Auto-encoding graph-valued data with applications to brain connectomes

Our interest focuses on developing statistical methods for analysis of brain structural connectomes. Nodes in the brain connectome graph correspond to different regions of interest (ROIs) while edges correspond to white matter fiber connections between these ROIs. Due to the high-dimensionality and non-Euclidean nature of the data, it becomes challenging to conduct analyses of the population distribution of brain connectomes and relate connectomes to other factors, such as cognition. Current approaches focus on summarizing the graph using either pre-specified topological features or principal components analysis (PCA). In this article, we instead develop a nonlinear latent factor model for summarizing the brain graph in both unsupervised and supervised settings. The proposed approach builds on methods for hierarchical modeling of replicated graph data, as well as variational auto-encoders that use neural networks for dimensionality reduction. We refer to our method as Graph AuTo-Encoding (GATE). We compare GATE with tensor PCA and other competitors through simulations and applications to data from the Human Connectome Project (HCP).