In the field of brain science, data sharing across servers is becoming increasingly challenging due to issues such as industry competition, privacy security, and administrative procedure policies and regulations. Therefore, there is an urgent need to develop new methods for data analysis and processing that enable scientific collaboration without data sharing. In view of this, this study proposes to study and develop a series of efficient non-negative coupled tensor decomposition algorithm frameworks based on federated learning called FCNCP for the EEG data arranged on different servers. It combining the good discriminative performance of tensor decomposition in high-dimensional data representation and decomposition, the advantages of coupled tensor decomposition in cross-sample tensor data analysis, and the features of federated learning for joint modelling in distributed servers. The algorithm utilises federation learning to establish coupling constraints for data distributed across different servers. In the experiments, firstly, simulation experiments are carried out using simulated data, and stable and consistent decomposition results are obtained, which verify the effectiveness of the proposed algorithms in this study. Then the FCNCP algorithm was utilised to decompose the fifth-order event-related potential (ERP) tensor data collected by applying proprioceptive stimuli on the left and right hands. It was found that contralateral stimulation induced more symmetrical components in the activation areas of the left and right hemispheres. The conclusions drawn are consistent with the interpretations of related studies in cognitive neuroscience, demonstrating that the method can efficiently process higher-order EEG data and that some key hidden information can be preserved.

翻译：在脑科学领域，由于行业竞争、隐私安全以及行政程序政策法规等问题，跨服务器的数据共享正变得日益困难。因此，亟需开发无需数据共享即可实现科学合作的新型数据分析与处理方法。鉴于此，本研究提出并开发了一系列基于联邦学习的高效非负耦合张量分解算法框架，称为FCNCP，用于部署在不同服务器上的脑电图（EEG）数据。该算法结合了张量分解在高维数据表示与分解中的良好判别性能、耦合张量分解在跨样本张量数据分析中的优势，以及联邦学习在分布式服务器中联合建模的特点。该算法利用联邦学习为分布在不同服务器上的数据建立耦合约束。实验中，首先使用模拟数据进行仿真实验，获得了稳定且一致的分解结果，验证了本研究提出算法的有效性。随后，利用FCNCP算法对施加本体感觉刺激于左右手时采集的五阶事件相关电位（ERP）张量数据进行分解，发现对侧刺激诱发了左右半球激活区域中更为对称的分量。所得结论与认知神经科学相关研究的解释一致，表明该方法能够高效处理高阶EEG数据，并保留部分关键隐藏信息。