  Functional brain connectivity, as revealed through distant correlations in
the signals measured by functional Magnetic Resonance Imaging (fMRI), is a
promising source of biomarkers of brain pathologies. However, establishing and
using diagnostic markers requires probabilistic inter-subject comparisons.
Principled comparison of functional-connectivity structures is still a
challenging issue. We give a new matrix-variate probabilistic model suitable
for inter-subject comparison of functional connectivity matrices on the
manifold of Symmetric Positive Definite (SPD) matrices. We show that this model
leads to a new algorithm for principled comparison of connectivity coefficients
between pairs of regions. We apply this model to comparing separately
post-stroke patients to a group of healthy controls. We find
neurologically-relevant connection differences and show that our model is more
sensitive that the standard procedure. To the best of our knowledge, these
results are the first report of functional connectivity differences between a
single-patient and a group and thus establish an important step toward using
functional connectivity as a diagnostic tool.
