基于非负矩阵分解的低秩矩阵恢复模型  

Low-rank Matrix Recovery Model Based on Non-negative Matrix Factorization

作　　者：徐梦珂 许道云[2] 魏明俊[2] XU Mengke;XU Daoyun;WEI Mingjun(College of Mathematics and Statistics,Guizhou University,Guiyang 550025;College of Computer Science and Technology,Guizhou University,Guiyang 550025)

机构地区：[1]贵州大学数学与统计学院,贵阳550025 [2]贵州大学计算机科学与计算学院,贵阳550025

出　　处：《计算机与数字工程》2017年第6期1019-1024,共6页Computer & Digital Engineering

基　　金：国家自然科学基金项目(编号:61262006,61540050);贵州省重大应用基础研究项目(编号:黔科合JZ字[2014]2001);贵州省科技厅联合基金(编号:黔科合LH字[2014]7636)资助

摘　　要：针对低秩矩阵恢复需要求解大规模矩阵核范数奇异值分解,计算复杂度高的缺陷,提出基于非负矩阵分解的低秩矩阵恢复模型。新模型通过对传统低秩矩阵恢复模型中的低秩矩阵进行非负因子分解,不但可以保持原始数据的局部特征,而且其低秩性可以快速求解矩阵低秩分解,从而避免了矩阵核范数求解大规模奇异值分解问题。在算法上采用多乘子交替迭代法(ADMM),将全局问题分解为多个易求解的局部子问题,对每个子问题利用拉格朗日乘子法分别对低秩矩阵和稀疏矩阵进行迭代求解。在ORL,AL_Gore和Windows三个图像数据库中Matlab仿真实验结果表明,新模型求解算法比传统低秩矩阵恢复模型识别率高,降秩效果明显,算法的时间复杂度低,从而提高算法运行速度。To overcome the shortage of large-scale nuclear matrix singular value decomposition existing in low-rank matrix re?covery model,the paper proposed low-rank matrix recovery model based on non-negative matrix factorization.Non-negative matrixfactorization(NMF)applied to the low-rank matrix,which could quickly deal with the problem of the decomposition matrix oflow-rank and avoid large-scale nuclear matrix singular value decomposition.Then the algorithm used alternarting directions methodof multipliers(ADMM).ADMM divided the global problem into partial sub-problems.Each sub-problem used Lagrange multipliersto solve low rank matrix and sparse matrix.Experimental results in ORL,AL_Gore and Windows databases showed that low-rank re?covery model based NMF has higher recognition rate,better reduction rank and lower the complexity of the algorithm than other tra?ditional low-rank recovery model.

关 键 词：非负矩阵分解 低秩矩阵恢复 多乘子交替迭代法 奇异值分解 图像识别 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]