Towards effective graph representations by leveraging geometric concepts

• Main Author: Lee, See Hian
• Other Authors: Tay Wee Peng
• Format: Thesis-Doctor of Philosophy
• Language: English
• Published: Nanyang Technological University 2024
• Subjects: Computer and Information Science; Graph neural networks; Graph representation learning; Machine learning
• Online Access: https://hdl.handle.net/10356/177895
• Institution: Nanyang Technological University

The field of graph representation learning (GRL) is dedicated to the task of encoding graph-structured data into low-dimensional vectors, often referred to as embeddings. Obtaining effective representations for various graph-related tasks, such as node classification and link prediction, hinges on effectively leveraging both the attributes and structural aspects of the graph data. A prominent approach for acquiring these graph representations involves the utilization of Graph Neural Networks (GNNs), a specialized class of neural networks designed for learning from graph data. Existing GNNs have limitations that can be mitigated by tailoring refinements based on the graph data's characteristics, enabling a more effective capture of graph intricacies. These improvements stand to benefit various applications, such as recommendation systems and social networks, as the graph structure often unveils valuable latent information. This thesis investigates the application of geometric concepts in GNNs and proposes techniques inspired by these concepts to improve the embeddings learned. Firstly, we propose an approach that leverages multiple geometric spaces to embed nodes, guided by a hyperbolicity measure. This accounts for the diverse underlying geometry in different regions of a graph, minimizing distortion and yielding refined representations by selecting the more appropriate space. Secondly, we present a method that integrates geometric structures, such as triangles and tetrahedrons, into GNNs by incorporating the concept of simplicial complexes. This integration enriches the expressive power of GNNs, enabling them to capture complex interactions that extend beyond pairwise connections. Lastly, we present a method that leverages multiple graphs with different topologies and geometries during the learning process. These additional graphs are generated by introducing latent variables into the framework. Learning the distribution of these graphs reveals useful topologies and geometries, providing additional information for both training and inference. Besides novel designs, we have conducted empirical assessments on graph-related tasks using benchmark datasets and compared our approaches to relevant baselines, confirming their effectiveness in improving graph representations. In summary, this thesis contributes to the progress in GRL by introducing three enhanced GNNs based on geometric concepts.