  Data fusion modeling can identify common features across diverse data sources
while accounting for source-specific variability. Here we introduce the concept
of a \textit{coupled generator decomposition} and demonstrate how it
generalizes sparse principal component analysis (SPCA) for data fusion.
Leveraging data from a multisubject, multimodal (electro- and
magnetoencephalography (EEG and MEG)) neuroimaging experiment, we demonstrate
the efficacy of the framework in identifying common features in response to
face perception stimuli, while accommodating modality- and subject-specific
variability. Through split-half cross-validation of EEG/MEG trials, we
investigate the optimal model order and regularization strengths for models of
varying complexity, comparing these to a group-level model assuming shared
brain responses to stimuli. Our findings reveal altered $\sim170ms$ fusiform
face area activation for scrambled faces, as opposed to real faces,
particularly evident in the multimodal, multisubject model. Model parameters
were inferred using stochastic optimization in PyTorch, demonstrating
comparable performance to conventional quadratic programming inference for SPCA
but with considerably faster execution. We provide an easily accessible toolbox
for coupled generator decomposition that includes data fusion for SPCA,
archetypal analysis and directional archetypal analysis. Overall, our approach
offers a promising new avenue for data fusion.
