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Geodesic Optimization for Predictive Shift Adaptation on EEG data
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Proposes GOPSA, a test-time multi-source domain adaptation method that learns per-domain geodesic parallel-transport (re-centering) parameters jointly with a shared Ridge regressor on SPD covariance matrices, to handle joint shifts in EEG features and age labels.
Problem
Cross-site EEG age prediction where both the covariance features X and the target outcome y distribution shift across source sites, which standard re-centering domain adaptation methods fail to handle.
Approach
Parallel transport each domain's SPD covariance matrices along the geodesic from its Riemannian mean toward the identity with a learned per-domain parameter alpha (sigmoid-reparameterized), jointly learning alpha and a shared Ridge regression on the tangent-space features; at test time only the target alpha is fit so the mean prediction matches the known target mean outcome.
Key results
- GOPSA achieved mean Spearman's rho 0.77 ± 0.02, R^2 0.59 ± 0.04, and MAE 8.37 ± 0.32 across site combinations, the best averages among compared methods.
- GOPSA significantly outperformed DO Intercept in five site combinations for MAE, four for Spearman's rho and three for R^2.
- Learned alpha values for GOPSA showed a linear relationship with site mean age (R^2 = 0.99).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use GOPSA instead of DO Intercept | Age prediction from HarMNqEEG EEG · HarMNqEEG mean across site combinations | Spearman's ρ: 0.75 ± 0.02 -> 0.77 ± 0.02 | Helped |
| Use GOPSA instead of DO Intercept | Age prediction from HarMNqEEG EEG · HarMNqEEG mean across site combinations | R² score: 0.57 ± 0.02 -> 0.59 ± 0.04 | Helped |
| Use GOPSA instead of DO Intercept | Age prediction from HarMNqEEG EEG · HarMNqEEG mean across site combinations | MAE: 8.64 ± 0.19 -> 8.37 ± 0.32 | Helped |
| Use GOPSA instead of DO Intercept | Age prediction from HarMNqEEG EEG · Individual HarMNqEEG site combinations | R² score | Mixed |
| Use GOPSA instead of DO Intercept | Age prediction from HarMNqEEG EEG · Individual HarMNqEEG site combinations | Spearman's ρ | Mixed |
| Use GOPSA instead of DO Intercept | Age prediction from HarMNqEEG EEG · Individual HarMNqEEG site combinations | MAE | Helped |
Surprising findings
- Re-centering all domains to a common reference point (Re-center) performed poorly on age prediction, with negative mean R^2 (-0.35), because the Riemannian mean correlates with age.
- The GREEN deep network, not designed for domain adaptation, was relatively robust to shifts in simulations and beat several DA baselines on HarMNqEEG.
Limitations
- Requires knowing or estimating the mean outcome of each target domain.
- Improvements over DO Intercept are significant only in some site combinations.
- Evaluated only with shallow Ridge regression models.
Experimental setup
Datasets: HarMNqEEG
Benchmarks: HarMNqEEG
Metrics: R^2 MAE Spearman's rho
Baselines: DO Dummy No DA Re-center Re-scale DO Intercept GREEN
Builds on: Riemannian re-centering Riemannian Procrustes Analysis GREEN
Closest papers by meaning
- SPDIM: Source-Free Unsupervised Conditional and Label Shift Adaptation in EEG (ICLR 2025 · similarity 0.90)
- SPD domain-specific batch normalization to crack interpretable unsupervised domain adaptation in EEG (NeurIPS 2022 · similarity 0.89)
- Riemannian Flow Matching for Brain Connectivity Matrices via Pullback Geometry (NeurIPS 2025 · similarity 0.86)
- NeuroAtlas: Benchmarking Foundation Models for Clinical EEG and Brain-Computer Interfaces (NeurIPS 2026 · similarity 0.85)
- Implicit Gaussian process representation of vector fields over arbitrary latent manifolds (ICLR 2024 · similarity 0.84)
- LAtte: Hyperbolic Lorentz Attention for Joint-Subject EEG Classification (NeurIPS 2026 · similarity 0.83)
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