Recent Developments in Boolean Matrix Factorization

TL;DR

This survey reviews recent advances in Boolean Matrix Factorization, highlighting its interpretability, computational challenges, and cross-disciplinary interest, while identifying open research questions for future exploration.

Contribution

It provides a comprehensive summary of developments across multiple communities and discusses open questions in Boolean Matrix Factorization.

Findings

BMF offers interpretable binary factorization of data matrices.

Despite computational hardness, BMF has gained wide interest.

Open questions remain in algorithm development and theoretical understanding.

Abstract

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.