Completion of tree metrics and rank 2 matrices

作者：Bernstein Daniel Irving^*

来源：Linear Algebra and Its Applications, 2017, 533: 1-13.

DOI：10.1016/j.laa.2017.07.016

• Low-rank matrix completion
• Algebraic matroids
• Tropical geometry
• Tree-metric completion

Motivated by applications to low-rank matrix completion, we give a combinatorial characterization of the independent sets in the algebraic matroid associated to the collection of m x n rank-2 matrices and n x n skew-symmetric rank-2 matrices. Our approach is to use tropical geometry to reduce this to a problem about phylogenetic trees which we then solve. In particular, we give a combinatorial description of the collections of pairwise distances between several taxa that may be arbitrarily prescribed while still allowing the resulting dissimilarity map to be completed to a tree metric. Published by Elsevier Inc.

• 出版日期2017-11-15