Topological correlation of brain signals

Electroencephalography (EEG) is an important neurophysiological modality for understanding brain functions and disorders. Topological data analysis (TDA) can decode patterns in EEG signals that are not captured by standard temporal and spectral features. Gradient filtration is a recently advanced TDA framework for extracting topological features in a signal treated as a two-dimensional curve and filtered with a straight line moving in an arbitrary direction. In this study, we propose a new correlation measure for EEG signals by correlating topological features across multiple directions. We compare its performance with standard correlation measures in simulation studies and application to EEG signals recorded in dogs with epilepsy.