Algebraic boundary of matrices of nonnegative rank at most three

作者: Rob H Eggermont , Emil Horobeţ , Kaie Kubjas , None

DOI: 10.1016/J.LAA.2016.06.036

关键词:

摘要: Understanding the boundary of set matrices nonnegative rank at most r is important for applications in nonconvex optimization. The Zariski closure 3 reducible. We give a minimal generating ideal each irreducible component. In fact, this Grobner basis with respect to graded reverse lexicographic order. This solves conjecture by Robeva, Sturmfels and last author.

参考文章(24)
Sebastian Ewert, Meinard Müller, Masataka Goto, Meinard Muller, Markus Schedl, Score-informed Source Separation for Music Signals Multimodal Music Processing. ,vol. 3, pp. 73- 94 ,(2012) , 10.4230/DFU.VOL3.11041.73
Pablo A. Parrilo, Hamza Fawzi, Self-scaled bounds for atomic cone ranks: applications to nonnegative rank and cp-rank Mathematical Programming. ,vol. 158, pp. 417- 465 ,(2016) , 10.1007/S10107-015-0937-7
Daniel D. Lee, H. Sebastian Seung, Learning the parts of objects by non-negative matrix factorization Nature. ,vol. 401, pp. 788- 791 ,(1999) , 10.1038/44565
Fabio Rapallo, Cristiano Bocci, Enrico Carlini, Perturbation of matrices and non-negative rank with a view toward statistical models arXiv: Combinatorics. ,(2010)
A. P. Dempster, N. M. Laird, D. B. Rubin, Maximum Likelihood from Incomplete Data Via theEMAlgorithm Journal of the Royal Statistical Society: Series B (Methodological). ,vol. 39, pp. 1- 22 ,(1977) , 10.1111/J.2517-6161.1977.TB01600.X
Stephen A. Vavasis, On the Complexity of Nonnegative Matrix Factorization Siam Journal on Optimization. ,vol. 20, pp. 1364- 1377 ,(2009) , 10.1137/070709967
Bernd Sturmfels, Maximum likelihood for matrices with rank constraints Proceedings of the 39th International Symposium on Symbolic and Algebraic Computation - ISSAC '14. pp. 17- 17 ,(2014) , 10.1145/2608628.2627490