The machine learning community has shown increasing interest in addressing the domain adaptation problem on symmetric positive definite (SPD) manifolds. This interest is primarily driven by the complexities of neuroimaging data generated from brain signals, which often exhibit shifts in data distribution across recording sessions. These neuroimaging data, represented by signal covariance matrices, possess the mathematical properties of symmetry and positive definiteness. However, applying conventional domain adaptation methods is challenging because these mathematical properties can be disrupted when operating on covariance matrices. In this study, we introduce a novel geometric deep learning-based approach utilizing optimal transport on SPD manifolds to manage discrepancies in both marginal and conditional distributions between the source and target domains. We evaluate the effectiveness of this approach in three cross-session brain-computer interface scenarios and provide visualized results for further insights. The GitHub repository of this study can be accessed at https://github.com/GeometricBCI/Deep-Optimal-Transport-for-Domain-Adaptation-on-SPD-Manifolds.

翻译：机器学习领域对解决对称正定（SPD）流形上的域自适应问题表现出日益浓厚的兴趣。这一兴趣主要源于脑信号生成的神经影像数据的复杂性，这些数据在不同记录会话间常呈现数据分布的偏移。以信号协方差矩阵表示的神经影像数据具有对称性和正定性的数学特性。然而，应用传统域自适应方法面临挑战，因为对协方差矩阵进行操作时可能破坏这些数学特性。本研究提出了一种新颖的基于几何深度学习的方法，利用SPD流形上的最优传输来处理源域与目标域之间边际分布和条件分布的差异。我们在三种跨会话脑机接口场景中评估了该方法的有效性，并提供可视化结果以进一步阐释。本研究的GitHub存储库可通过https://github.com/GeometricBCI/Deep-Optimal-Transport-for-Domain-Adaptation-on-SPD-Manifolds访问。