Topological Data Analysis of Single-Trial Electroencephalographic Signals.

Epilepsy is a neurological disorder that can negatively affect the visual, audial and motor functions of the human brain. Statistical analysis of neurophysiological recordings, such as electroencephalogram (EEG), facilitates the understanding and diagnosis of epileptic seizures. Standard statistical methods, however, do not account for topological features embedded in EEG signals. In the current study, we propose a persistent homology (PH) procedure to analyze single-trial EEG signals. The procedure denoises signals with a weighted Fourier series (WFS), and tests for topological difference between the denoised signals with a permutation test based on their PH features persistence landscapes (PL). Simulation studies show that the test effectively identifies topological difference and invariance between two signals. In an application to a single-trial multichannel seizure EEG dataset, our proposed PH procedure was able to identify the left temporal region to consistently show topological invariance, suggesting that the PH features of the Fourier decomposition during seizure is similar to the process before seizure. This finding is important because it could not be identified from a mere visual inspection of the EEG data and was in fact missed by earlier analyses of the same dataset.