Algebraic boundary of matrices of nonnegative rank at most three

Rob H. Eggermont*, Emil Horobeţ, Kaie Kubjas

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

2 Citations (Scopus)

Abstract

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

Original languageEnglish
Pages (from-to)62-80
Number of pages19
JournalLinear Algebra and Its Applications
Volume508
DOIs
Publication statusPublished - 1 Nov 2016
MoE publication typeA1 Journal article-refereed

Keywords

  • Equivariant Gröbner basis
  • Mixture model
  • Nonnegative rank
  • Stabilization

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