Binary Component Decomposition Part I: The Positive-Semidefinite Case
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Abstract (arXiv)
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.
Key facts. Cited by 5 papers in the map (data through 14 Oct 2026). First posted on arXiv 31 Jul 2019.
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Citing papers per year: 2021: 1; 2022: 2; 2023: 1; 2024: 0; 2025: 0; 2026: 1.
5 papers.
- 2022Bounded Simplex-Structured Matrix Factorization: Algorithms, Identifiability and Applicationscited by 5
- 2021Symmetric Sparse Boolean Matrix Factorization and Applicationscited by 3
- 2022Fast and Low-Memory Deep Neural Networks Using Binary Matrix Factorizationcited by 0
- 2023Empirical Bayes Covariance Decomposition, and a Solution to the Multiple Tuning Problem in Sparse PCAcited by 0
- 2026On the Complexity of Low-Rank Matrix Signing and Entrywise Power Matrix Factorizationcited by 0
- 2026On the Complexity of Low-Rank Matrix Signing and Entrywise Power Matrix Factorization6 Jul 2026
- 2023Empirical Bayes Covariance Decomposition, and a Solution to the Multiple Tuning Problem in Sparse PCA6 Dec 2023
- 2022Fast and Low-Memory Deep Neural Networks Using Binary Matrix Factorization24 Oct 2022
- 2022Bounded Simplex-Structured Matrix Factorization: Algorithms, Identifiability and Applications26 Sep 2022
- 2021Symmetric Sparse Boolean Matrix Factorization and Applications2 Feb 2021