The Boolean matrix factorization problem consists in approximating a matrix by the Boolean product of two smaller Boolean matrices. To obtain optimal solutions when the matrices to be factorized are small, we propose SAT and MaxSAT encoding; however, when the matrices to be factorized are large, we propose a heuristic based on the search for maximal biclique edge cover. We experimentally demonstrate that our approaches allow a better factorization than existing approaches while keeping reasonable computation times. Our methods also allow the handling of incomplete matrices with missing entries.

翻译：布尔基体因子化问题包括由两个较小的布尔基体组成的布尔产品对一个矩阵进行近似比对。为了在要因子化的矩阵小时获得最佳解决办法,我们建议采用SAT和MaxSAT编码;然而,当要因子化的矩阵大时,我们建议采用基于寻找最大双子边缘覆盖的超常法。我们实验性地证明,我们的方法比现有的方法允许更好的因子化,同时保持合理的计算时间。我们的方法也允许处理缺少条目的不完整矩阵。