  This study addresses the problem of performing clustering in the presence of
two types of background knowledge: pairwise constraints and monotonicity
constraints. To achieve this, the formal framework to perform clustering under
monotonicity constraints is, firstly, defined, resulting in a specific distance
measure. Pairwise constraints are integrated afterwards by designing an
objective function which combines the proposed distance measure and a pairwise
constraint-based penalty term, in order to fuse both types of information. This
objective function can be optimized with an EM optimization scheme. The
proposed method serves as the first approach to the problem it addresses, as it
is the first method designed to work with the two types of background knowledge
mentioned above. Our proposal is tested in a variety of benchmark datasets and
in a real-world case of study.
