Nonnegative Matrix Factorization Requires Irrationality

Dmitry Chistikov; Stefan Kiefer; Ines Marušić; Mahsa Shirmohammadi; James Worrell

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arXiv · 1605.06848

Nonnegative Matrix Factorization Requires Irrationality

Dmitry Chistikov·Stefan Kiefer·Ines Marušić·Mahsa Shirmohammadi·James Worrell

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Abstract

Nonnegative matrix factorization (NMF) is the problem of decomposing a given nonnegative $n \times m$ matrix $M$ into a product of a nonnegative $n \times d$ matrix $W$ and a nonnegative $d \times m$ matrix $H$. A longstanding open question, posed by Cohen and Rothblum in 1993, is whether a rational matrix $M$ always has an NMF of minimal inner dimension $d$ whose factors $W$ and $H$ are also rational. We answer this question negatively, by exhibiting a matrix for which $W$ and $H$ require irrational entries.

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BibTeX RIS

Dmitry Chistikov, Stefan Kiefer, Ines Marušić, Mahsa Shirmohammadi, James Worrell. 2016-05-22. Nonnegative Matrix Factorization Requires Irrationality. https://arxiv.org/abs/1605.06848

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