  In exploratory tensor mining, a common problem is how to analyze a set of
variables across a set of subjects whose observations do not align naturally.
For example, when modeling medical features across a set of patients, the
number and duration of treatments may vary widely in time, meaning there is no
meaningful way to align their clinical records across time points for analysis
purposes. To handle such data, the state-of-the-art tensor model is the
so-called PARAFAC2, which yields interpretable and robust output and can
naturally handle sparse data. However, its main limitation up to now has been
the lack of efficient algorithms that can handle large-scale datasets.
  In this work, we fill this gap by developing a scalable method to compute the
PARAFAC2 decomposition of large and sparse datasets, called SPARTan. Our method
exploits special structure within PARAFAC2, leading to a novel algorithmic
reformulation that is both fast (in absolute time) and more memory-efficient
than prior work. We evaluate SPARTan on both synthetic and real datasets,
showing 22X performance gains over the best previous implementation and also
handling larger problem instances for which the baseline fails. Furthermore, we
are able to apply SPARTan to the mining of temporally-evolving phenotypes on
data taken from real and medically complex pediatric patients. The clinical
meaningfulness of the phenotypes identified in this process, as well as their
temporal evolution over time for several patients, have been endorsed by
clinical experts.
