, which restricts their ability to fully exploit collaborative potential; or (2) employing a single shared representation module, which hinders the capture of diverse, view-specific representations. To tackle these challenges, we introduce Deep Multi-View Clustering via Collaborative Experts (DMVC-CE), a novel MVC approach that employs the Mixture of Experts (MoE) framework. DMVC-CE incorporates a gating network that dynamically selects multiple experts for handling each data sample, capturing diverse and complementary information from different views. Additionally, to ensure balanced expert utilization and maintain their diversity, we introduce an equilibrium loss and a multi-expert distinctiveness enhancer. The equilibrium loss prevents excessive reliance on specific experts, while the distinctiveness enhancer encourages each expert to specialize in different aspects of the data, thereby promoting diversity in learned representations. Comprehensive experiments on various multi-view benchmark datasets demonstrate the superiority of DMVC-CE compared to state-of-the-art MVC baselines.

Identifying anomalous graphs is essential in real-world scenarios such as molecular and social network analysis, yet anomalous samples are generally scarce and unavailable. This paper proposes a Self-Discriminative Modeling (SDM) framework that trains a deep neural network only on normal graphs to detect anomalous graphs. The neural network simultaneously learns to construct pseudo-anomalous graphs from normal graphs and learns an anomaly detector to recognize these pseudo-anomalous graphs. As a result, these pseudo-anomalous graphs interpolate between normal graphs and real anomalous graphs, which leads to a reliable decision boundary of anomaly detection. In this framework, we develop three algorithms with different computational efficiencies and stabilities for anomalous graph detection. Extensive experiments on 12 different graph benchmarks demonstrated that the three variants of SDM consistently outperform the state-of-the-art GLAD baselines. The success of our methods stems from the integration of the discriminative classifier and the well-posed pseudo-anomalous graphs, which provided new insights for graph-level anomaly detection.

A fundamental challenge in graph-level anomaly detection (GLAD) is the scarcity of anomalous graph data, as the training dataset typically contains only normal graphs or very few anomalies. This imbalance hinders the development of robust detection models. In this paper, we propose Anomalous Graph Diffusion (AGDiff), a framework that explores the potential of diffusion models in generating pseudo-anomalous graphs for GLAD. Unlike existing diffusion-based methods that focus on modeling data normality, AGDiff leverages the latent diffusion framework to incorporate subtle perturbations into graph representations, thereby generating pseudo-anomalous graphs that closely resemble normal ones. By jointly training a classifier to distinguish these generated graph anomalies from normal graphs, AGDiff learns more discriminative decision boundaries. The shift from solely modeling normality to explicitly generating and learning from pseudo graph anomalies enables AGDiff to effectively identify complex anomalous patterns that other approaches might overlook. Comprehensive experimental results demonstrate that the proposed AGDiff significantly outperforms several state-of-the-art GLAD baselines.

Variable Subset Forecasting (VSF) poses critical challenges in time series analysis when entire variables become unavailable during inference. Existing imputation methods relying on inter-variable correlations fail catastrophically in VSF due to two inherent limitations: (1) Missing variable collapse, where the complete absence of certain variables invalidates correlation-based dependency learning, and (2) Temporal covariate shift, where time-evolving data distributions destabilize correlation patterns learned from training data. To address these fundamental issues, we propose Generative Imputation with Multi-level Causal Consistency (GIMCC ), establishing causality-driven imputation as the first principled solution for VSF. Our key innovation lies in enforcing causal invariance through dual consistency constraints: global causal isomorphism ensures the imputed variables preserve the ground-truth causal graph structure of the complete system, while local causal subgraph alignment maintains consistency between observed variables and their causal neighborhood dependencies. By decoupling causality from spurious correlations, GIMCC provides time-invariant imputation signals robust to distribution shifts, which explicitly preserves causal relationships via multivariate spectral convolutions. Extensive experiments across five real-world domains demonstrate that GIMCC achieves average improvements of 20-60% in MAE/RMSE over correlation-based imputation baselines, remarkably outperforming full-variable training ( Oracle ) in temporal covariate shift scenarios. Our work bridges the critical gap between causal analysis and practical forecasting systems under variable absence, offering theoretically grounded guarantees for real-world deployment.

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.

Many well-known and effective anomaly detection methods assume that a reasonable decision boundary has a hypersphere shape, which however is difficult to obtain in practice and is not sufficiently compact, especially when the data are in high-dimensional spaces. In this paper, we first propose a novel deep anomaly detection model that improves the original hypersphere learning through an orthogonal projection layer, which ensures that the training data distribution is consistent with the hypersphere hypothesis, thereby increasing the true positive rate and decreasing the false negative rate. Moreover, we propose a bi-hypersphere compression method to obtain a hyperspherical shell that yields a more compact decision region than a hyperball, which is demonstrated theoretically and numerically. The proposed methods are not confined to common datasets such as image and tabular data, but are also extended to a more challenging but promising scenario, graph-level anomaly detection, which learns graph representation with maximum mutual information between the substructure and global structure features while exploring orthogonal single- or bi-hypersphere anomaly decision boundaries. The numerical and visualization results on benchmark datasets demonstrate the superiority of our methods in comparison to many baselines and state-of-the-art methods.

Graph anomaly detection (GAD) aims to identify anomalous graphs that significantly deviate from other ones, which has raised growing attention due to the broad existence and complexity of graph-structured data in many real-world scenarios. However, existing GAD methods usually execute with centralized training, which may lead to privacy leakage risk in some sensitive cases, thereby impeding collaboration among organizations seeking to collectively develop robust GAD models. Although federated learning offers a promising solution, the prevalent non-IID problems and high communication costs present significant challenges, particularly pronounced in collaborations with graph data distributed among different participants. To tackle these challenges, we propose an effective federated graph anomaly detection framework (FGAD). We first introduce an anomaly generator to perturb the normal graphs to be anomalous and train a powerful anomaly detector by distinguishing generated anomalous graphs from normal ones. We subsequently leverage a student model to distill knowledge from the trained anomaly detector (teacher model), which aims to maintain the personality of local models and alleviate the adverse impact of non-IID problems. Additionally, we design an effective collaborative learning mechanism that facilitates the personalization preservation of local models and significantly reduces communication costs among clients. Empirical results of diverse GAD tasks demonstrate the superiority and efficiency of FGAD.

Deep learning-based clustering methods, especially those incorporating deep generative models, have recently shown noticeable improvement on many multimedia benchmark datasets. However, existing generative models still suffer from unstable training, and the gradient vanishes, which results in the inability to learn desirable embedded features for clustering. In this paper, we aim to tackle this problem by exploring the capability of Wasserstein embedding in learning representative embedded features and introducing a new clustering module for jointly optimizing embedding learning and clustering. To this end, we propose Wasserstein embedding clustering (WEC), which integrates robust generative models with clustering. By directly minimizing the discrepancy between the prior and marginal distribution, we transform the optimization problem of Wasserstein distance from the original data space into embedding space, which differs from other generative approaches that optimize in the original data space. Consequently, it naturally allows us to construct a joint optimization framework with the designed clustering module in the embedding layer. Due to the substitutability of the penalty term in Wasserstein embedding, we further propose two types of deep clustering models by selecting different penalty terms. Comparative experiments conducted on nine publicly available multimedia datasets with several state-of-the-art methods demonstrate the effectiveness of our method.

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.

The goal of multi-view learning is to learn latent patterns from various data sources. Most of previous research focused on fitting feature embedding in target tasks. There is very limited research on the connection between feature representations with hidden layers of neural networks. In this paper, a multi-view deep matrix factorization model is proposed to learn a shared feature representation. The proposed model automatically explores the most discriminative features of multi-view data and makes these features meet the requirements of specific applications. Here we explore the connection between deep learning and feature representations. First, the model constructs a scalable neural network with shared hidden layers for exploring a low-dimensional representations of all views. Second, the quality of representation matrix is evaluated via relaxed graph regularization and evaluators to improve the feature representation capability of matrix factorization. Finally, the effectiveness of the proposed method is verified through comparative experiments with eight state-of-the-art multi-view clustering algorithms on eight real-world datasets.

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.

Recently deep learning methods have shown significant progress in data clustering tasks. Deep clustering methods (including distance-based methods and subspace-based methods) integrate clustering and feature learning into a unified framework, where there is a mutual promotion between clustering and representation. However, deep subspace clustering methods are usually in the framework of self-expressive model and hence have quadratic time and space complexities, which prevents their applications in large-scale clustering and real-time clustering. In this paper, we propose a new mechanism for deep clustering. We aim to learn the subspace bases from deep representation in an iterative refining manner while the refined subspace bases help learning the representation of the deep neural networks in return. The proposed method is out of the self-expressive framework, scales to the sample size linearly, and is applicable to arbitrarily large datasets and online clustering scenarios. More importantly, the clustering accuracy of the proposed method is much higher than its competitors. Extensive comparison studies with state-of-the-art clustering approaches on benchmark datasets demonstrate the superiority of the proposed method.

Multi-view data often contain redundant information that cannot be simply spliced. Many existing methods for processing them by assigning weights to each view cannot capture features dynamically. Therefore, we propose a multi-view deep matrix factorization method via neural networks that captures semantic hierarchical information of the data and dynamically produces a consistent representation using the complementarity of multi-view features. Due to the usefulness of deep matrix factorization, the generated representation is easily interpretable. The proposed method yields a harmonized representation directly from multi-view data without an extra weight learning process. In addition, we use a multi-path network to search for a consensual solution and obtain an optimal result. Additional feature optimization is used to enhance the discriminative characterization of the representation matrix. Finally, experiments on four real-world datasets show that the proposed method is superior to state-of-the-arts.