Statistical Persistent Homology of Brain Signals

Topological data analysis (TDA) extracts hidden topological features in signals that cannot be easily decoded by standard signal processing tools. A key TDA method is persistent homology (PH), which summarizes the changes of connected components in a signal through a multiscale descriptor such as the persistent landscape (PL). A recent development indicates that statistical inference on PLs of scalp electroencephalographic (EEG) signals produces markers for localizing seizure foci. However, a key obstacle of applying PH to large-scale clinical EEGs is the ambiguity of performing statistical inference. To address this problem, we develop a unified permutation-based inference framework for testing statistical indifference in PLs of EEG signals before and during an epileptic seizure. Compared with the standard permutation test, the proposed framework is shown to have more robustness when signals undergo non-topological changes and more sensitivity when topological changes occur. Furthermore, the proposed new method drastically improves the average computation time by 15000 folds.