Matrix tri-factorization over the tropical semiring
This work addresses a gap in network analysis tools for researchers in fields like bioinformatics and control systems, though it is incremental as it extends existing tropical factorization methods.
The paper tackles the lack of a tropical matrix tri-factorization method for analyzing multipartite networks by proposing the triFastSTMF algorithm, which shows similar performance to Fast-NMTF on full networks and outperforms it by several orders of magnitude in error when predicting whole networks from subnetworks.
Tropical semiring has proven successful in several research areas, including optimal control, bioinformatics, discrete event systems, or solving a decision problem. In previous studies, a matrix two-factorization algorithm based on the tropical semiring has been applied to investigate bipartite and tripartite networks. Tri-factorization algorithms based on standard linear algebra are used for solving tasks such as data fusion, co-clustering, matrix completion, community detection, and more. However, there is currently no tropical matrix tri-factorization approach, which would allow for the analysis of multipartite networks with a high number of parts. To address this, we propose the triFastSTMF algorithm, which performs tri-factorization over the tropical semiring. We apply 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 whole 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.