  In this work clustering schemes for uncertain and structured data are
considered relying on the notion of Wasserstein barycenters, accompanied by
appropriate clustering indices based on the intrinsic geometry of the
Wasserstein space where the clustering task is performed. Such type of
clustering approaches are highly appreciated in many fields where the
observational/experimental error is significant (e.g. astronomy, biology,
remote sensing, etc.) or the data nature is more complex and the traditional
learning algorithms are not applicable or effective to treat them (e.g. network
data, interval data, high frequency records, matrix data, etc.). Under this
perspective, each observation is identified by an appropriate probability
measure and the proposed clustering schemes rely on discrimination criteria
that utilize the geometric structure of the space of probability measures
through core techniques from the optimal transport theory. The advantages and
capabilities of the proposed approach and the geodesic criterion performance
are illustrated through a simulation study and the implementation in two real
world applications: (a) clustering eurozone countries according to their
observed government bond yield curves and (b) classifying the areas of a
satellite image to certain land uses categories, a standard task in remote
sensing.
