# Recent Developments in Boolean Matrix Factorization

arXiv: https://arxiv.org/abs/2012.03127 · HTML: https://mlsanity.com/paper/2012.03127/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Dec 2020.

## Built on by (most cited first, 15 of 15)

- [Large-Scale Differentiable Causal Discovery of Factor Graphs](https://mlsanity.com/paper/2206.07824/) (2022)
- [LegoFormer: Transformers for Block-by-Block Multi-view 3D Reconstruction](https://mlsanity.com/paper/2106.12102/) (2021)
- [Structured Neural Networks for Density Estimation and Causal Inference](https://mlsanity.com/paper/2311.02221/) (2023)
- [Symmetric Sparse Boolean Matrix Factorization and Applications](https://mlsanity.com/paper/2102.01570/) (2021)
- [Efficiently Factorizing Boolean Matrices using Proximal Gradient Descent](https://mlsanity.com/paper/2307.07615/) (2023)
- [Algorithms for Boolean Matrix Factorization using Integer Programming](https://mlsanity.com/paper/2305.10185/) (2023)
- [Matrix Factorization for Inferring Associations and Missing Links](https://mlsanity.com/paper/2503.04680/) (2025)
- [Boolean Matrix Factorization with SAT and MaxSAT](https://mlsanity.com/paper/2106.10105/) (2021)
- [Boolean and mathbbFp-Matrix Factorization: From Theory to Practice](https://mlsanity.com/paper/2207.11917/) (2022)
- [Clustering Categorical Data: Soft Rounding k-modes](https://mlsanity.com/paper/2210.09640/) (2022)
- [Visualizing Overlapping Biclusterings and Boolean Matrix Factorizations](https://mlsanity.com/paper/2307.07396/) (2023)
- [Matrix Completion in Group Testing: Bounds and Simulations](https://mlsanity.com/paper/2501.13780/) (2025)
- [Algorithms for Boolean Matrix Factorization using Integer Programming and Heuristics](https://mlsanity.com/paper/2512.03807/) (2025)
- [A Bayesian Boolean Matrix Factorization with Application to Copy Number Analysis in Cancer](https://mlsanity.com/paper/2606.17491/) (2026)
- [Trustworthy Domain-Specific AI for Structured Knowledge Retrieval and Reasoning](https://mlsanity.com/paper/2610.08894/) (2026)

## Abstract (arXiv)

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.