Closed-Form Solutions to A Category of Nuclear Norm Minimization Problems

Details Closed-Form Solutions to A Category of Nuclear Norm Minimization Problems Closed-Form Solutions to A Category of Nuclear Norm Minimization Problems

2010-11-22

arxiv.org/abs/1011.4829v2

NIPS Workshop on Low-Rank Methods for Large-Scale Machine Learning, 2010

Computer Science

Information Theory

Scientific paper

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 $X$ and $A$ 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.

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