A pipeline to analyze multinational EEG cross-spectra data in the Euclidean space
Presenting author:
Most of the classical statistics analysis, i.e., causality, mediation, linear mixed model, etc., are defined for the Euclidean space. With the increasing availability of EEG data, it has become of great interest to perform this analysis on EEG covariance and cross-spectral matrices that instead lie in a Riemannian Manifold space of positive definite matrices. We propose a pipeline for this kind of data that allows using these classical and valuable techniques on positive definite matrices. Our pipeline consists of three main steps. First, we check if the data is positive definite and apply the Hilbert-Schmidt regularization method in case it is not. Then we standardize the data employing average reference, and lastly, we map from the Manifold space to the Euclidean space using the theory of Riemannian Geometry. This mapping includes a vectorization operator that lets the data ready for the classical statistical analysis aforementioned. Our method is tested in a twelve-multinational cross-spectra dataset of seven countries. The results of this processing are used in the poster titled Quantitative EEG Analysis based on Riemannian metric.