# Binary component decomposition Part II: The asymmetric case

arXiv: https://arxiv.org/abs/1907.13602 · HTML: https://mlsanity.com/paper/1907.13602/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Jul 2019.

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

- [Symmetric Sparse Boolean Matrix Factorization and Applications](https://mlsanity.com/paper/2102.01570/) (2021)
- [Fast and Low-Memory Deep Neural Networks Using Binary Matrix Factorization](https://mlsanity.com/paper/2210.13468/) (2022)
- [On the Complexity of Low-Rank Matrix Signing and Entrywise Power Matrix Factorization](https://mlsanity.com/paper/2607.04875/) (2026)

## Abstract (arXiv)

This paper studies the problem of decomposing a low-rank matrix into a factor with binary entries, either from ± 1 or from 0,1, and an unconstrained factor. The research answers fundamental questions about the existence and uniqueness of these decompositions. It also leads to tractable factorization algorithms that succeed under a mild deterministic condition. This work builds on a companion paper that addresses the related problem of decomposing a low-rank positive-semidefinite matrix into symmetric binary factors.