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In recent years, there has been significant interest in solving the domainadaptation (DA) problem on symmetric positive definite (SPD) manifolds withinthe machine learning community. This interest stems from the fact that complexneurophysiological data generated by medical equipment, such aselectroencephalograms, magnetoencephalograms, and diffusion tensor imaging,often exhibit a shift in data distribution across different domains. These datarepresentations, represented by signal covariance matrices, possess propertiesof symmetry and positive definiteness. However, directly applying previousexperiences and solutions to the DA problem poses challenges due to themanipulation complexities of covariance matrices.To address this, our researchintroduces a category of deep learning-based transfer learning approachescalled deep optimal transport. This category utilizes optimal transport theoryand leverages the Log-Euclidean geometry for SPD manifolds. Additionally, wepresent a comprehensive categorization of existing geometric methods to tacklethese problems effectively. This categorization provides practical solutionsfor specific DA problems, including handling discrepancies in marginal andconditional distributions between the source and target domains on the SPDmanifold. To evaluate the effectiveness, we conduct experiments on threepublicly available highly non-stationary cross-session brain-computer interfacescenarios. Moreover, we provide visualization results on the SPD cone to offerfurther insights into the framework.

Deep Optimal Transport for Domain Adaptation on SPD Manifolds