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Addressing the interpretability problem of NMF on Boolean data, BooleanMatrix Factorization (BMF) uses Boolean algebra to decompose the input intolow-rank Boolean factor matrices. These matrices are highly interpretable andvery useful in practice, but they come at the high computational cost ofsolving an NP-hard combinatorial optimization problem. To reduce thecomputational burden, we propose to relax BMF continuously using a novelelastic-binary regularizer, from which we derive a proximal gradient algorithm.Through an extensive set of experiments, we demonstrate that our method workswell in practice: On synthetic data, we show that it converges quickly,recovers the ground truth precisely, and estimates the simulated rank exactly.On real-world data, we improve upon the state of the art in recall, loss, andruntime, and a case study from the medical domain confirms that our results areeasily interpretable and semantically meaningful.

Efficiently Factorizing Boolean Matrices using Proximal Gradient Descent