# Binary Matrix Factorisation via Column Generation

arXiv: https://arxiv.org/abs/2011.04457 · HTML: https://mlsanity.com/paper/2011.04457/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Nov 2020.

## Built on by (most cited first, 3 of 3)

- [Large-Scale Differentiable Causal Discovery of Factor Graphs](https://mlsanity.com/paper/2206.07824/) (2022)
- [Interpretable and Fair Boolean Rule Sets via Column Generation](https://mlsanity.com/paper/2111.08466/) (2021)
- [Binary Matrix Factorisation and Completion via Integer Programming](https://mlsanity.com/paper/2106.13434/) (2021)

## Abstract (arXiv)

Identifying discrete patterns in binary data is an important dimensionality reduction tool in machine learning and data mining. In this paper, we consider the problem of low-rank binary matrix factorisation (BMF) under Boolean arithmetic. Due to the hardness of this problem, most previous attempts rely on heuristic techniques. We formulate the problem as a mixed integer linear program and use a large scale optimisation technique of column generation to solve it without the need of heuristic pattern mining. Our approach focuses on accuracy and on the provision of optimality guarantees. Experimental results on real world datasets demonstrate that our proposed method is effective at producing highly accurate factorisations and improves on the previously available best known results for 15 out of 24 problem instances.