Nonnegative Matrix Factorization Requires Irrationality | Zendy

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

AI Assistant Blog Pricing

Home ZAIA Blog

Open Access

Nonnegative Matrix Factorization Requires Irrationality

Author(s) -

Dmitry Chistikov,

Stefan Kiefer,

Ines Marušić,

Mahsa Shirmohammadi,

James Worrell

Publication year - 2017

Publication title -

siam journal on applied algebra and geometry

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.052

H-Index - 15

ISSN - 2470-6566

DOI - 10.1137/16m1078835

Subject(s) - nonnegative matrix , non negative matrix factorization , mathematics , matrix (chemical analysis) , combinatorics , irrationality , matrix decomposition , dimension (graph theory) , irrational number , factorization , symmetric matrix , pure mathematics , algebra over a field , rationality , algorithm , physics , eigenvalues and eigenvectors , chemistry , philosophy , geometry , quantum mechanics , chromatography , epistemology

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

The content you want is available to Zendy users.

Already have an account? Click here to sign in.

Having issues? You can contact us here

Accelerating Research