Sparse Probabilistic Parallel Factor Analysis for the Modeling of PET and Task-fMRI Data

Modern datasets are often multiway in nature and can contain patterns common to a mode of the data (e.g. space, time, and subjects). Multiway decomposition such as parallel factor analysis (PARAFAC) take into account the intrinsic structure of the data, and sparse versions of these methods improve interpretability of the results. Here we propose a variational Bayesian parallel factor analysis (VB-PARAFAC) model and an extension with sparse priors (SP-PARAFAC). Notably, our formulation admits time and subject specific noise modeling as well as subject specific offsets (i.e., mean values). We confirmed the validity of the models through simulation and performed exploratory analysis of positron emission tomography (PET) and functional magnetic resonance imaging (fMRI) data. Although more constrained, the proposed models performed similarly to more flexible models in approximating the PET data, which supports its robustness against noise. For fMRI, both models correctly identified task-related components, but were not able to segregate overlapping activations.