Grassmannians in the brain

A major problem in the analysis of EEG data is signal leakage. Electrical currents in the brain are measured almost simultaneously by multiple EEG electrodes and this fact complicates the interpretation of the underlying currents from the measured data. A way to approach this problem is to study those features of the EEG data that are invariant under signal leakage. In the paper “Construction of invariant features for time-domain EEG/MEG  signals using Grassmann manifolds” (preprint) by VU mathematicians Rikkert Hindriks and Thomas Rot, and University of Twente scientists Michel van Putten and Prejaas Tewarie, a structured investigation to all possible invariant EEG features was done. The authors show that the invariant features can be identified with functions on a Grassmannian manifold, a classical object of study in differential geometry. This enables to exploit the geometric properties of Grassmann manifolds to study invariant EEG features. In the paper, newly derived invariant EEG features are applied to EEG data of comatose survivors of cardiac arrest.