  Functional connectivity (FC) studies have demonstrated the overarching value
of studying the brain and its disorders through the undirected weighted graph
of fMRI correlation matrix. Most of the work with the FC, however, depends on
the way the connectivity is computed, and further depends on the manual
post-hoc analysis of the FC matrices. In this work we propose a deep learning
architecture BrainGNN that learns the connectivity structure as part of
learning to classify subjects. It simultaneously applies a graphical neural
network to this learned graph and learns to select a sparse subset of brain
regions important to the prediction task. We demonstrate the model's
state-of-the-art classification performance on a schizophrenia fMRI dataset and
demonstrate how introspection leads to disorder relevant findings. The graphs
learned by the model exhibit strong class discrimination and the sparse subset
of relevant regions are consistent with the schizophrenia literature.
