Riemannian SPD Manifold Analysis of BigP3BCI and Lee2019_ERP

This technical note reports a Riemannian SPD (symmetric positive definite) manifold analysis of the BigP3BCI dataset (Mainsah et al. 2025, PhysioNet), a large multi-cohort P300 BCI corpus spanning healthy subjects (Study A, N=12) and ALS patients across three cohorts (Studies B, F, and L). Key findings are independently replicated in Lee2019_ERP (Lee et al. 2019, GigaDB; 54 healthy subjects, 62-channel gel EEG, RC P300 speller). ERPCovariance matrices were estimated using the pyriemann library and embedded via Riemannian SpectralEmbedding (AIRM metric). Seven findings are reported: (1) cross-headset geometry is preserved when reducing from 32 to 16 channels in BigP3BCI (Spearman ρ=0.946, p=5×10⁻³³); (2) ALS patients separate completely from healthy subjects in an unsupervised joint embedding (zero overlap, t=−200, p=4.3×10⁻¹³³); (3) ALS patients diverge progressively from the group Fréchet mean over time (0.30→0.92 AIRM over 6 sessions), consistent with heterogeneous neurodegeneration; (4) the aperiodic EEG exponent and Riemannian covariance geometry are complementary, not redundant biomarkers; (5) the K=16 channel sub-selection replicates in Lee2019_ERP (ρ=0.739, p=5×10⁻²³⁸, N=1378 pairs, 53 subjects); (6) Riemannian embedding achieves zero ALS/healthy overlap where Euclidean PCA produces substantial overlap; and (7) covariance drift does not predict within-patient BCI accuracy, confirming it captures disease state rather than performance fluctuation. This note accompanies the companion preprint (doi:10.21203/rs.3.rs-9903869/v2) on aperiodic EEG exponents and P300 BCI performance in ALS.