  We consider the problem of clustering functional data according to their
covariance structure. We contribute a soft clustering methodology based on the
Wasserstein-Procrustes distance, where the in-between cluster variability is
penalised by a term proportional to the entropy of the partition matrix. In
this way, each covariance operator can be partially classified into more than
one group. Such soft classification allows for clusters to overlap, and arises
naturally in situations where the separation between all or some of the
clusters is not well-defined. We also discuss how to estimate the number of
groups and to test for the presence of any cluster structure. The algorithm is
illustrated using simulated and real data. An R implementation is available in
the Supplementary materials.
