  There has been huge interest in studying human brain connectomes inferred
from different imaging modalities and exploring their relationship with human
traits, such as cognition. Brain connectomes are usually represented as
networks, with nodes corresponding to different regions of interest (ROIs) and
edges to connection strengths between ROIs. Due to the high-dimensionality and
non-Euclidean nature of networks, it is challenging to depict their population
distribution and relate them to human traits. Current approaches focus on
summarizing the network using either pre-specified topological features or
principal components analysis (PCA). In this paper, building on recent advances
in deep learning, we develop a nonlinear latent factor model to characterize
the population distribution of brain graphs and infer the relationships between
brain structural connectomes and human traits. We refer to our method as Graph
AuTo-Encoding (GATE). We applied GATE to two large-scale brain imaging
datasets, the Adolescent Brain Cognitive Development (ABCD) study and the Human
Connectome Project (HCP) for adults, to understand the structural brain
connectome and its relationship with cognition. Numerical results demonstrate
huge advantages of GATE over competitors in terms of prediction accuracy,
statistical inference and computing efficiency. We found that structural
connectomes have a stronger association with a wide range of human cognitive
traits than was apparent using previous approaches.
