Matrix Tri-Factorization Over the Tropical Semiring

• Published in: IEEE access Vol. 11; pp. 69022 - 69032
• Main Authors: Omanovic, Amra, Oblak, Polona, Curk, Tomaz
• Format: Journal Article
• Language: English
• Published: Piscataway IEEE 2023; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Approximation algorithms; Bioinformatics; Clustering; Data integration; Discrete event systems; Factorization; four-partition network; Linear algebra; Matrices (mathematics); network structure analysis; Optimal control; Optimization; Partitioning algorithms; Prediction algorithms; Task analysis; tri-factorization; Tropical semiring
• DOI: 10.1109/ACCESS.2023.3287833
• ISSN: 2169-3536

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.