  Coupled matrix and tensor factorizations (CMTF) have emerged as an effective
data fusion tool to jointly analyze data sets in the form of matrices and
higher-order tensors. The PARAFAC2 model has shown to be a promising
alternative to the CANDECOMP/PARAFAC (CP) tensor model due to its flexibility
and capability to handle irregular/ragged tensors. While fusion models based on
a PARAFAC2 model coupled with matrix/tensor decompositions have been recently
studied, they are limited in terms of possible regularizations and/or types of
coupling between data sets. In this paper, we propose an algorithmic framework
for fitting PARAFAC2-based CMTF models with the possibility of imposing various
constraints on all modes and linear couplings, using Alternating Optimization
(AO) and the Alternating Direction Method of Multipliers (ADMM). Through
numerical experiments, we demonstrate that the proposed algorithmic approach
accurately recovers the underlying patterns using various constraints and
linear couplings.
