  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.
