Contact Info
Department of Applied Mathematics
University of Waterloo
Waterloo, Ontario
Canada N2L 3G1
Phone: 519-888-4567, ext. 32700
Fax: 519-746-4319
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Duy Nguyen | Applied Mathematics, University of Waterloo
Some Mathematical Perspectives of Graph Neural Networks
Many real-world entities can be modelled as graphs, such as molecular structures, social networks, or images. Despite coming with such a great expressive power, the complex structure of graphs poses significant challenges to traditional deep learning methods, which have been extremely successful in many machine learning tasks on other input data structures, such as texts and images data. Recently, there have been many attempts in developing neural network architectures on graphical data, namely graph neural networks (GNNs). In this thesis, we first introduce some mathematical notations for graphs and different aspects of training a feedforward neural network. We then discuss several notable GNN architectures including Graph Convolutional Neural Networks, Graph Attention Networks, GraphSAGE, and PinSAGE. Some special aspects of GNN training are also presented. Finally, we investigate a neighborhood sampling approach on PinSAGE to a product-user recommendation problem.
Contact Info
Department of Applied Mathematics
University of Waterloo
Waterloo, Ontario
Canada N2L 3G1
Phone: 519-888-4567, ext. 32700
Fax: 519-746-4319
PDF files require Adobe Acrobat Reader
The University of Waterloo acknowledges that much of our work takes place on the traditional territory of the Neutral, Anishinaabeg and Haudenosaunee peoples. Our main campus is situated on the Haldimand Tract, the land granted to the Six Nations that includes six miles on each side of the Grand River. Our active work toward reconciliation takes place across our campuses through research, learning, teaching, and community building, and is co-ordinated within the Office of Indigenous Relations.