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Electroencephalography (EEG) is a widely used cerebral activity measuring device for both clinical and everyday life applications. In addition to denoising and potential classification, a crucial step in EEG processing is to extract relevant features. Topological data analysis (TDA) as an emerging tool enables to analyse and understand data from a different angle than traditionally used methods. As a higher dimensional analogy of graph analysis, TDA can model rich interactions beyond pairwise relations. It also distinguishes different dynamics of EEG time series. TDA remains largely unknown to the EEG processing community while it fits well the heterogeneous nature of EEG signals. This short review aims to give a quick introduction to TDA and how it can be applied to EEG analysis in various applications including brain-computer interfaces (BCIs). After introducing the objective of the article, the main concepts and ideas of TDA are explained. Next, how to implement it for EEG processing is detailed, and lastly the article discusses the benefits and limitations of the method.

Topological Data Analysis as a New Tool for EEG Processing