Exploratory analysis of brain signals through low dimensional embedding

In this paper, we develop computationally efficient and theoretically justified tools for analyzing high dimensional brain signals. Our approach is to extract the optimal lower dimensional representations for each brain region and then characterize and estimate connectivity between regions through these factors. This approach is motivated by our observation that electroencephalograms (EEGs) from many channels within each region exhibit a high degree of multicollinearity and synchrony thereby suggesting that it would be sensible to extract summary factors for each region. Here, the summary factors are the encodings that lead to the lowest reconstruction error. We focus on two special cases of linear auto encoder and decoder. The first characterizes the factors as instantaneous linear mixing of the observed signals. In the second approach, the factors are convolutions of the observed signals (which is more general than the first). These methods were compared through simulations under different conditions and the results provide insights on advantages and limitations of each. Finally, we performed exploratory analysis of resting state EEG data. The spectral properties of the factors were estimated and connectivity between regions via the factors using coherence measures were computed. We implemented these methods in a Matlab toolbox XHiDiTS (https://goo.gl/uXc8ei). The toolbox was utilized to investigate consistency of these factors across all epochs during the entire resting-state period.