- The perturbation analysis of nonconvex low-rank matrix robust recovery Huang Jianwen(hjw1303987297126.com) Wang Wendong(d.sylanfoxmail.com) Zhang Feng(zhangfemail.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: 12/25/2019Entry Accepted: 12/26/2019Entry Last Modified: 12/25/2019Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Optmization Society.