摘要
针对在许多实际应用中数据以矩阵形式而非向量形式存在的问题,重点讨论含缺失成分的矩阵低秩逼近问题的广义版本,即如何对一组含缺失成分的矩阵进行低秩逼近.首先构造一个最优化问题来表达原始的广义低秩逼近问题,该最优化问题最小化输入矩阵组中已知成分的总重构误差;然后提出了一种迭代优化算法来求解上述的最优化问题;最后给出详细的算法分析.大量的模拟实验与真实图像实验结果表明,文中算法具有较好的性能.
Considering that data used in many applications are intrinsically in matrix form rather than in vector form, this paper focuses on the generalized version of the problem of a low-rank approximation of a matrix with missing components, i.e. low-rank approximations of a set of matrices with missing components. This generalized problem is formulated as an optimization problem at first, which minimizes the total reconstruction error of the known components in these matrices. Then, an iterative algorithm is designed for calculating the generalized low-rank approximations of matrices with missing components, called GLRAMMC. Finally, detailed algorithmic analysis is given. Extensive experimental results on synthetic data as well as on real image data show the effectiveness of our proposed algorithm.
出处
《计算机辅助设计与图形学学报》
EI
CSCD
北大核心
2015年第11期2065-2076,共12页
Journal of Computer-Aided Design & Computer Graphics
基金
国家自然科学基金(61375042
61273290)
国家"八六三"高技术研究发展计划(2014AA015202)
中央高校基本科研业务费专项基金(2013JBZ003)
教育部博士点基金(20120009110008)
教育部新世纪优秀人才支持计划(NCET-12-0768)
关键词
广义低秩逼近
缺失成分
重构误差
迭代优化算法
generalized low-rank approximation
missing components
reconstruction error
iterative algorithm
