Parameter investigation of topological data analysis for EEG signals

Topological data analysis (TDA) methods have become appealing in EEG signal processing, because they may help the scientists explore new features of complex and large amount of data by simplifying the process from a geometrical perspective. Time delay embedding is a common approach to embed EEG signals into the state space. Parameters of this embedding method are variable and the structure of the state space can be entirely different depending on their selection. Additionally, extracted persistent homologies of the state spaces depend on filtration level and the number of points used. In this study, we showed how to adapt false nearest neighbor (FNN) test to find out the suitable/optimal time embedding parameters (i.e., time delay and embedding dimension) for EEG signals, and compared their effects on different types of artefacts and motor intention waves that are commonly used in brain-computer interfaces. We extracted and compared persistent homologies of state spaces that were reconstructed with four different sets of parameters. Later, the effect of filtration level on extracted persistent homologies was compared, and statistical significance levels were computed between leftand right-hand movement imaginations. Finally, computational cost of the discussed methods was found, and the adaptability of this method to a real-time application was evaluated. We demonstrated that the discussed parameters of the TDA approach were highly crucial to extract true topological features of the EEG signals, and the adapted testing approaches depicted the applicability of this approach on real-time analysis of EEG signals.