Does topological data analysis work for EEG-based brain-computer interfaces?

Objective.Brain-computer interfaces (BCIs) are systems that establish a direct communication pathway with machines through brain activity only, recorded for example via electroencephalography (EEG). Topological data analysis (TDA) extracts topological features of the shape of the data and showed promising results in various applications. However, the work evaluating TDA systematically on EEG-based BCI is rare. Our study aims to fill this gap.Approach.The hypothesis is that the topology of the EEG dynamics is different under different mental states so that the topological features are discriminant. By adopting a dynamical system point of view, the non-stationary nature of EEG is respected. In practice, topological information is encoded by the persistence diagram. To turn it into a feature vector, some classical vector- and function-based representations are used. Each feature vector is then classified by several basic linear and non-linear classifiers.Main results.A benchmark comparing TDA with the gold standard methods was established on 3 publicly available datasets (2 active BCI datasets based on motor-imagery, 1 passive BCI dataset for mental workload estimation). TDA had significantly lower performance in intra-subject classification, yet comparable and sometimes higher performance in inter-subject classification. The persistence consistently outperformed all other topological features. We explained theoretically the link between persistence and spectral power and demonstrated it experimentally.Significance.To our knowledge, this is the first study that evaluates TDA in both intra- and inter-subject classification on various types of datasets. Insights on the connection between persistence and classical EEG features are also given for the first time.