A novel approach to Boolean matrix factorization (BMF) is presented. Instead of solving the BMF problem directly, this approach solves a nonnegative optimization problem with the constraint over an auxiliary matrix whose Boolean structure is identical to the initial Boolean data. Then the solution of the nonnegative auxiliary optimization problem is thresholded to provide a solution for the BMF problem. We provide the proofs for the equivalencies of the two solution spaces under the existence of an exact solution. Moreover, the nonincreasing property of the algorithm is also proven. Experiments on synthetic and real datasets are conducted to show the effectiveness and complexity of the algorithm compared to other current methods.

翻译：介绍了一种新颖的布尔语矩阵因子化(BMF)方法。这个方法不是直接解决BMF问题,而是解决一个非负优化问题,其制约是对一个辅助矩阵的制约,其布尔语结构与初始布尔语数据完全相同。然后将非负辅助优化问题的解决作为解决布尔语矩阵因子化问题的起点。我们为两种解决方案空间在存在精确解决方案的情况下的等同性提供了证据。此外,算法的不增加特性也得到了证明。对合成和真实数据集进行了实验,以显示算法与其他当前方法相比的有效性和复杂性。