Construction of invariant features for time-domain EEG/MEG signals using Grassmann manifolds

A challenge in interpreting features derived from source-space electroencephalography (EEG) and mag- netoencephalography (MEG) signals is residual mixing of the true source signals. A common approach is to use features that are invariant under linear and instantaneous mixing. In the context of this approach, it is of interest to know which invariant features can be constructed from a given set of source-projected EEG/MEG signals. We address this question by exploiting the fact that invariant features can be viewed as functions on the Grassmann manifold. By embedding the Grassmann man- ifold in a vector space, coordinates are obtained that serve as building blocks for invariant features, in the sense that all invariant features can be constructed from them. We illustrate this approach by constructing several new bivariate, higher-order, and multidimensional functional connectivity mea- sures for static and time-resolved analysis of time-domain EEG/MEG signals. Lastly, we apply such an invariant feature derived from the Grassmann manifold to EEG data from comatose survivors of cardiac arrest and show its superior sensitivity to identify changes in functional connectivity.