Minimum distance to mean (MDM)

MDM is the simplest Riemannian classifier and often a strong baseline. In training it computes one geometric (Fréchet) mean covariance per class using the chosen metric; to classify a new trial's covariance it assigns the class whose mean is nearest in geodesic distance. There are no hyperparameters beyond the metric and no feature vector, so classification happens directly on the manifold.

Because it relies only on class means and a proper Riemannian distance, MDM is remarkably robust to noise and to session and subject shifts, and it degrades gracefully with few training trials. Its limitation is that a single mean per class is a unimodal, essentially nearest-centroid model: it cannot capture multimodal class structure or fine discriminative directions, for which tangent-space classifiers or FgMDM do better.