FastSTMF: Efficient tropical matrix factorization algorithm for sparse data

Abstract: Matrix factorization, one of the most popular methods in machine learning, has recently benefited from introducing non-linearity in prediction tasks using tropical semiring. The non-linearity enables a better fit to extreme values and distributions, thus discovering high-variance patterns that differ from those found by standard linear algebra. However, the optimization process of various tropical matrix factorization methods is slow. In our work, we propose a new method FastSTMF based on Sparse Tropical Matrix Factorization (STMF), which introduces a novel strategy for updating factor matrices that results in efficient computational performance. We evaluated the efficiency of FastSTMF on synthetic and real gene expression data from the TCGA database, and the results show that FastSTMF outperforms STMF in both accuracy and running time. Compared to NMF, we show that FastSTMF performs better on some datasets and is not prone to overfitting as NMF. This work sets the basis for developing other matrix factorization techniques based on many other semirings using a new proposed optimization process.