Riemannian geometry meets fMRI: the advantages of modeling correlation manifolds and eigenvector subspaces
Correlation matrices are fundamental summaries of functional brain networks, yet standard analyses often treat entries independently, ignoring the curved geometry of correlation space. Existing geometric methods frequently lack closed-form operations or depend on arbitrary region ordering, limiting scalability. We introduce a scalable geometric framework with two components: (i) the Off-log metric, a smooth transformation mapping correlation matrices to symmetric zero-diagonal matrices. This enables closed-form expressions for distances, Frechet means, and linear models, allowing standard statistical modeling without complex manifold optimization. (ii) Grassmannian subspace discrimination...
| Authors | Mario Severino, Manuela Moretto, Robert A. McCutcheon et al. |
|---|---|
| Primary category | cs.LG |
| Published | 21 May 2026 |
| Last updated at source | 21 May 2026 |
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