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arXiv 2011.044572020-11math.OCcs.DMcs.LG

Binary Matrix Factorisation via Column Generation

University of Oxford（牛津大学）；The Alan Turing Institute（艾伦图灵研究所）；Cornell University（康奈尔大学）

Reka A. Kovacs, Oktay Gunluk, Raphael A. Hauser

备注：: final version as published by AAAI2021, plus including Appendix

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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.

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