校正几何错位：针对类别不平衡脑电图的无在线源适配
Rectifying Geometric Misalignment: Online Source-Free Adaptation for Class-Imbalanced EEG
AI总结：
针对类别不平衡脑电图的在线源适配问题，提出OSPDIM框架，通过流形约束偏置参数的实时优化校正几何错位，在运动想象数据集上显著优于标准黎曼基线。
AI中文摘要：
基于脑电图（EEG）的脑机接口（BCI）通常需要无监督域自适应（UDA）来实现跨被试和跨会话的泛化。尽管黎曼对齐方法如黎曼中心化变换（RCT）在处理协变量偏移方面有效，但它们隐含假设类别先验分布平衡。然而，在现实的在线BCI场景中，标签分布会动态变化（标签偏移），导致标准对齐技术使目标数据分布发生几何错位。本研究提出OSPDIM（在线对称正定（SPD）流形信息最大化），一种用于解决黎曼流形上标签偏移的无在线源UDA框架。OSPDIM在切空间映射中引入流形约束的偏置参数，通过信息最大化优化该参数以校正由不平衡数据流引起的几何偏差。与依赖全局批量统计的离线方法不同，OSPDIM可实时估计并校正几何偏差。对2D SPD矩阵的仿真直观证明，OSPDIM成功校正了标准中心化方法失效的错位问题。在多个运动想象数据集上的大量实验表明，OSPDIM显著优于标准黎曼基线，尤其在类别不平衡严重的挑战性在线适配场景中表现突出，为实用即插即用BCI系统提供了稳健解决方案。
英文摘要：
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.
