  The PARAFAC2 model provides a flexible alternative to the popular
CANDECOMP/PARAFAC (CP) model for tensor decompositions. Unlike CP, PARAFAC2
allows factor matrices in one mode (i.e., evolving mode) to change across
tensor slices, which has proven useful for applications in different domains
such as chemometrics, and neuroscience. However, the evolving mode of the
PARAFAC2 model is traditionally modelled implicitly, which makes it challenging
to regularise it. Currently, the only way to apply regularisation on that mode
is with a flexible coupling approach, which finds the solution through
regularised least-squares subproblems. In this work, we instead propose an
alternating direction method of multipliers (ADMM)-based algorithm for fitting
PARAFAC2 and widen the possible regularisation penalties to any proximable
function. Our numerical experiments demonstrate that the proposed ADMM-based
approach for PARAFAC2 can accurately recover the underlying components from
simulated data while being both computationally efficient and flexible in terms
of imposing constraints.
