Nonnegative rank

Nonnegative rank

Nonnegative Matrices and Stochastic Matrices

Published in Leslie Hogben, Richard Brualdi, Anne Greenbaum, Roy Mathias, Handbook of Linear Algebra, 2006

A nonnegative factorization of a nonnegative matrix A ∈ Rm×n is a representation A = LR of A with L and R as nonnegative matrices. The nonnegative rank of A is the smallest number of columns of L (rows of R) in such a factorization.

Conic optimization-based algorithms for nonnegative matrix factorization

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Journal Information

Published in Optimization Methods and Software, 2023

Valentin Leplat, Yurii Nesterov, Nicolas Gillis, François Glineur

The minimum factorization rank K for which an exact NMF exists is called the nonnegative rank of V and is denoted . We have The computation of the nonnegative rank is NP-hard [30] and is a research topic on its own; see [13, Chapter 3][8,9] and the references therein for recent progress on this question.

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Nonnegative Matrices and Stochastic Matrices

Conic optimization-based algorithms for nonnegative matrix factorization