Hypergraph learning: modeling and analysis for advanced graph mining

<p dir="ltr">Graphs are a fundamental tool for modeling complex relationships and interactions in many real-world domains, such as social networks, biological systems, and recommendation engines. While traditional graph-based models excel at capturing pairwise relationships between nodes, they often fail to adequately represent higher-order interactions, which are essential in more intricate systems. Additionally, many real-world graphs are dynamic and heterogeneous, with interactions evolving over time and involving multiple types of entities. These challenges hinder the ability of existing graph learning techniques to fully capture the richness and complexity of such networks. </p><p dir="ltr">This thesis addresses key challenges in dynamic and heterogeneous graph settings by proposing novel methods for both node and graph-level classification. First, a framework for node classification in dynamic heterogeneous networks is introduced, which leverages dynamic heterogeneous hypergraph embeddings to capture non-pairwise interactions and their evolution over time. This significantly enhances node classification performance in complex, dynamic environments. The focus then shifts to selfsupervised learning for graph-level classification, presenting a framework that effectively captures high-order relationships and semantic information in heterogeneous graphs, without relying on computationally expensive techniques like meta-paths. A multi-hop attention mechanism is introduced to capture long-range dependencies and relational dynamics across graph neighborhoods, along with an informative pooling strategy that aggregates both local and global graph features for more effective graph-level learning. </p><p dir="ltr">The thesis further extends self-supervised learning for heterogeneous hypergraphs through a novel contrastive learning framework that incorporates adaptive augmentations and high-order connectivity to enhance graph-level representations, especially when working with sparse or unlabeled data. A time-aware model for dynamic graph-level classification is also proposed, capturing evolving interactions and high-order connectivity in dynamic graphs, making it particularly effective for applications such as graph similarity ranking and anomaly detection. </p><p dir="ltr">The proposed methods are rigorously evaluated on real-world datasets and outperform existing baselines, demonstrating significant improvements in classification accuracy and the ability to handle the complexities of dynamic, heterogeneous, and high-order graph data. These contributions provide powerful new tools for modeling and analyzing complex networks, offering novel solutions to key challenges in graph mining.</p>