01521nas a2200157   4500008004100000245005700041210005700098260003100155520103200186100002001218700001901238700001701257700002001274700001901294856005001313       2015                        eng d00aClustering Formulation Using Constraint Optimization0 aClustering Formulation Using Constraint Optimization  bSpringer Berlin Heidelberg3 aThe problem of clustering a set of data is a textbook machine learning problem, but at the same time, at heart, a typical optimization problem. Given an objective function, such as minimizing the intra-cluster distances or maximizing the inter-cluster distances, the task is to find an assignment of data points to clusters that achieves this objective. In this paper, we present a constraint programming model for a centroid based clustering and one for a density based clustering. In particular, as a key contribution, we show how the expressivity introduced by the formulation of the problem by constraint programming makes the standard problem easy to be extended with other constraints that permit to generate interesting variants of the problem. We show this important aspect in two different ways: first, we show how the formulation of the density-based clustering by constraint programming makes it very similar to the label propagation problem and then, we propose a variant of the standard label propagation approach.1 aGrossi, Valerio1 aMonreale, Anna1 aNanni, Mirco1 aPedreschi, Dino1 aTurini, Franco  uhttp://dx.doi.org/10.1007/978-3-662-49224-6_9