  A connectional brain template (CBT) is a normalized graph-based
representation of a population of brain networks also regarded as an average
connectome. CBTs are powerful tools for creating representative maps of brain
connectivity in typical and atypical populations. Particularly, estimating a
well-centered and representative CBT for populations of multi-view brain
networks (MVBN) is more challenging since these networks sit on complex
manifolds and there is no easy way to fuse different heterogeneous network
views. This problem remains unexplored with the exception of a few recent works
rooted in the assumption that the relationship between connectomes are mostly
linear. However, such an assumption fails to capture complex patterns and
non-linear variation across individuals. Besides, existing methods are simply
composed of sequential MVBN processing blocks without any feedback mechanism,
leading to error accumulation. To address these issues, we propose Deep Graph
Normalizer (DGN), the first geometric deep learning (GDL) architecture for
normalizing a population of MVBNs by integrating them into a single
connectional brain template. Our end-to-end DGN learns how to fuse multi-view
brain networks while capturing non-linear patterns across subjects and
preserving brain graph topological properties by capitalizing on graph
convolutional neural networks. We also introduce a randomized weighted loss
function which also acts as a regularizer to minimize the distance between the
population of MVBNs and the estimated CBT, thereby enforcing its centeredness.
We demonstrate that DGN significantly outperforms existing state-of-the-art
methods on estimating CBTs on both small-scale and large-scale connectomic
datasets in terms of both representativeness and discriminability (i.e.,
identifying distinctive connectivities fingerprinting each brain network
population).
