BACKGROUND: Topological signal processing is a novel approach for decoding multiscale features of signals recorded through electroencephalography (EEG) based on topological data analysis (TDA). New method: We establish stability properties of the TDA descriptor persistence landscape (PL) in event-related potential (ERP) across multi-trial EEG signals, state algorithms for computing PL, and propose an exact inference framework on persistence and PLs. RESULTS: We apply the topological signal processing and inference framework to compare ERPs between individuals with post-stroke aphasia and healthy controls under a speech altered auditory feedback (AAF) paradigm. Results show significant PL difference in the ERP response of aphasic individuals and healthy controls over the parietal-occipital and occipital regions with respect to speech onset, and no significant PL difference in any regions with respect to the two pitch-shift stimuli. Comparison with existing methods: In comparison, spatial patterns of difference between aphasic individuals and healthy controls by persistence, local variance, and spectral powers are much more diffuse than the PL patterns. In simulation results, the exact test on persistence and PLs has more robust performance than the baseline tests on local variance and spectral powers. CONCLUSIONS: Persistence features provide a more robust EEG marker than local variance, and spectral powers. It could be a potentially powerful tool for comparing electrophysiological correlates in neurological disorders.
