distance metrics for averaging correlation matrices

[andrewheusser]

Our current implementation computed subject-wise correlation matrices, fisher's r2zs them, computes the euclidean mean and then inverts the fisher's r2z (i.e. z2r)

We could explore other distance functions such as log-euclidean and riemannian. The logic being that SPD matrices live on a curved manifold, so euclidean averaging might be sub-optimal.

This figure gives a good intuition for why a non-euclidean distance metric might be better:

[andrewheusser]

here's a link to a python implementation of riemannian distance: https://pythonhosted.org/pyriemann/generated/pyriemann.utils.distance.distance_riemann.html#pyriemann.utils.distance.distance_riemann