| Title: | Symmetric nonnegative trifactorization of pattern matrices |
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| Authors: | ID Kokol-Bukovšek, Damjana (Author)
ID Šmigoc, Helena (Author) |
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| Files: |  PDF - Presentation file, download (553,93 KB)
MD5: 70DF3387714FD5FB510F148F101DC301
 URL - Source URL, visit https://www.sciencedirect.com/science/article/pii/S0024379524002295
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| Language: | English |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: |  IMFM - Institute of Mathematics, Physics, and Mechanics
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| Abstract: | A factorization of an $n \times n$ nonnegative symmetric matrix $A$ of the form $BCB^T$, where $C$ is a $k \times k$ symmetric matrix, and both $B$ and $C$ are required to be nonnegative, is called the Symmetric Nonnegative Matrix Trifactorization (SN-Trifactorization). The SNT-rank of $A$ is the minimal $k$ for which such factorization exists. The SNT-rank of a simple graph $G$ that allows loops is defined to be the minimal possible SNT-rank of all symmetric nonnegative matrices whose zero-nonzero pattern is prescribed by the graph $G$. We define set-join covers of graphs, and show that finding the SNT-rank of $G$ is equivalent to finding the minimal order of a set-join cover of $G$. Using this insight we develop basic properties of the SNT-rank for graphs and compute it for trees and cycles without loops. We show the equivalence between the SNT-rank for complete graphs and the Katona problem, and discuss uniqueness of patterns of matrices in the factorization. |
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| Keywords: | mathematics, mathematical economy, matrix algebra, nonnegative matrix factorization, nonnegative symmetric matrices, symmetric nonnegative trifactorization, pattern matrices |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 01.09.2025 |
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| Year of publishing: | 2025 |
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| Number of pages: | str. 310-338 |
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| Numbering: | Vol. 721 |
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| PID: | 20.500.12556/DiRROS-23982  |
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| UDC: | 512 |
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| ISSN on article: | 0024-3795 |
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| DOI: | 10.1016/j.laa.2024.05.017 |
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| COBISS.SI-ID: | 197444611 |
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| Publication date in DiRROS: | 03.11.2025 |
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| Views: | 117 |
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| Downloads: | 60 |
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