An integer programming approach for the hyper-rectangular clustering problem with axis-parallel clusters and outliers

Abstract

We present a mixed integer programming formulation for the problem of clustering a set of points in Rd with axis-parallel clusters, while allowing to discard a pre-specified number of points, thus declared to be outliers. We identify a family of valid inequalities separable in polynomial time, we prove that some inequalities from this family induce facets of the associated polytope, and we show that the dynamic addition of cuts coming from this family is effective in practice.