  Multi-subject fMRI studies are challenging due to the high variability of
both brain anatomy and functional brain topographies across participants. An
effective way of aggregating multi-subject fMRI data is to extract a shared
representation that filters out unwanted variability among subjects. Some
recent work has implemented probabilistic models to extract a shared
representation in task fMRI. In the present work, we improve upon these models
by incorporating temporal information in the common latent structures. We
introduce a new model, Shared Gaussian Process Factor Analysis (S-GPFA), that
discovers shared latent trajectories and subject-specific functional
topographies, while modelling temporal correlation in fMRI data. We demonstrate
the efficacy of our model in revealing ground truth latent structures using
simulated data, and replicate experimental performance of time-segment matching
and inter-subject similarity on the publicly available Raider and Sherlock
datasets. We further test the utility of our model by analyzing its learned
model parameters in the large multi-site SPINS dataset, on a social cognition
task from participants with and without schizophrenia.
