  In immunological and clinical studies, matrix-valued time-series data
clustering is increasingly popular. Researchers are interested in finding
low-dimensional embedding of subjects based on potentially high-dimensional
longitudinal features and investigating relationships between static clinical
covariates and the embedding. 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 an immunological data set from
patients with SARs-CoV-2 infection.
