Continuous Representations of Brain Connectivity

Brain connectivity ("connectomics") has recently become a popular
frame of analysis in medical imaging. Almost synonymous with this is a
graph-theoretic representation of brain, in which gray matter regions
are nodes and the observed interactions between these regions are
edges. While graph theory is a convenient abstraction, this view of
connectivity requires the choice of a specific set of regions a
priori, and thus is not able to easily model uncertainty between
region choices. In general popular graph summary statistics are also
not robust to changing region sets.

This talk will focus on recent work that instead introduces a
continuous representation of connectivity. I will start by presenting
a point process model of structural connectivity, as well a KDE method
for direct estimation of model parameters. I will then show a
connection to a subset of the discrete graph representations
(exponential random graphs), and recent work on connectivity based
parcellation (region selection) exploiting this connection.