Binary Component Decomposition Part I: The Positive-Semidefinite Case
This paper studies the problem of decomposing a low-rank positive-semidefinite matrix into symmetric factors with binary entries, either {± 1} or {0,1}. This 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. A companion paper addresses the related problem of decomposing a low-rank rectangular matrix into a binary factor and an unconstrained factor.
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