Topological data analysis in EEG signal processing: a review

Abstract

Electroencephalogram (EEG) is a non-invasive technique that measures the brain's electrical activity from the cerebral cortex. EEG has been adopted in many studies for disease diagnosis, brain state recognition, and perception evaluation due to its high temporal resolution and low cost. Conventional data analysis methods such as traditional statistics and machine learning, suffer from several limitations, including being sensitive to artifacts when applied to EEG signal processing. As an alternative to these approaches, topological data analysis (TDA) enhances the EEG analysis by focusing on the robust topological invariants in EEG data. The rapid development of the TDA method generates a variety of studies with different TDA-based EEG processing pipelines tailored to diverse research objectives. A comprehensive review of these studies is necessary to serve as a guide for practitioners to gain deeper insight into EEG processing with TDA. This review also identifies the strengths, weaknesses, and future directions of TDA in EEG studies.