Matrix Tri-Factorization Over the Tropical Semiring

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.