Analysis of EEG data using complex geometric structurization

Electroencephalogram (EEG) is a common tool used to understand brain activities. The data are typically obtained by placing electrodes at the surface of the scalp and recording the oscillations of currents passing through the electrodes. These oscillations can sometimes lead to various interpretations, depending on the subject's health condition, the experiment carried out, the sensitivity of the tools used, human manipulations etc. The data obtained over time can be considered a time series. There is evidence in the literature that epilepsy EEG data may be chaotic. Either way, the embedding theory in dynamical systems suggests that time series from a complex system could be used to reconstruct its phase space under proper conditions. In this paper, we propose an analysis of epilepsy electroencephalogram time series data based on a novel approach dubbed complex geometric structurization. Complex geometric structurization stems from the construction of strange attractors using embedding theory from dynamical systems. The complex geometric structures are themselves obtained using a geometry tool, namely the $\alpha$-shapes from shape analysis. Initial analyses show a proof of concept in that these complex structures capture the expected changes brain in lobes under consideration. Further, a deeper analysis suggests that these complex structures can be used as biomarkers for seizure changes.