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We present an example of a subfield $\mathcal{F}\subset\mathbb{R}$ and a matrix $A$ whose conventional and nonnegative ranks equal five, but the nonnegative rank with respect to $\mathcal{F}$ equals six.
R. Krone, K. Kubjas, Nonnegative rank four boundaries, preprint (2019) arXiv:1902.02868
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S. Fiorini, S. Massar, S. Pokutta, H. R. Tiwary, R. de Wolf, Linear vs. semidefinite extended formulations: exponential separation and strong lower bounds, in Proceedings of the Forty-Fourth Annual ACM Symposium on Theory of Computing,
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A. Moitra, An almost optimal algorithm for computing nonnegative rank, Proceedings of the Twenty-Fourth Annual ACM-SIAM Symposium on Discrete Algorithms
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N. Gillis, The why and how of nonnegative matrix factorization, Regularization, Optimization, Kernels, and Support Vector Machines
R. H. Eggermont, E. Horobet, K. Kubjas, Algebraic boundary of matrices of nonnegative rank at most three
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D. Chistikov, S. Kiefer, I. Marušić, M. Shirmohammadi, J. Worrell, Nonnegative Matrix Factorization Requires Irrationality, SIAM J. Appl. Algebra Geometry
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2014
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K. Kubjas, E. Robeva, B. Sturmfels, Fixed points of the EM algorithm and nonnegative rank boundaries, Annals of Statistics
2015
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Y. Shitov, Nonnegative rank depends on the field, preprint (2015) arXiv:1505.01893v1
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D. Speyer, Re: Polynomial with two repeated roots
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