弱监督协方差矩阵对齐：基于Stiefel矩阵估计的MEG应用
Weakly supervised covariance matrices alignment through Stiefel matrices estimation for MEG applications
AI总结：
本文提出混合模型Stiefel适应（MSA）域适应技术，利用最优传输假设和未标记数据，通过估计Stiefel矩阵对齐协方差，在MEG脑龄回归任务中优于现有方法。
摘要：
本文提出了一种针对时间序列数据的新型域适应技术，称为混合模型Stiefel适应（MSA），专门解决目标数据集中标记信号有限的问题。利用依赖于域的混合模型和最优传输域适应假设，我们通过建立域间具有等效信号方差的成对对应关系，充分利用目标域中丰富的未标记数据来确保有效预测。本文为识别关键的Stiefel矩阵奠定了理论基础，这些矩阵对于从观测信号协方差的黎曼表示中恢复潜在信号方差至关重要。我们提出一个集成的代价函数，该函数同时学习这些矩阵、成对域关系以及预测器、分类器或回归器（取决于任务）。应用于神经科学问题，MSA在使用Cam-CAN数据集中的脑磁图（MEG）信号进行带任务变化的脑龄回归任务中，优于近期方法。
英文摘要：
This paper introduces a novel domain adaptation technique for time series data, called Mixing model Stiefel Adaptation (MSA), specifically addressing the challenge of limited labeled signals in the target dataset. Leveraging a domain-dependent mixing model and the optimal transport domain adaptation assumption, we exploit abundant unlabeled data in the target domain to ensure effective prediction by establishing pairwise correspondence with equivalent signal variances between domains. Theoretical foundations are laid for identifying crucial Stiefel matrices, essential for recovering underlying signal variances from a Riemannian representation of observed signal covariances. We propose an integrated cost function that simultaneously learns these matrices, pairwise domain relationships, and a predictor, classifier, or regressor, depending on the task. Applied to neuroscience problems, MSA outperforms recent methods in brain-age regression with task variations using magnetoencephalography (MEG) signals from the Cam-CAN dataset.
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