  Most approaches to the estimation of brain functional connectivity from the
functional magnetic resonance imaging (fMRI) data rely on computing some
measure of statistical dependence, or more generally, a distance between
univariate representative time series of regions of interest (ROIs) consisting
of multiple voxels. However, summarizing a ROI's multiple time series with its
mean or the first principal component (1PC) may result to the loss of
information as, for example, 1PC explains only a small fraction of variance of
the multivariate signal of the neuronal activity.
  We propose to compare ROIs directly, without the use of representative time
series, defining a new measure of multivariate connectivity between ROIs, not
necessarily consisting of the same number of voxels, based on the Wasserstein
distance. We assess the proposed Wasserstein functional connectivity measure on
the autism screening task, demonstrating its superiority over commonly used
univariate and multivariate functional connectivity measures.
