6 research outputs found
Nonnegative Matrix Factorization Requires Irrationality
Nonnegative matrix factorization (NMF) is the problem of decomposing a given
nonnegative matrix into a product of a nonnegative matrix and a nonnegative matrix . A longstanding open
question, posed by Cohen and Rothblum in 1993, is whether a rational matrix
always has an NMF of minimal inner dimension whose factors and are
also rational. We answer this question negatively, by exhibiting a matrix for
which and require irrational entries.Comment: Journal version, to appear in the SIAM Journal on Applied Algebra and
Geometry (SIAGA