  Identifying discrete patterns in binary data is an important dimensionality
reduction tool in machine learning and data mining. In this paper, we consider
the problem of low-rank binary matrix factorisation (BMF) under Boolean
arithmetic. Due to the hardness of this problem, most previous attempts rely on
heuristic techniques. We formulate the problem as a mixed integer linear
program and use a large scale optimisation technique of column generation to
solve it without the need of heuristic pattern mining. Our approach focuses on
accuracy and on the provision of optimality guarantees. Experimental results on
real world datasets demonstrate that our proposed method is effective at
producing highly accurate factorisations and improves on the previously
available best known results for 15 out of 24 problem instances.
