基于准范数与零范数的矩阵恢复  

Matrix recovery based on quasi-norm and zero norm

作　　者：张令威 刘光宇[1] 吴哲夫 刘光灿 ZHANG Ling-wei;LIU Guang-yu;WU Zhe-fu;LIU Guang-can(Jiangsu Key Laboratory of Big Data Analysis Technology,Nanjing University of Information Science and Technology,Nanjing 210044,China)

机构地区：[1]南京信息工程大学江苏省大数据分析技术重点实验室

出　　处：《计算机工程与设计》2020年第1期85-89,共5页Computer Engineering and Design

基　　金：国家自然科学基金优秀青年基金项目(61622305);国家自然科学基金青年基金项目(61502238);江苏省自然科学基金杰出青年基金项目(BK20160040)

摘　　要：针对高维度矩阵的低秩恢复问题中核范数与l1范数过惩罚导致的结果偏差,提出一种矩阵恢复方法。使用准范数代替低秩恢复问题中常用的核范数约束,使用零范数代替l1范数约束。对于准范数的求解问题,采用与准范数等价的Frobenius/核混合范数进行替代,提出基于交替近似的线性最小化方法对目标函数进行求解。在合成数据与真实数据上的实验结果表明,该算法在主观视觉效果与客观数值比较上都能获得更好的结果。Since the nuclear norm and the l1 norm over-penalize large entries and result in a biased solution for low rank recovery problem of high-dimensional matrices,a matrix recovery method was proposed.Quasi-norm and l0 norm were used to replace nuclear norm and l1 norm prevalently adopted in previous work.Because of the equivalence relation between the quasi-norm and the Frobenius/nuclear hybrid norm,solving quasi-norm was equivalent to solving the Frobenius/nuclear norm.Based on this,an efficient proximal alternating linearized minimization algorithm was designed for solving matrix recovery problems.Experimental results on synthetic data and real-word data show that the proposed algorithm is more accurate than existing matrix recovery algorithms.

关 键 词：核范数 矩阵恢复 准范数 混合范数 交替近似法 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程]