  Tensor factorizations have been widely used for the task of uncovering
patterns in various domains. Often, the input is time-evolving, shifting the
goal to tracking the evolution of underlying patterns instead. To adapt to this
more complex setting, existing methods incorporate temporal regularization but
they either have overly constrained structural requirements or lack uniqueness
which is crucial for interpretation. In this paper, in order to capture the
underlying evolving patterns, we introduce t(emporal)PARAFAC2 which utilizes
temporal smoothness regularization on the evolving factors. We propose an
algorithmic framework that employs Alternating Optimization (AO) and the
Alternating Direction Method of Multipliers (ADMM) to fit the model.
Furthermore, we extend the algorithmic framework to the case of partially
observed data. Our numerical experiments on both simulated and real datasets
demonstrate the effectiveness of the temporal smoothness regularization, in
particular, in the case of data with missing entries. We also provide an
extensive comparison of different approaches for handling missing data within
the proposed framework.
