This poster presents research by A. S. Belokopytov and A. E. Osadchiy from the HSE University Center for Bioelectric Interfaces regarding methods for the physiological interpretation of non-linear embeddings in electroencephalography (EEG) and magnetoencephalography (MEG) data. While non-linear dimensionality reduction techniques like UMAP and t-SNE effectively reveal geometric patterns and clusters within high-dimensional covariance matrices, the resulting low-dimensional coordinates generally lack direct physiological meaning, making it difficult to pinpoint which neural populations generate the observed structures.
To solve this issue, the authors introduce TriCo (Covariance-to-Coordinate Co-modulation analysis), a method designed to make non-linear latent spaces physiologically explainable. The technique adapts cross-entropy loss optimization on the Riemannian manifold of symmetric positive-definite matrices to find spatial filters and map topological variability directly back to cortical sources.
The algorithm was validated using EEG and MEG data recorded while participants listened to 120-second audio segments under various conditions, including resting states with eyes open or closed, metronome beats, waltzes, and non-rhythmic musical compositions. The procedure filters signal data into target frequency bands, epoch-wise covariance matrices are calculated, and pairwise distances are measured to project data into two- or three-dimensional spaces. By iteratively applying gradient descent optimization and extracting specific source components, the algorithm allows researchers to isolate and remove individual source contributions to re-evaluate remaining data topology.
Overall, the proposed approach overcomes a major limitation of standard non-linear dimensionality reduction by explicitly connecting abstract clusters in low-dimensional visual space to specific physiological generators of brain activity.