Unsupervised functional stage detection from EEG using topological data analysis.

Electroencephalogram (EEG) segmentation is still largely performed manually by specialists. Recent studies have proposed the state-detecting algorithm (SDA) - an automated technique for detecting functional stages with minimal human intervention - which has proven effective using spectral features. This paper introduces an alternative feature engineering approach that explores the spatial structure of data using the emerging field of topological data analysis (TDA). We propose an algorithm to extract a comprehensive topological description of EEG with tens of thousands of features and introduce the quick state-detecting algorithm (QSDA), a feature selection framework based on SDA performance. Next, we apply the procedure to EEG recordings from two distinct domains - Guhyasamaja Tantra meditation and whole-night polysomnographic sleep - and observe well-separated stage boundaries across most recordings, suggesting that TDA may complement or outperform spectral features in some settings. We also observed encouraging performance on noisy data, whereas shuffled epochs produced substantially weaker boundaries, supporting the robustness of the technique within the settings examined. Overall, the algorithm appears to be a promising feature engineering approach for SDA and suggests that the spatial structure of EEG may contain informative patterns. These findings motivate further investigation of their possible physiological interpretation, as well as an assessment across broader EEG paradigms.