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.

We evaluate the performance of DMFA on a synthetic and two real large-scale fMRI datasets.

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.

An efficient way to learn deep density models that have many layers of latent variables is to learn one layer at a time using a model that has only one layer of latent variables. After learning each layer, samples from the posterior distributions for that layer are used as training data for learning the next layer. This approach is commonly used with Restricted Boltzmann Machines, which are undirected graphical models with a single hidden layer, but it can also be used with Mixtures of Factor Analysers (MFAs) which are directed graphical models. In this paper, we present a greedy layer-wise learning algorithm for Deep Mixtures of Factor Analysers (DMFAs). Even though a DMFA can be converted to an equivalent shallow MFA by multiplying together the factor loading matrices at different levels, learning and inference are much more efficient in a DMFA and the sharing of each lower-level factor loading matrix by many different higher level MFAs prevents overfitting. We demonstrate empirically that DM-FAs learn better density models than both MFAs and two types of Restricted Boltzmann Machine on a wide variety of datasets.