Closed-Form Solutions to A Category of Nuclear Norm Minimization Problems
Information Theory
2010-11-24 v2 Computer Vision and Pattern Recognition
math.IT
Abstract
It is an efficient and effective strategy to utilize the nuclear norm approximation to learn low-rank matrices, which arise frequently in machine learning and computer vision. So the exploration of nuclear norm minimization problems is gaining much attention recently. In this paper we shall prove that the following Low-Rank Representation (LRR) \cite{icml_2010_lrr,lrr_extention} problem: {eqnarray*} \min_{Z} \norm{Z}_*, & {s.t.,} & X=AZ, {eqnarray*} has a unique and closed-form solution, where and are given matrices. The proof is based on proving a lemma that allows us to get closed-form solutions to a category of nuclear norm minimization problems.
Keywords
Cite
@article{arxiv.1011.4829,
title = {Closed-Form Solutions to A Category of Nuclear Norm Minimization Problems},
author = {Guangcan Liu and Ju Sun and Shuicheng Yan},
journal= {arXiv preprint arXiv:1011.4829},
year = {2010}
}