Modeling hierarchical topological structure in scientific images with graph neural networks

Topological analysis reveals meaningful structure in data from a variety of domains. Tasks such as image segmentation can be effectively performed on an image's topological connectivity using graph neural networks (GNNs). We propose two methods for using GNNs to learn from the hierarchical information captured by complexes at multiple levels of topological persistence: one modifies the training procedure of an existing GNN, and one extends the message passing across all levels of the complex. Experiments on real-world data from three domains show the performance benefits to GNNs from using a hierarchical topological structure.