In many machine learning applications on signals and biomedical data, especially electroencephalogram (EEG), one major challenge is the variability of the data across subjects, sessions, and hardware devices. In this work, we propose a new method called Convolutional Monge Mapping Normalization (CMMN), which consists in filtering the signals in order to adapt their power spectrum density (PSD) to a Wasserstein barycenter estimated on training data. CMMN relies on novel closed-form solutions for optimal transport mappings and barycenters and provides individual test time adaptation to new data without needing to retrain a prediction model. Numerical experiments on sleep EEG data show that CMMN leads to significant and consistent performance gains independent from the neural network architecture when adapting between subjects, sessions, and even datasets collected with different hardware. Notably our performance gain is on par with much more numerically intensive Domain Adaptation (DA) methods and can be used in conjunction with those for even better performances.

翻译：在信号和生物医学数据的许多机器学习应用中，尤其是脑电图（EEG），一个主要挑战是数据在不同受试者、实验会话和硬件设备之间的变异性。本文提出了一种名为卷积蒙日映射归一化（CMMN）的新方法，该方法通过对信号进行滤波，使其功率谱密度（PSD）适应于在训练数据上估计的Wasserstein重心。CMMN基于最优传输映射和重心的新型闭式解，能够对新数据进行个体化的测试时自适应，而无需重新训练预测模型。在睡眠EEG数据上的数值实验表明，当在不同受试者、实验会话甚至不同硬件采集的数据集之间进行自适应时，CMMN能够带来与神经网络架构无关的显著且一致的性能提升。值得注意的是，我们的性能增益与计算成本高得多的领域自适应（DA）方法相当，并且可与这些方法结合使用以获得更好的性能。