  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).
