  This paper studies change-points in human brain functional connectivity (FC)
and seeks patterns that are common across multiple subjects under identical
external stimulus. FC relates to the similarity of fMRI responses across
different brain regions when the brain is simply resting or performing a task.
While the dynamic nature of FC is well accepted, this paper develops a formal
statistical test for finding {\it change-points} in times series associated
with FC. It represents short-term connectivity by a symmetric positive-definite
matrix, and uses a Riemannian metric on this space to develop a graphical
method for detecting change-points in a time series of such matrices. It also
provides a graphical representation of estimated FC for stationary subintervals
in between the detected change-points. Furthermore, it uses a temporal
alignment of the test statistic, viewed as a real-valued function over time, to
remove inter-subject variability and to discover common change-point patterns
across subjects. This method is illustrated using data from Human Connectome
Project (HCP) database for multiple subjects and tasks.
