Clustering instantaneous phase-locking states with a rank-two Bures-Wasserstein distance

Bures-Wasserstein distance between rank-two iPL matrices preserves sensitivity to phase-lag size in resting-state EEG, resolving phase-gradient states that other LEiDA distances merge.

• Why it matters: Existing iPL clustering compares decompositions with distances that ignore the iPL sample-space geometry, making phase-lag differences hard to detect when channels oscillate nearly in phase.
• What they did: The method weights each iPL’s two eigenvectors by the square roots of their eigenvalues, then uses optimal orthogonal Procrustes alignment to compute the Bures-Wasserstein distance for clustering.
• The result: In EEG, this distance distinguishes phase-gradient states that other methods merge into a single global in-phase state, and in simulations it separates states differing in both lag size and spatial pattern.

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