Binary Component Decomposition Part I: The Positive-Semidefinite Case

2019/07/31 by Kueng, Richard, Tropp, Joel A.
#15A21 #15B48 (Primary) #52A20 #52B12 #90C27 (Secondary) #Data Structures and Algorithms (cs.DS) #FOS: Computer and information sciences #FOS: Mathematics #Metric Geometry (math.MG) #Optimization and Control (math.OC) #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.1907.13603

Abstract

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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