Characterizing EEG signals of meditative states using persistent homology and Hodge spectral entropy
Kurusetti Vinay Gupta, Jyotiranjan Beuria, Laxmidhar Behera
Abstract
We present a novel topological characterization of EEG time series signals associated with two meditative states: autobiographical self-reflection and mantra-based meditation. The results demonstrate significant information geometric differences among the two groups of meditators and the control group for two brain regions, namely anterior frontal (AF) and temporoparietal (TP). The analysis involves global topological invariants and persistent homology features of the point cloud data constructed from the EEG time series using Takens’s embedding. While traditional EEG analyses face the well-known issues of noise and artefacts, the persistent homology approach is robust to them due to its emphasis on the overall topological changes rather than the transient structures. We analyse the characteristics of the Betti areas, peak location of Betti curves, persistent entropy, persistent amplitude and Hodge spectral entropy of the meditative states for up to the second homology dimension. We find that the mantra- based meditative state is rich in persistent features compared to autobiographical self-reflection. Also, the entropic measures indicate reduced chaotic dynamics and enhanced topological structure formation for the former. Moreover, the correlation of Hodge spectral entropy with persistent entropy or Betti area in a group is a key feature in differentiating the TP and AF channels. These topological features can be used to classify the meditative states with more than 95% accuracy.