Binary Matrix Factorisation via Column Generation
It addresses the challenge of identifying discrete patterns in binary data for machine learning and data mining, offering optimality guarantees in a domain where previous methods were heuristic.
The paper tackles the problem of low-rank binary matrix factorization under Boolean arithmetic by formulating it as a mixed integer linear program and solving it using column generation, achieving highly accurate factorizations and improving best known results for 15 out of 24 real-world datasets.
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.