Repetitive Branch-and-Bound Using Constraint Programming for Constrained Minimum Sum-of-Squares Clustering

Minimum sum-of-squares clustering (MSSC) is a widely studied task and numerous approximate as well as a number of exact algorithms have been developed for it. Recently the interest of integrating prior knowledge in data mining has been shown, and much attention has gone into incorporating user constraints into clustering algorithms in a generic way. Exact methods for MSSC using integer linear programming or constraint programming have been shown to be able to incorporate a wide range of constraints. However, a better performing method for unconstrained exact clustering is the Repetitive Branch-and-Bound Algorithm (RBBA) algorithm. In this paper we show that both approaches can be combined. The key idea is to replace the internal branch-and-bound of RBBA by a constraint programming solver, and use it to compute tight lower and upper bounds. To achieve this, we integrate the computed bounds into the solver using a novel constraint. Our method combines the best of both worlds, and is generic as well as performing better than other exact constrained methods. Furthermore, we show that our method can be used for multiobjective MSSC clustering, including constrained multi-objective clustering.