Deep Markov Factor Analysis: Towards Concurrent Temporal and Spatial Analysis of fMRI Data

Factor analysis methods have been widely used in neuroimaging to transfer high dimensional imaging data into low dimensional, ideally interpretable representations. However, most of these methods overlook the highly nonlinear and complex temporal dynamics of neural processes when factorizing their imaging data. In this paper, we present deep Markov factor analysis (DMFA), a generative model that employs Markov property in a chain of low dimensional temporal embeddings together with spatial inductive assumptions, all related through neural networks, to capture temporal dynamics in functional magnetic resonance imaging (fMRI) data, and tackle their high spatial dimensionality, respectively. Augmented with a discrete latent, DMFA is able to cluster fMRI data in its low dimensional temporal embedding with regard to subject and cognitive state variability, therefore, enables validation of a variety of fMRI-driven neuroscientific hypotheses. Experimental results on both synthetic and real fMRI data demonstrate the capacity of DMFA in revealing interpretable clusters and capturing nonlinear temporal dependencies in these high dimensional imaging data.