EEG covariance matrices live on a curved manifold. Riemannian geometry reveals the true structure of brain state space — and why classical methods fail across patients.

Theoretical visualization
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SPD Manifold
Each EEG recording window becomes a covariance matrix — a point on the manifold of Symmetric Positive Definite matrices. Healthy brain states cluster in one region; seizure states in another.
Classification works by asking: is this brain state closer to seizure or to baseline? The manifold is curved — Euclidean distance through flat space misrepresents the true separation between brain states.
Knowing a patient's polarity turns an unreliable cross-patient classifier into a reliable personal one.
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