… the max-product semiring rather than the plusproduct semiring common in traditional linear
algebra. We apply this semiring matrix factorization framework on two tasks: sparse rank …

… corresponding rank functions on matrices of … matrix factorization become polynomial time
solvable when restricted to this class of matrices, and we also show that the nonnegative rank …

… With the introduction of the tropical semiring, we can achieve … semiring for matrix factorization
and provide their strengths and limitations. We show that the tropical matrix factorization …

… of ranks and determinants for matrices over semirings. The … determinant and rank functions
for matrices over semirings is … for ranks of sums and products of matrices in the context of …

… two notions of rank of matrices over semirings: semiring rank and column rank. These two
… value of r for which the column rank and semiring rank of all m X n matrices over a given …

… using the relationship between semiprime matrices and their row spaces. … matrix with full
semiring rank can be expressed as a product of elementary matrices and semiprime matrices. …

… First, we compare different tropical matrix factorization methods on the synthetic data matrix
… ], where we have shown that matrix factorization over the tropical semiring is more robust to …

… It is based on a semiring matrix factorisation … for matrix factorisation, we employ semiring
theory. In the following chapters, we will show how to use the semiring rank matrix factorisation …

… In our work, we use tropical semiring to introduce non-linearity into matrix factorization
models. We propose a method called Sparse Tropical Matrix Factorization (STMF) for the …

… In our NP-completeness proof for the k-TMF problem, we will use the matrices over a
certain extension of the tropical semiring which we call here the extended tropical …