Recent Developments in Boolean Matrix Factorization
This survey provides a concise overview of BMF for researchers and practitioners interested in interpretable binary matrix decomposition, highlighting its growing interdisciplinary relevance.
This paper surveys recent developments in Boolean Matrix Factorization (BMF), a method for approximating binary matrices as a product of two low-rank binary factor matrices using Boolean algebra. It summarizes efforts across data mining, formal concept analysis, machine learning, and theoretical communities, and identifies open questions for future research.
The goal of Boolean Matrix Factorization (BMF) is to approximate a given binary matrix as the product of two low-rank binary factor matrices, where the product of the factor matrices is computed under the Boolean algebra. While the problem is computationally hard, it is also attractive because the binary nature of the factor matrices makes them highly interpretable. In the last decade, BMF has received a considerable amount of attention in the data mining and formal concept analysis communities and, more recently, the machine learning and the theory communities also started studying BMF. In this survey, we give a concise summary of the efforts of all of these communities and raise some open questions which in our opinion require further investigation.