This paper seeks to discover common change-point patterns, associated with functional connectivity (FC) in human brain, across multiple subjects. FC, represented as a covariance or a correlation matrix, relates to the similarity of fMRI responses across different brain regions, when a brain is simply resting or performing a task under an external stimulus. While the dynamical nature of FC is well accepted, this paper develops a formal statistical test for finding change-points in times series associated with FC observed over time. It represents instantaneous 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 detected change-points. Furthermore, it uses a temporal alignment of the test statistic, viewed as a real-valued function over time, to remove temporal variability and to discover common change-point patterns across subjects, tasks, and regions. This method is illustrated using HCP database for multiple subjects and tasks.
Functional connectivity Change-point Riemmanian metric Covariance estimation Function alignment
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This research was supported in part by NSF grants DMS 1621787 and CCF 1617397 to AS. ZZ was partially supported by NSF grant DMS-1127914 to SAMSI. Data were provided in part by the HCP, WU-Minn Consortium (Principal Investigators: David Van Essen and Kamil Ugurbil; 1U54MH091657).
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