Constrained Clustering allows to make the clustering task more accurate by integrating user constraints, which can be instance-level or cluster-level constraints. Few works consider the integration of different kinds of constraints, they are usually based on declarative frameworks and they are often exact methods, which either enumerate all the solutions satisfying the user constraints, or find a global optimum when an optimization criterion is specified. In a previous work, we have proposed a model for Constrained Clustering based on a Constraint Programming framework. It is declarative, allowing a user to integrate user constraints and to choose an optimization criterion among several ones. In this article we present a new and substantially improved model for Constrained Clustering, still based on a Constraint Programming framework. It differs from our earlier model in the way partitions are represented by means of variables and constraints. It is also more flexible since the number of clusters does not need to be set beforehand; only a lower and an upper bound on the number of clusters have to be provided. In order to make the model-based approach more efficient, we propose new global optimization constraints with dedicated filtering algorithms. We show that such a framework can easily be embedded in a more general process and we illustrate this on the problem of finding the optimal Pareto front of a bi-criterion constrained clustering task. We compare our approach with existing exact approaches, based either on a branch-and-bound approach or on graph coloring on twelve datasets. Experiments show that the model outperforms exact approaches in most cases.

Abstract. In recent years, clustering has been extended to constrained clustering, so as to integrate knowledge on objects or on clusters, but adding such constraints generally requires to develop new algorithms. We propose a declarative and generic framework, based on Constraint Programming, which enables to design clustering tasks by specifying an optimization criterion and some constraints either on the clusters or on pairs of objects. In our framework, several classical optimization criteria are considered and they can be coupled with different kinds of constraints. Relying on Constraint Programming has two main advantages: the declarativity, which enables to easily add new constraints and the ability to find an optimal solution satisfying all the constraints (when there exists one). On the other hand, computation time depends on the constraints and on their ability to reduce the domain of variables, thus avoiding an exhaustive search.

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