  Boolean matrix factorization (BMF) is a popular and powerful technique for
inferring knowledge from data. The mining result is the Boolean product of two
matrices, approximating the input dataset. The Boolean product is a disjunction
of rank-1 binary matrices, each describing a feature-relation, called pattern,
for a group of samples. Yet, there are no guarantees that any of the returned
patterns do not actually arise from noise, i.e., are false discoveries. In this
paper, we propose and discuss the usage of the false discovery rate in the
unsupervised BMF setting. We prove two bounds on the probability that a found
pattern is constituted of random Bernoulli-distributed noise. Each bound
exploits a specific property of the factorization which minimizes the
approximation error---yielding new insights on the minimizers of Boolean matrix
factorization. This leads to improved BMF algorithms by replacing heuristic
rank selection techniques with a theoretically well-based approach. Our
empirical demonstration shows that both bounds deliver excellent results in
various practical settings.
