A smoothed and probabilistic PARAFAC model with covariates

Analysis and clustering of multivariate time-series data attract growing interest in immunological and clinical studies. In such applications, researchers are interested in clustering subjects based on potentially high-dimensional longitudinal features, and in investigating how clinical covariates may affect the clustering results. These studies are often challenging due to high dimensionality, as well as the sparse and irregular nature of sample collection along the time dimension. We propose a smoothed probabilistic PARAFAC model with covariates (SPACO) to tackle these two problems while utilizing auxiliary covariates of interest. We provide intensive simulations to test different aspects of SPACO and demonstrate its use on immunological data sets from two recent cohorts of SARs-CoV-2 patients.