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Boolean matrix factorization (BMF) is a popular and powerful technique forinferring knowledge from data. The mining result is the Boolean product of twomatrices, approximating the input dataset. The Boolean product is a disjunctionof 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 returnedpatterns do not actually arise from noise, i.e., are false discoveries. In thispaper, we propose and discuss the usage of the false discovery rate in theunsupervised BMF setting. We prove two bounds on the probability that a foundpattern is constituted of random Bernoulli-distributed noise. Each boundexploits a specific property of the factorization which minimizes theapproximation error---yielding new insights on the minimizers of Boolean matrixfactorization. This leads to improved BMF algorithms by replacing heuristicrank selection techniques with a theoretically well-based approach. Ourempirical demonstration shows that both bounds deliver excellent results invarious practical settings.

The Trustworthy Pal: Controlling the False Discovery Rate in Boolean Matrix Factorization