Fisher geodesic MDM (FgMDM)

FgMDM augments plain MDM with a supervised geodesic filtering step: covariances are projected to the tangent space, a Fisher-discriminant (LDA-style) projection selects the most class-discriminative directions there, the data are mapped back to the manifold, and only then are class means computed and MDM classification applied. The filtering suppresses non-discriminative variance so the class means become better separated, typically giving a solid accuracy gain over MDM while keeping its robustness and interpretability.

It sits between bare MDM (no learned discriminative directions) and a full tangent-space classifier (fully discriminative but more prone to overfitting), and is a common default in Riemannian BCI toolboxes. Like all supervised steps it needs enough labeled data and can overfit with high channel counts unless the Fisher step is regularized.