Long-range correlations in alpha-band of electroencephalogram: a nonlinear embedding and detrended fluctuation analysis

Understanding the temporal organization of brain activity requires methods that capture scale-free dynamics while accounting for the high-dimensional, spatially correlated nature of the electroencephalogram (EEG) data. We propose a novel framework that integrates nonlinear manifold learning (Isometric mapping) with detrended fluctuation analysis (DFA) to quantify long-range temporal correlations (LRTC) in the alpha-band of EEG signals. We applied this framework to two music related EEG datasets, as music is known to evoke different emotions and synchronize brain activity. The first dataset was obtained during live Indian classical music (ICM) listening that included two ragas, Yaman and Puriya Dhanashree. EEG was recorded from 13 healthy volunteers (24 channels, sampled at 500 Hz). The second dataset is the Music BCI dataset (006-2015), which includes Jazz and Synth-pop musical clips, with EEG collected from 11 subjects (64 channels, downsampled to 200 Hz). The EEG data from both datasets were preprocessed, band-limited to 8–13 Hz, and segmented into non-overlapping 2-s windows. Alpha-band power was extracted from each channel to form the feature matrix used for embedding. For the ICM dataset, Isometric mapping (Isomap) produced a low-dimensional representation (d = 3), which we analyzed using two approaches: (i) a norm-based approach and (ii) a mean-based approach. For comparison, an equivalent PCA-based pipeline (d = 5) was implemented. The Isomap mean-based DFA yielded consistent scaling exponents (α) in the range of 0.66–0.70, with higher goodness-of-fit (R2) and narrower bootstrap confidence intervals than the norm-based approach. PCA produced similar trends but required more dimensions. Paired t-tests showed that the Isomap mean-based approach detected music-related changes more sensitively than PCA (Yaman p = 0.02; Puriya Dhanashree p = 0.008). Comparable results were also observed for the second Music BCI dataset, where Isomap achieved a compact representation with d = 5, compared to d = 8 for PCA. In this dataset as well, the mean-based DFA yielded α values in the range of 0.62–0.65 and higher goodness-of-fit. Overall, the results suggest that combining nonlinear manifold embeddings with mean-based DFA provides a compact and robust framework for characterizing scale-free temporal structure in EEG data.