  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.
