# A divide-and-conquer algorithm for binary matrix completion

arXiv: https://arxiv.org/abs/1907.04251 · HTML: https://mlsanity.com/paper/1907.04251/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Jul 2019.

## Built on by (most cited first, 2 of 2)

- [Binary Matrix Factorisation and Completion via Integer Programming](https://mlsanity.com/paper/2106.13434/) (2021)
- [One-Bit Matrix Completion with Differential Privacy](https://mlsanity.com/paper/2110.00719/) (2021)

## Abstract (arXiv)

We propose an algorithm for low rank matrix completion for matrices with binary entries which obtains explicit binary factors. Our algorithm, which we call TBMC (Tiling for Binary Matrix Completion), gives interpretable output in the form of binary factors which represent a decomposition of the matrix into tiles. Our approach is inspired by a popular algorithm from the data mining community called PROXIMUS: it adopts the same recursive partitioning approach while extending to missing data. The algorithm relies upon rank-one approximations of incomplete binary matrices, and we propose a linear programming (LP) approach for solving this subproblem. We also prove a 2-approximation result for the LP approach which holds for any level of subsampling and for any subsampling pattern. Our numerical experiments show that TBMC outperforms existing methods on recommender systems arising in the context of real datasets.