Application of tropical semiring for matrix factorization

Matrix factorization methods employ standard linear algebra, i.e. linear models, for recommender systems. With the introduction of the tropical semiring, we can achieve non-linearity. We review algorithms that use the tropical semiring for matrix factorization and provide their strengths and limitations. We show that the tropical matrix factorization yields better results than non-negative matrix factorization for the synthetic data created by the underlying process of the tropical semiring.