Keywords: graph neural networks, topological data analysis, persistent homology, image segmentation
TL;DR: We develop new methods for using graph neural networks to model multiscale topological structure in images.
Abstract: Topological analysis reveals meaningful structure in data from a variety of domains. Tasks such as image segmentation can be effectively performed on the network structure of an image's topological complex 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, while one extends the message passing across all levels of the complex. Experiments on real-world data from three different domains shows the performance benefits to GNNs from using hierarchical topological structure.