A divide-and-conquer algorithm for binary matrix completion
This work addresses the need for interpretable matrix completion in binary data, such as recommender systems, but is incremental as it builds on existing data mining approaches.
The authors tackled the problem of low-rank matrix completion for binary matrices by proposing TBMC, an algorithm that provides interpretable binary factors and outperforms existing methods on real-world recommender system datasets.
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 (\emph{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.