Constrained Clustering Using Column Generation

In recent years, it has been realized that many problems in data mining can be seen as pure optimisation problems. In this work, we investigate the problem of constraint-based clustering from an optimisation point of view. The use of constraints in clustering is a recent development and allows to encode prior beliefs about desirable clusters. This paper proposes a new solution for minimum-sum-of-squares clustering under constraints, where the constraints considered are must-link constraints, cannot-link constraints and anti-monotone constraints on individual clusters. Contrary to most earlier approaches, it is exact and provides a fundamental approach for including these constraints. The proposed approach uses column generation in an integer linear programming setting. The key insight is that these constraints can be pushed into a branch-and-bound algorithm used for generating new columns. Experimental results show the feasibility of the approach and the promise of the branch-and-bound algorithm that solves the subproblem directly.