  We present a methodology for clustering N objects which are described by
multivariate time series, i.e. several sequences of real-valued random
variables. This clustering methodology leverages copulas which are
distributions encoding the dependence structure between several random
variables. To take fully into account the dependence information while
clustering, we need a distance between copulas. In this work, we compare
renowned distances between distributions: the Fisher-Rao geodesic distance,
related divergences and optimal transport, and discuss their advantages and
disadvantages. Applications of such methodology can be found in the clustering
of financial assets. A tutorial, experiments and implementation for
reproducible research can be found at www.datagrapple.com/Tech.
