  In this paper, we address the the major hurdle of high dimensionality in EEG
analysis by extracting the optimal lower dimensional representations. Using our
approach, connectivity between regions in a high-dimensional brain network is
characterized through the connectivity between region-specific factors. The
proposed approach is motivated by our observation that electroencephalograms
(EEGs) from channels within each region exhibit a high degree of
multicollinearity and synchrony. These observations suggest that it would be
sensible to extract summary factors for each region. We consider the general
approach for deriving summary factors which are solutions to the criterion of
squared error reconstruction. In this work, we focus on two special cases of
linear auto encoder and decoder. In the first approach, the factors are
characterized as instantaneous linear mixing of the observed high dimensional
time series. In the second approach, the factors signals are linear filtered
versions of the original signal which is more general than an instantaneous
mixing. This exploratory analysis is the starting point to the multi-scale
factor analysis model where the concatenated factors from all regions are
represented by vector auto-regressive model that captures the connectivity in
high dimensional signals. We performed evaluations on the two approaches via
simulations under different conditions. The simulation results provide insights
on the performance and application scope of the methods. We also performed
exploratory analysis of EEG recorded over several epochs during resting state.
Finally, we implemented these exploratory methods in a Matlab toolbox XHiDiTS
available from https://goo.gl/uXc8ei .
