Abstract: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, which compares subjects via principal-angle distances between eigenvector subspaces, resolving inherent sign and basis ambiguities. Both components integrate into standard machine-learning workflows for inference, regression, and classification. Validated across two clinical cohorts (Parkinson's and psychosis) and three ageing fMRI datasets, the Off-log metric increased sensitivity in permutation tests and matched or exceeded Riemannian and Euclidean baselines in classification. Brain-age prediction performance was comparable, with Riemannian metrics excelling in two of three cohorts. The Grassmannian method consistently outperformed Euclidean baselines, highlighting disease-relevant networks. Overall, geometry-aware representations improve sensitivity and predictive performance while remaining straightforward to deploy at scale.
| Subjects: | Machine Learning (cs.LG) |
| Cite as: | arXiv:2605.22334 [cs.LG] |
| (or arXiv:2605.22334v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2605.22334 arXiv-issued DOI via DataCite (pending registration) |
From: Mario Severino [view email]
[v1]
Thu, 21 May 2026 11:22:31 UTC (9,046 KB)
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