Symmetric nonnegative trifactorization of pattern matrices

Kokol-Bukovšek, Damjana (avtor), Šmigoc, Helena (avtor)

A factorization of an $n$ x $n$ nonnegative symmetric matrix $A$ of the form $BCB^T$, where $C$ is a $k$ x $k$ 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.

• Jezik: Angleški jezik
• Ključne besede: mathematics, mathematical economy, matrix algebra, nonnegative matrix factorization, nonnegative symmetric matrices, symmetric nonnegative trifactorization, pattern matrices
• Vrsta gradiva: Članek v reviji
• Tipologija: 1.01 - Izvirni znanstveni članek
• Organizacija: EF - Ekonomska fakulteta
• Status publikacije: Objavljeno
• Različica publikacije: Objavljena publikacija
• Leto izida: 2025
• Št. strani: Str. 310-338
• Številčenje: Vol. 721
• PID: 20.500.12556/RUL-169499
• UDK: 330.4
• ISSN pri članku: 0024-3795
• DOI: 10.1016/j.laa.2024.05.017
• COBISS.SI-ID: 197444611
• Datum objave v RUL: 30.05.2025

Gradivo je del revije

• Naslov: Linear algebra and its applications
• Skrajšan naslov: Linear algebra appl.
• Založnik: Elsevier
• ISSN: 0024-3795
• COBISS.SI-ID: 1119247

Licence

• Licenca: CC BY-NC 4.0, Creative Commons Priznanje avtorstva-Nekomercialno 4.0 Mednarodna
• Povezava: http://creativecommons.org/licenses/by-nc/4.0/deed.sl
• Opis: Licenca Creative Commons, ki prepoveduje komercialno uporabo, vendar uporabniki ne rabijo upravljati materialnih avtorskih pravic na izpeljanih delih z enako licenco.

Sekundarni jezik

• Jezik: Slovenski jezik
• Ključne besede: matematika, matematična ekonomija, matrična algebra

Projekti

• Financer: ARIS - Javna agencija za znanstvenoraziskovalno in inovacijsko dejavnost Republike Slovenije
• Številka projekta: P1-0222
• Naslov: Algebra, teorija operatorjev in finančna matematika