Electroencephalography (EEG) is an electrophysiological monitoring method to record electrical activity of the brain i.e. measure voltage fluctuations resulting from ionic current within the neurons of the brain. EEG data are being recorded by placing electrodes on the scalp of a subject, which sample electric signal in a specific frequency (e.g. 128Hz). An electrode capturing brainwave activity is called an EEG channel. Therefore, EEG data can be seen as 2-dimensional arrays/tensors (channels x time).


Analyzing EEG data, especially ones that are recorded using several channels, is extremely challenging due to their high dimensionality and complexity. Furthermore, the small size of EEG datasets can make things even worst. All these reasons compromise both computability and theoretical guarantee of classical statistical analysis methods, which uses vectors as covariates. Naively turning a 2-dimensional array into a vector is not a satisfactory solution, since it results in a larger number of covariates that need to be estimated and more seriously destroys the inherent spatial structure of the 2-dimensional array that may possess wealth of information.


This motivated Althexis to develop TensEEG tool for analyzing EEG data that reduces the number of covariates and at the same time preserves the spatial information of the data. This was achieved by exploiting multi-linear/tensor algebra tools. TensEEG conducts a supervised version of CANDECOMP/PARAFAC decomposition of the EEG data, which permits to conclude about the importance of each one of the channels, as well as, the time stamps towards a successful and meaningful EEG data analysis.


Figures 1 and 2 present two example EEG recordings, out of 95 available, sampled at 64Hz using 14 channels. During the data recording, the subject was asked to imagine that she moves her left or her right arm. The duration of each imagery task was one second. Figure 1 presents EEG data for one imagery task where the subject imagines that moves her left arm. Figure 2 present the same when the imagery task is right hand movement. By using TensEEG and examining the resulting decomposition of the recorded data we can conclude that the most important channels for discriminating between the two motion imagery tasks are channels 2, 5, 9 and 13. Furthermore, the same decomposition permits us to conclude about the time stamps when the brain activity for the two motion imagery tasks is different. This can be seen in the colormap (the red color corresponds to the same brain activity while the blue to different) beside channel 1 in both images.

Figure 1: EEG for left hand motion imagery
Figure 1: EEG for left hand motion imagery
Figure 2: EEG for left hand motion imagery
Figure 2: EEG for right hand motion imagery