Published July 31, 2019
| Version Submitted
Discussion Paper
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Binary Component Decomposition. Part I: The Positive-Semidefinite Case
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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.
Additional Information
Date: 31 July 2019. The authors thank Benjamin Recht for helpful conversations at an early stage of this project and Madeleine Udell for valuable comments regarding the related work section. Peter Jung suggested activity detection in massive MIMO system as a potential application. This research was partially funded by ONR awards N00014-11-1002, N00014-17-12146, and N00014-18-12363. Additional support was provided by the Gordon & Betty Moore Foundation.Attached Files
Submitted - 1907.13603.pdf
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1907.13603.pdf
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Additional details
Identifiers
- Eprint ID
- 107223
- Resolver ID
- CaltechAUTHORS:20201218-154441081
Related works
- Describes
- http://arxiv.org/abs/1907.13603 (URL)
Funding
- Office of Naval Research (ONR)
- N00014-11-1002
- Office of Naval Research (ONR)
- N00014-17-12146
- Office of Naval Research (ONR)
- N00014-18-12363
- Gordon and Betty Moore Foundation
Dates
- Created
-
2020-12-21Created from EPrint's datestamp field
- Updated
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2023-06-02Created from EPrint's last_modified field