低秩矩阵恢复算法综述

将鲁棒主成分分析、矩阵补全和低秩表示统称为低秩矩阵恢复,并对近年来出现的低秩矩阵恢复算法进行了简要的综述。讨论了鲁棒主成分分析的各种优化模型及相应的迭代算法,分析了矩阵补全问题及求解它的不精确增广拉格朗日乘子算法,介绍了低秩表示的优化模型及求解算法。最后指出了有待进一步研究的问题。

Survey on algorithms of low-rank matrix recovery

This paper collectively referred robust principal component analysis, matrix completion and low-rank representation to as low-rank matrix recovery, and made a brief survey on the existing algorithms of low-rank matrix recovery. Firstly, it discussed various optimization models and the corresponding iterative algorithms for robust principal component analysis. Next, it analyzed the matrix completion problem and proposed the inexact augmented Lagrange multipliers algorithm to solve the problem. In addition, it introduced the optimization models for the low-rank representation problem and presented the iterative algorithm. Finally, this paper discussed several problems which need further research.