University of Twente Student Theses
Understanding the Performance of Hyperbolic Graph Neural Networks
Petrov, B.P. (2023) Understanding the Performance of Hyperbolic Graph Neural Networks.
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| Abstract: | Hyperbolic graph neural networks (HGNNs) have been gaining prominence in the field of machine learning. They have been shown to perform better than their Euclidian counterparts on a wide variety of datasets with underlying hyperbolic geometry. However, a persisting problem of HGNNs is the lack of understanding of what exactly causes this performance gap, and thus in which specific cases their usage is recommended. In this thesis we investigate the correlation between dataset properties and HGNN performance, in particular by taking HGCN and GCN as comparable models. Experiments show that delta-hyperbolicity, specifically delta-average is a reliable indicator that HGCN will perform better than GCN on the given dataset, except when the dataset used is very dense. In the latter case the degree distribution should be considered, and other properties like clustering or Balanced Forman curvature do not give a good indication. Furthermore, our experiments show that, when the underlying hyperbolic geometry is present, the HGCN is good at handling noise in the graph structure, whereas the GCN benefits when noise in the features is present. The role of the learnable curvature of the HGCN is investigated and appears to likely not relate directly to curvature in the data. Lastly, experiments show that, when the given dataset is highly hyperbolic, the HGCN does very well in case the embedding dimension is low and does not benefit greatly from a higher embedding dimension. The GCN performs poorly when the dimension is low and improves steadily when the dimension increases. On the other hand, when the dataset is not hyperbolic, both models perform very similar, but the HGCN still maintains a slight edge when the embedding dimension is low. |
| Item Type: | Essay (Master) |
| Faculty: | EEMCS: Electrical Engineering, Mathematics and Computer Science |
| Subject: | 31 mathematics |
| Programme: | Applied Mathematics MSc (60348) |
| Link to this item: | https://purl.utwente.nl/essays/97332 |
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