Unsupervised graph-level anomaly detection (UGAD) has garnered increasing attention in recent years due to its significance. Most existing methods that rely on traditional GNNs mainly consider pairwise relationships between first-order neighbors, which is insufficient to capture the complex high-order dependencies often associated with anomalies. This limitation underscores the necessity of exploring high-order node interactions in UGAD. In addition, most previous works ignore the underlying properties (e.g., hierarchy and power-law structure) which are common in real-world graph datasets and therefore are indispensable factors in the UGAD task. In this paper, we propose a novel Dual Hyperbolic Contrastive Learning for Unsupervised Graph-Level Anomaly Detection (HC-GLAD in short). To exploit high-order node group information, we construct hypergraphs based on pre-designed gold motifs and subsequently perform hypergraph convolution. Furthermore, to preserve the hierarchy of real-world graphs, we introduce hyperbolic geometry into this field and conduct both graph and hypergraph embedding learning in hyperbolic space with the hyperboloid model. To the best of our knowledge, this is the first work to simultaneously apply hypergraph with node group information and hyperbolic geometry in this field. Extensive experiments on 13 real-world datasets of different fields demonstrate the superiority of HC-GLAD on the UGAD task. The code is available at https://github.com/Yali-F/HC-GLAD.
In recent years, Cross-Domain Recommendation (CDR) has drawn significant attention, which utilizes user data from multiple domains to enhance the recommendation performance. However, current CDR methods require sharing user data across domains, thereby violating the General Data Protection Regulation (GDPR). Consequently, numerous approaches have been proposed for Federated Cross-Domain Recommendation (FedCDR). Nevertheless, the data heterogeneity across different domains inevitably influences the overall performance of federated learning. In this study, we propose FedHCDR, a novel Federated Cross-Domain Recommendation framework with Hypergraph signal decoupling. Specifically, to address the data heterogeneity across domains, we introduce an approach called hypergraph signal decoupling (HSD) to decouple the user features into domain-exclusive and domain-shared features. The approach employs high-pass and low-pass hypergraph filters to decouple domain-exclusive and domain-shared user representations, which are trained by the local-global bi-directional transfer algorithm. In addition, a hypergraph contrastive learning (HCL) module is devised to enhance the learning of domain-shared user relationship information by perturbing the user hypergraph. Extensive experiments conducted on three real-world scenarios demonstrate that FedHCDR outperforms existing baselines significantly.
The multimodal recommendation has gradually become the infrastructure of online media platforms, enabling them to provide personalized service to users through a joint modeling of user historical behaviors (e.g., purchases, clicks) and item various modalities (e.g., visual and textual). The majority of existing studies typically focus on utilizing modal features or modal-related graph structure to learn user local interests. Nevertheless, these approaches encounter two limitations: (1) Shared updates of user ID embeddings result in the consequential coupling between collaboration and multimodal signals; (2) Lack of exploration into robust global user interests to alleviate the sparse interaction problems faced by local interest modeling. To address these issues, we propose a novel Local and Global Graph Learning-guided Multimodal Recommender (LGMRec), which jointly models local and global user interests. Specifically, we present a local graph embedding module to independently learn collaborative-related and modality-related embeddings of users and items with local topological relations. Moreover, a global hypergraph embedding module is designed to capture global user and item embeddings by modeling insightful global dependency relations. The global embeddings acquired within the hypergraph embedding space can then be combined with two decoupled local embeddings to improve the accuracy and robustness of recommendations. Extensive experiments conducted on three benchmark datasets demonstrate the superiority of our LGMRec over various state-of-the-art recommendation baselines, showcasing its effectiveness in modeling both local and global user interests.
Embedding-based methods for reasoning in knowledge hypergraphs learn a representation for each entity and relation. Current methods do not capture the procedural rules underlying the relations in the graph. We propose a simple embedding-based model called ReAlE that performs link prediction in knowledge hypergraphs (generalized knowledge graphs) and can represent high-level abstractions in terms of relational algebra operations. We show theoretically that ReAlE is fully expressive and provide proofs and empirical evidence that it can represent a large subset of the primitive relational algebra operations, namely renaming, projection, set union, selection, and set difference. We also verify experimentally that ReAlE outperforms state-of-the-art models in knowledge hypergraph completion, and in representing each of these primitive relational algebra operations. For the latter experiment, we generate a synthetic knowledge hypergraph, for which we design an algorithm based on the Erdos-R'enyi model for generating random graphs.
From social networks to protein complexes to disease genomes to visual data, hypergraphs are everywhere. However, the scope of research studying deep learning on hypergraphs is still quite sparse and nascent, as there has not yet existed an effective, unified framework for using hyperedge and vertex embeddings jointly in the hypergraph context, despite a large body of prior work that has shown the utility of deep learning over graphs and sets. Building upon these recent advances, we propose \textit{Deep Hyperedges} (DHE), a modular framework that jointly uses contextual and permutation-invariant vertex membership properties of hyperedges in hypergraphs to perform classification and regression in transductive and inductive learning settings. In our experiments, we use a novel random walk procedure and show that our model achieves and, in most cases, surpasses state-of-the-art performance on benchmark datasets. Additionally, we study our framework's performance on a variety of diverse, non-standard hypergraph datasets and propose several avenues of future work to further enhance DHE.