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Binary component decomposition Part II: The asymmetric case
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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.
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Cited by 1 Pith paper
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On the Complexity of Low-Rank Matrix Signing and Entrywise Power Matrix Factorization
Exact low-rank matrix signing is strongly NP-hard in general, polynomial-time for fixed rank and FPT for generic matrices, while Frobenius approximation is already NP-hard at rank 2.
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