The geometry of financial institutions -- Wasserstein clustering of
  financial data
Lorenz Riess Mathias Beiglböck Johannes Temme Andreas Wolf Julio Backhoff
The increasing availability of granular and big data on various objects of
interest has made it necessary to develop methods for condensing this
information into a representative and intelligible map. Financial regulation is
a field that exemplifies this need, as regulators require diverse and often
highly granular data from financial institutions to monitor and assess their
activities. However, processing and analyzing such data can be a daunting task,
especially given the challenges of dealing with missing values and identifying
clusters based on specific features.
  To address these challenges, we propose a variant of Lloyd's algorithm that
applies to probability distributions and uses generalized Wasserstein
barycenters to construct a metric space which represents given data on various
objects in condensed form. By applying our method to the financial regulation
context, we demonstrate its usefulness in dealing with the specific challenges
faced by regulators in this domain. We believe that our approach can also be
applied more generally to other fields where large and complex data sets need
to be represented in concise form.