Electroencephalogram (EEG) are used in signal processing as tools to measure abnormalities in brain waves. Their nonlinearity often conveys information about the brain health condition of a subject. It was shown that they possess deterministic chaos and thus a strange attractor. In this talk, I will show how to use Takens' embedding theory to embed a strange attractor constructed from chaotic EEG into a manifold of high dimension, then use dimension reduction (Isomap, Kernel Ridge Regression, Fast ICA, or tSNE) and data morphometry to obtain a complex structure whose volume is a biomarker in the case of Epilepsy or sleep data.