  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.
