Topological Seizure Detection in Single-Trial Electroencephalographic Signals

Persistent homology is a novel multi-scale topological method that is gaining popularity in data analysis. It has proven effective in revealing nonlinear patterns of high-dimensional imaging data that are otherwise undetected by existing mono-scale techniques. Among several descriptors of persistent homology, the recently proposed PL possess many desirable properties for rigorous statistical inference. A weighted Fourier series (WFS) expansion equivalent to diffusion wavelet transform provides a smoothed version of the data on which persistence landscape (PL) is constructed. We utilize the combined approach for seizure detection in electroencaphalographic (EEG) signals recorded before and during a seizure attack of a patient diagnosed with left temporal epilepsy. We successfully identified T3 as the origin of the seizure attack. Simulation results also showed that the combined approach is robust in terms of Type-1 and Type-2 errors.