Exploratory Analysis of High Dimensional Time Series with Applications to Multichannel Electroencephalograms

Abstract: 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 .