Graph-Based Approaches for Prediction and Similarity Analysis

This thesis explores graph-based approaches for prediction and similarity analysis problems within networks and hypergraphs. While existing algorithms for link prediction in networks predominantly target the existence or weights of edges, our study expands the scope by delving into the prediction of both vertex and edge weights using metric geometry and machine learning approaches. Additionally, our investigation extends into weight prediction in higher-order networks, often referred to as hypergraphs. We propose a novel notion of neighborhood for hyperedges, utilizing the topological structures of hypergraphs and weights of hyperedges from a given training set. We construct metric spaces on the set of hyperedges based on the neighborhood information. Furthermore, we explore the practical application of graph similarity algorithms in DNA sequence analysis, introducing an accurate and computationally efficient approach to analyze the similarities among DNA sequences. Our proposed methods were tested on diverse real-world datasets and yielded promising results. The main implication of our research is offering a more comprehensive framework for prediction tasks in networks and hypergraphs, providing alternative avenues to gain a deeper understanding of the intricate relationships within complex networks.