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.

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