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The perturbation analysis of nonconvex low-rank matrix robust recovery

Huang Jianwen(hjw1303987297***at***126.com)
Wang Wendong(d.sylan***at***foxmail.com)
Zhang Feng(zhangf***at***email.swu.edu.cn)

Abstract: In this paper, we bring forward a completely perturbed nonconvex Schatten $p$-minimization to address a model of completely perturbed low-rank matrix recovery. The paper that based on the restricted isometry property generalizes the investigation to a complete perturbation model thinking over not only noise but also perturbation, gives the restricted isometry property condition that guarantees the recovery of low-rank matrix and the corresponding reconstruction error bound. In particular, the analysis of the result reveals that in the case that $p$ decreases $0$ and $a>1$ for the complete perturbation and low-rank matrix, the condition is the optimal sufficient condition $\delta_{2r}<1$ \cite{Recht et al 2010}. The numerical experiments are conducted to show better performance, and provides outperformance of the nonconvex Schatten $p$-minimization method comparing with the convex nuclear norm minimization approach in the completely perturbed scenario.

Keywords: Low rank matrix recovery; Perturbation of linear transformation; Nonconvex Schatten $p$-minimization

Category 1: Applications -- Science and Engineering

Category 2: Applications -- Science and Engineering (Data-Mining )

Citation: Tiansheng Road No. 2, Beibei district, Chongqing, 400715, China,12/2019

Download: [PDF]

Entry Submitted: 12/25/2019
Entry Accepted: 12/26/2019
Entry Last Modified: 12/25/2019

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