论文标题
在SPD歧管上适应域的深度最佳运输
Deep Optimal Transport for Domain Adaptation on SPD Manifolds
论文作者
论文摘要
几何深度学习的最新进展引起了机器学习社区的越来越多的关注，对对称正定（SPD）歧管的域适应性，尤其是对于通常在跨课程中分布转移的神经影像学数据而言。这些数据通常表示为大脑信号的协方差矩阵，由于它们的对称性和积极的确定性而固有地位于SPD歧管上。但是，当直接应用于协方差矩阵时，常规域适应方法通常会忽略这种几何结构，这可能会导致次优性能。为了解决这个问题，我们引入了一个新的几何深度学习框架，该框架将最佳运输理论与SPD歧管的几何形状结合在一起。我们的方法在尊重流形结构的同时使数据分布保持一致，从而有效地减少了边际和条件差异。我们在三个跨课程大脑计算机接口数据集（KU，BNCI2014001和BNCI2015001）上验证了我们的方法，在该数据集中，它始终超过基线接近，同时保持数据的内在几何形状。我们还提供定量结果和可视化，以更好地说明学习嵌入的行为。
Recent progress in geometric deep learning has drawn increasing attention from the machine learning community toward domain adaptation on symmetric positive definite (SPD) manifolds, especially for neuroimaging data that often suffer from distribution shifts across sessions. These data, typically represented as covariance matrices of brain signals, inherently lie on SPD manifolds due to their symmetry and positive definiteness. However, conventional domain adaptation methods often overlook this geometric structure when applied directly to covariance matrices, which can result in suboptimal performance. To address this issue, we introduce a new geometric deep learning framework that combines optimal transport theory with the geometry of SPD manifolds. Our approach aligns data distributions while respecting the manifold structure, effectively reducing both marginal and conditional discrepancies. We validate our method on three cross-session brain computer interface datasets, KU, BNCI2014001, and BNCI2015001, where it consistently outperforms baseline approaches while maintaining the intrinsic geometry of the data. We also provide quantitative results and visualizations to better illustrate the behavior of the learned embeddings.
