Topological inference and correlation of signals with application to electroencephalography in epilepsy

Abstract

Electroencephalography (EEG) is an important neurophysiological modality for understanding brain functions and disorders. Topological signal processing allows us to capture how local variations in EEG signals affect their global structures. It reveals changes of topological structures across different temporal and spectral scales of signals that may not be observable through the standard signal processing methods. A topological signal processing framework that tracks the evolution of time segments corresponding to electric potential below a horizontal threshold has shown promise in applications to EEG studies of brain disorders. Gradient filtration is a generalization of the framework for extracting topological features in a signal treated as a two-dimensional curve and tracks the evolution of arcs in the curve cut off by a straight line moving in an arbitrary direction. In this study, we set up a statistical inference framework on gradient filtrations and an improved topological correlation measure for EEG signals by correlating features across gradient filtrations in multiple directions. We compare its performance with standard correlation measures in simulation studies and application to intracranial EEG signals recorded in canine with epilepsy.