Binary component decomposition Part II: The asymmetric case

Abstract: This paper studies the problem of decomposing a low-rank matrix into a factor with binary entries, either from ${\pm 1}$ 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.