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).

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.

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.