Matrix tri-factorization over the tropical semiring

Omanović, Amra (author), Oblak, Polona (author), Curk, Tomaž (author)

Tropical semiring has proven successful in several research areas, including optimal control, bioinformatics, discrete event systems, and decision problems. Previous studies have applied a matrix two-factorization algorithm based on the tropical semiring to investigate bipartite and tripartite networks. Tri-factorization algorithms based on standard linear algebra are used to solve tasks such as data fusion, co-clustering, matrix completion, community detection, and more. However, there is currently no tropical matrix tri-factorization approach that would allow for the analysis of multipartite networks with many parts. To address this, we propose the triFastSTMF algorithm, which performs tri-factorization over the tropical semiring. We applied it to analyze a four-partition network structure and recover the edge lengths of the network. We show that triFastSTMF performs similarly to Fast-NMTF in terms of approximation and prediction performance when fitted on the whole network. When trained on a specific subnetwork and used to predict the entire network, triFastSTMF outperforms Fast-NMTF by several orders of magnitude smaller error. The robustness of triFastSTMF is due to tropical operations, which are less prone to predict large values compared to standard operations.

• Language: English
• Keywords: tropical semiring, tri-factorization, network structure analysis, four-partition network
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FRI - Faculty of Computer and Information Science
• Publication status: Published
• Publication version: Version of Record
• Publication date: 01.01.2023
• Year: 2023
• Number of pages: Str. 69022-69032
• Numbering: Vol. 11
• PID: 20.500.12556/RUL-148483
• UDC: 004:51
• ISSN on article: 2169-3536
• DOI: 10.1109/ACCESS.2023.3287833
• COBISS.SI-ID: 162079235
• Publication date in RUL: 24.08.2023

Record is a part of a journal

• Title: IEEE access
• Publisher: Institute of Electrical and Electronics Engineers
• ISSN: 2169-3536
• COBISS.SI-ID: 519839513

Licences

• License: CC BY 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
• Description: This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.

Secondary language

• Language: Slovenian
• Keywords: tropski polkolobar, trifaktorizacija, analiza strukture omrežja, štiriparticijsko omrežje

Projects

• Funder: ARRS - Slovenian Research Agency
• Project number: P1-0222
• Name: Algebra, teorija operatorjev in finančna matematika

• Funder: ARRS - Slovenian Research Agency
• Project number: P2-0209
• Name: Umetna inteligenca in inteligentni sistemi