Sparse data embedding and prediction by tropical matrix factorization

Abstract

Abstract Background Matrix factorization methods are linear models, with limited capability to model complex relations. In our work, we use tropical semiring to introduce non-linearity into matrix factorization models. We propose a method called Sparse Tropical Matrix Factorization () for the estimation of missing (unknown) values in sparse data. Results We evaluate the efficiency of the method on both synthetic data and biological data in the form of gene expression measurements downloaded from The Cancer Genome Atlas (TCGA) database. Tests on unique synthetic data showed that approximation achieves a higher correlation than non-negative matrix factorization (), which is unable to recover patterns effectively. On real data, outperforms on six out of nine gene expression datasets. While assumes normal distribution and tends toward the mean value, can better fit to extreme values and distributions. Conclusion is the first work that uses tropical semiring on sparse data. We show that in certain cases semirings are useful because they consider the structure, which is different and simpler to understand than it is with standard linear algebra.