A branch-and-price algorithm for the hyper-rectangular clustering problem with axis-parallel clusters and outliers

Abstract

We address 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 present an integer programming formulation for this problem which employs exponentially-many variables and we develop an exact algorithm to solve it, based on branch-and-price techniques. We solve the linear relaxation of the proposed model by applying column generation and we propose two different integer programming formulations to tackle the associated pricing subproblem. For the branch-and-price algorithm, we propose a branching rule specifically tailored for the problem. Finally, we provide computational experiments showing that the proposed approach is effective in practice.