Spatio-temporally separable non-linear latent factor learning: an application to somatomotor cortex fMRI data

Functional magnetic resonance imaging (fMRI) data contain complex spatiotemporal dynamics, thus researchers have developed approaches that reduce the dimensionality of the signal while extracting relevant and interpretable dynamics. Models of fMRI data that can perform whole-brain discovery of dynamical latent factors are understudied. The benefits of approaches such as linear independent component analysis models have been widely appreciated, however, nonlinear extensions of these models present challenges in terms of identification. Deep learning methods provide a way forward, but new methods for efficient spatial weight-sharing are critical to deal with the high dimensionality of the data and the presence of noise. Our approach generalizes weight sharing to non-Euclidean neuroimaging data by first performing spectral clustering based on the structural and functional similarity between voxels. The spectral clusters and their assignments can then be used as patches in an adapted multi-layer perceptron (MLP)-mixer model to share parameters among input points. To encourage temporally independent latent factors, we use an additional total correlation term in the loss. Our approach is evaluated on data with multiple motor sub-tasks to assess whether the model captures disentangled latent factors that correspond to each sub-task. Then, to assess the latent factors we find further, we compare the spatial location of each latent factor to the motor homunculus. Finally, we show that our approach captures task effects better than the current gold standard of source signal separation, independent component analysis (ICA).