  In many classification tasks, the set of target classes can be organized into
a hierarchy. This structure induces a semantic distance between classes, and
can be summarised under the form of a cost matrix, which defines a finite
metric on the class set. In this paper, we propose to model the hierarchical
class structure by integrating this metric in the supervision of a prototypical
network. Our method relies on jointly learning a feature-extracting network and
a set of class prototypes whose relative arrangement in the embedding space
follows an hierarchical metric. We show that this approach allows for a
consistent improvement of the error rate weighted by the cost matrix when
compared to traditional methods and other prototype-based strategies.
Furthermore, when the induced metric contains insight on the data structure,
our method improves the overall precision as well. Experiments on four
different public datasets - from agricultural time series classification to
depth image semantic segmentation - validate our approach.
