| Summary: | 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 <monospace>triFastSTMF</monospace> 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 <monospace>triFastSTMF</monospace> performs similarly to <monospace>Fast-NMTF</monospace> 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, <monospace>triFastSTMF</monospace> outperforms <monospace>Fast-NMTF</monospace> by several orders of magnitude smaller error. The robustness of <monospace>triFastSTMF</monospace> is due to tropical operations, which are less prone to predict large values compared to standard operations.
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