Hypergraph Learning: From Algorithms to Applications

Graphs are a general language for describing and modeling interconnected systems. To learn graph data, Graph Neural Networks (GNNs) have been introduced. However, traditional graph data structures often fall short of describing the higher-order complex relationships within these systems. Hypergraphs, with their natural ability to capture such higher-order relations, offer a promising alternative. Despite their potential, GNNs are inherently designed for simple graphs and do not extend naturally to hypergraphs, leaving a gap in effectively leveraging hypergraph structures. To address this gap, Hypergraph Neural Networks (HyperGNNs) have been proposed. HyperGNNs offer enhanced capabilities to learn higher-order complex relationships beyond the scope of traditional GNNs. However, despite their potential, there remains a gap in effectively leveraging HyperGNNs for complex real-world problems due to limitations in current methodologies and applications. This dissertation aims to bridge this gap by developing and presenting new models for HyperGNN and examining their applications in real-world challenges. This work is built upon four pivotal studies, each emphasizing the development of novel HyperGNNs to tackle complex issues, especially in biomedical contexts, while also advancing methodologies to achieve superior outcomes.