FCNCP: A Coupled Nonnegative CANDECOMP/PARAFAC Decomposition Based on Federated Learning

Cognitive neuroscience is currently a field of research highly valued by many countries worldwide, and fostering corresponding international collaboration can accelerate the development of cognitive neuroscience in our country. However, challenges related to industry competition, privacy, and regulatory policies hinder international collaboration that relies on cross-server data sharing. Considering the current limitations of tensor decomposition methods in establishing constraints between cross-server data, this study leverages the advantages of federated learning to develop a federated non-negative coupled tensor decomposition framework (FCNCP), aimed at establishing coupling constraints across different servers while preserving privacy. In experiments validating the effectiveness of the algorithm, we conducted 50 decompositions on synthetic tensor data, achieving an average tensor fit coefficient of 0.996, and the results demonstrated successful establishment of the coupling constraint. In real ERP data decomposition experiments, we applied the FCNCP algorithm to decompose ERP tensor data collected during proprioceptive stimulation applied to the left and right hands. The decomposition results revealed symmetrical activation areas in the left and right hemispheres induced by contralateral stimulation, with components in the beta and gamma frequency bands. These components are consistent with findings from related studies in cognitive neuroscience, confirming that this method can effectively handle high-dimensional EEG data across servers. This study not only provides new tools and approaches for processing and analyzing high-dimensional EEG data across servers but also promotes the advancement of coupled tensor decomposition techniques and their integration with emerging federated learning frameworks, offering significant theoretical and practical value.