  Multi-label classification (MC) is a standard machine learning problem in
which a data point can be associated with a set of classes. A more challenging
scenario is given by hierarchical multi-label classification (HMC) problems, in
which every prediction must satisfy a given set of hard constraints expressing
subclass relationships between classes. In this paper, we propose C-HMCNN(h), a
novel approach for solving HMC problems, which, given a network h for the
underlying MC problem, exploits the hierarchy information in order to produce
predictions coherent with the constraints and to improve performance.
Furthermore, we extend the logic used to express HMC constraints in order to be
able to specify more complex relations among the classes and propose a new
model CCN(h), which extends C-HMCNN(h) and is again able to satisfy and exploit
the constraints to improve performance. We conduct an extensive experimental
analysis showing the superior performance of both C-HMCNN(h) and CCN(h) when
compared to state-of-the-art models in both the HMC and the general MC setting
with hard logical constraints.
