# Rectifying Geometric Misalignment: Online Source-Free Adaptation for Class-Imbalanced EEG

arXiv: https://arxiv.org/abs/2608.05315 · HTML: https://mlsanity.com/paper/2608.05315/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 30 references that are in the map.
- First posted on arXiv 5 Aug 2026.

## Builds on (most cited first, 14 of 14)

- [A Comprehensive Survey on Test-Time Adaptation under Distribution Shifts](https://mlsanity.com/paper/2303.15361/) (2023)
- [Generalized Source-free Domain Adaptation](https://mlsanity.com/paper/2108.01614/) (2021)
- [Source-Free Domain Adaptation for Semantic Segmentation](https://mlsanity.com/paper/2103.16372/) (2021)
- [Transfer Learning for EEG-Based Brain-Computer Interfaces: A Review of Progress Made Since 2016](https://mlsanity.com/paper/2004.06286/) (2020)
- [SPD domain-specific batch normalization to crack interpretable unsupervised domain adaptation in EEG](https://mlsanity.com/paper/2206.01323/) (2022)
- [Transfer Learning in Brain-Computer Interfaces](https://mlsanity.com/paper/1512.00296/) (2015)
- [2021 BEETL Competition: Advancing Transfer Learning for Subject Independence & Heterogenous EEG Data Sets](https://mlsanity.com/paper/2202.12950/) (2022)
- [T-TIME: Test-Time Information Maximization Ensemble for Plug-and-Play BCIs](https://mlsanity.com/paper/2412.07228/) (2024)
- [SPDIM: Source-Free Unsupervised Conditional and Label Shift Adaptation in EEG](https://mlsanity.com/paper/2411.07249/) (2024)
- [Geodesic Optimization for Predictive Shift Adaptation on EEG data](https://mlsanity.com/paper/2407.03878/) (2024)
- [On the interpretation of linear Riemannian tangent space model parameters in M/EEG](https://mlsanity.com/paper/2107.14398/) (2021)
- [SPD Matrix Learning for Neuroimaging Analysis: Perspectives, Methods, and Challenges](https://mlsanity.com/paper/2504.18882/) (2025)
- [Latent Alignment with Deep Set EEG Decoders](https://mlsanity.com/paper/2311.17968/) (2023)
- [HEEGNet: Hyperbolic Embeddings for EEG](https://mlsanity.com/paper/2601.03322/) (2026)

## Abstract (arXiv)

Electroencephalography (EEG) based Brain-Computer Interfaces (BCIs) often require unsupervised domain adaptation (UDA) to generalize across subjects and sessions. While Riemannian alignment methods like the Riemannian Centering Transformation (RCT) are effective for handling covariate shifts, they implicitly assume balanced class priors. However, in realistic online BCI scenarios, the label distributions vary dynamically (label shift), causing standard alignment techniques to geometrically misalign the target data distributions. In this work, we propose OSPDIM (Online SPD manifold information maximization), a source-free online UDA framework designed to address label shifts on the Riemannian manifold. OSPDIM introduces a manifold-constrained bias parameter into the tangent space mapping, which is optimized via information maximization to correct the geometric skew caused by imbalanced data streams. Unlike offline methods relying on global batch statistics, OSPDIM estimates and corrects geometric bias on-the-fly. Simulations on 2D SPD matrices visually demonstrate that OSPDIM successfully rectifies the misalignment where standard centering fails. Extensive experiments on multiple motor imagery datasets show that OSPDIM significantly outperforms standard Riemannian baselines, particularly in challenging online adaptation scenarios with severe class imbalance, offering a robust solution for practical, plug-and-play BCI systems.