Exact solutions in low-rank approximation with zeros
Algebraic Geometry
2022-04-26 v2 Optimization and Control
Abstract
Low-rank approximation with zeros aims to find a matrix of fixed rank and with a fixed zero pattern that minimizes the Euclidean distance to a given data matrix. We study the critical points of this optimization problem using algebraic tools. In particular, we describe special linear, affine, and determinantal relations satisfied by the critical points. We also investigate the number of critical points and how this number is related to the complexity of nonnegative matrix factorization problem.
Keywords
Cite
@article{arxiv.2010.15636,
title = {Exact solutions in low-rank approximation with zeros},
author = {Kaie Kubjas and Luca Sodomaco and Elias Tsigaridas},
journal= {arXiv preprint arXiv:2010.15636},
year = {2022}
}
Comments
revised version to appear on Linear Algebra and its Applications, 26 pages, 1 figure, 8 tables