Boolean matrix has been used to represent digital information in many fields, including bank transaction, crime records, natural language processing, protein-protein interaction, etc. Boolean matrix factorization (BMF) aims to find an approximation of a binary matrix as the Boolean product of two low rank Boolean matrices, which could generate vast amount of information for the patterns of relationships between the features and samples. Inspired by binary matrix permutation theories and geometric segmentation, we developed a fast and efficient BMF approach called MEBF (Median Expansion for Boolean Factorization). Overall, MEBF adopted a heuristic approach to locate binary patterns presented as submatrices that are dense in 1's. At each iteration, MEBF permutates the rows and columns such that the permutated matrix is approximately Upper Triangular-Like (UTL) with so-called Simultaneous Consecutive-ones Property (SC1P). The largest submatrix dense in 1 would lies on the upper triangular area of the permutated matrix, and its location was determined based on a geometric segmentation of a triangular. We compared MEBF with other state of the art approaches on data scenarios with different sparsity and noise levels. MEBF demonstrated superior performances in lower reconstruction error, and higher computational efficiency, as well as more accurate sparse patterns than popular methods such as ASSO, PANDA and MP. We demonstrated the application of MEBF on both binary and non-binary data sets, and revealed its further potential in knowledge retrieving and data denoising.

本研究开发了一种名为MEBF的快速、高效的布尔矩阵因式分解方法，采用启发式方法以定位“密集的1”的子矩阵为目标，其性能表现优于ASSO、PANDA和MP等其他常用方法，同时在二进制和非二进制数据集上的应用表明其具有知识检索和数据去噪的潜在能力。

基于几何分割的快速高效布尔矩阵分解