Factorizations of $k$-nonnegative matrices

Nonnegative Ranks, Decompositions, and Factorizations of Nonnegative Matrices

The nonnegative rank of a nonnegative matrix is the smallest number of nonnegative rank-one matrices into which the matrix can be decomposed additively. Such decompositions are useful in diverse scientific disciplines. We obtain characterizations and bounds and show that the nonnegative rank can be computed exactly over the reals by a finite algorithm.

Ela Binary Ranks and Binary Factorizations of Nonnegative Integer Matrices

Abstract. A matrix is binary if each of its entries is either 0 or 1. The binary rank of a nonnegative integer matrix A is the smallest integer b such that A = BC, where B and C are binary matrices, and B has b columns. In this paper, bounds for the binary rank are given, and nonnegative integer matrices that attain the lower bound are characterized. Moreover, binary ranks of nonnegative intege...

Binary ranks and binary factorizations of nonnegative integer matrices

A matrix is binary if each of its entries is either 0 or 1. The binary rank of a nonnegative integer matrix A is the smallest integer b such that A = BC, where B and C are binary matrices, and B has b columns. In this paper, bounds for the binary rank are given, and nonnegative integer matrices that attain the lower bound are characterized. Moreover, binary ranks of nonnegative integer matrices...

On nonnegative sign equivalent and sign similar factorizations of matrices

Computing Symmetric Nonnegative Rank Factorizations

An algorithm is described for the nonnegative rank factorization (NRF) of some completely positive (CP) matrices whose rank is equal to their CP-rank. The algorithm can compute the symmetric NRF of any nonnegative symmetric rank-r matrix that contains a diagonal principal submatrix of that rank and size with leading cost O(rm) operations in the dense case. The algorithm is based on geometric co...