# Geodesic Optimization for Predictive Shift Adaptation on EEG data

arXiv: https://arxiv.org/abs/2407.03878 · HTML: https://mlsanity.com/paper/2407.03878/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 62 references that are in the map.
- First posted on arXiv 4 Jul 2024.

## Builds on (most cited first, 12 of 12)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Deep Visual Domain Adaptation: A Survey](https://mlsanity.com/paper/1802.03601/) (2018)
- [A Riemannian Network for SPD Matrix Learning](https://mlsanity.com/paper/1608.04233/) (2016)
- [First-order Methods for Geodesically Convex Optimization](https://mlsanity.com/paper/1602.06053/) (2016)
- [Domain Adaptation for Time Series Under Feature and Label Shifts](https://mlsanity.com/paper/2302.03133/) (2023)
- [SPD domain-specific batch normalization to crack interpretable unsupervised domain adaptation in EEG](https://mlsanity.com/paper/2206.01323/) (2022)
- [Machine-Learning-Based Diagnostics of EEG Pathology](https://mlsanity.com/paper/2002.05115/) (2020)
- [Domain Adaptive Text Style Transfer](https://mlsanity.com/paper/1908.09395/) (2019)
- [Sliced-Wasserstein on Symmetric Positive Definite Matrices for M/EEG Signals](https://mlsanity.com/paper/2303.05798/) (2023)
- [Manifold-regression to predict from MEG/EEG brain signals without source modeling](https://mlsanity.com/paper/1906.02687/) (2019)
- [Preventing dataset shift from breaking machine-learning biomarkers](https://mlsanity.com/paper/2107.09947/) (2021)
- [On Target Shift in Adversarial Domain Adaptation](https://mlsanity.com/paper/1903.06336/) (2019)

## Built on by (most cited first, 10 of 10)

- [Riemannian Flow Matching for Brain Connectivity Matrices via Pullback Geometry](https://mlsanity.com/paper/2505.18193/) (2025)
- [SPDIM: Source-Free Unsupervised Conditional and Label Shift Adaptation in EEG](https://mlsanity.com/paper/2411.07249/) (2024)
- [SPD Matrix Learning for Neuroimaging Analysis: Perspectives, Methods, and Challenges](https://mlsanity.com/paper/2504.18882/) (2025)
- [Multi-dataset Joint Pre-training of Emotional EEG Enables Generalizable Affective Computing](https://mlsanity.com/paper/2510.22197/) (2025)
- [PTSM: Physiology-aware and Task-invariant Spatio-temporal Modeling for Cross-Subject EEG Decoding](https://mlsanity.com/paper/2508.11357/) (2025)
- [Convolutional Monge Mapping between EEG Datasets to Support Independent Component Labeling](https://mlsanity.com/paper/2509.01721/) (2025)
- [DLink: Distilling Layer-wise and Dominant Knowledge from EEG Foundation Models](https://mlsanity.com/paper/2604.15016/) (2026)
- [Interpretable MEG Decoding of Perceived Speech: Cortical Sources and the Stimulus Features That Drive Retrieval](https://mlsanity.com/paper/2608.01481/) (2026)
- [Rectifying Geometric Misalignment: Online Source-Free Adaptation for Class-Imbalanced EEG](https://mlsanity.com/paper/2608.05315/) (2026)
- [SPDAlign: Interpretable Riemannian Alignment for EEG Forward Modeling Shifts](https://mlsanity.com/paper/2610.06315/) (2026)

## Abstract (arXiv)

Electroencephalography (EEG) data is often collected from diverse contexts involving different populations and EEG devices. This variability can induce distribution shifts in the data X and in the biomedical variables of interest y, thus limiting the application of supervised machine learning (ML) algorithms. While domain adaptation (DA) methods have been developed to mitigate the impact of these shifts, such methods struggle when distribution shifts occur simultaneously in X and y. As state-of-the-art ML models for EEG represent the data by spatial covariance matrices, which lie on the Riemannian manifold of Symmetric Positive Definite (SPD) matrices, it is appealing to study DA techniques operating on the SPD manifold. This paper proposes a novel method termed Geodesic Optimization for Predictive Shift Adaptation (GOPSA) to address test-time multi-source DA for situations in which source domains have distinct y distributions. GOPSA exploits the geodesic structure of the Riemannian manifold to jointly learn a domain-specific re-centering operator representing site-specific intercepts and the regression model. We performed empirical benchmarks on the cross-site generalization of age-prediction models with resting-state EEG data from a large multi-national dataset (HarMNqEEG), which included 14 recording sites and more than 1500 human participants. Compared to state-of-the-art methods, our results showed that GOPSA achieved significantly higher performance on three regression metrics (R2, MAE, and Spearman's ρ) for several source-target site combinations, highlighting its effectiveness in tackling multi-source DA with predictive shifts in EEG data analysis. Our method has the potential to combine the advantages of mixed-effects modeling with machine learning for biomedical applications of EEG, such as multicenter clinical trials.