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Matrix factorization, one of the most popular methods in machine learning,has recently benefited from introducing non-linearity in prediction tasks usingtropical semiring. The non-linearity enables a better fit to extreme values anddistributions, thus discovering high-variance patterns that differ from thosefound by standard linear algebra. However, the optimization process of varioustropical matrix factorization methods is slow. In our work, we propose a newmethod FastSTMF based on Sparse Tropical Matrix Factorization (STMF), whichintroduces a novel strategy for updating factor matrices that results inefficient computational performance. We evaluated the efficiency of FastSTMF onsynthetic and real gene expression data from the TCGA database, and the resultsshow that FastSTMF outperforms STMF in both accuracy and running time. Comparedto NMF, we show that FastSTMF performs better on some datasets and is not proneto overfitting as NMF. This work sets the basis for developing other matrixfactorization techniques based on many other semirings using a new proposedoptimization process.

FastSTMF: Efficient tropical matrix factorization algorithm for sparse data