[1]王 臻,杨 敏.核范数随机矩阵求解新方法及其 RPCA 应用[J].计算机技术与发展,2017,27(12):71-76.[doi:10.3969/ j. issn.1673-629X.2017.12.016]
　WANG Zhen,YANG Min.A New Method for Solving Nuclear Norm with Random Matrix and Its Application in Robust Principal Component Analysis[J].Computer Technology and Development,2017,27(12):71-76.[doi:10.3969/ j. issn.1673-629X.2017.12.016]
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核范数随机矩阵求解新方法及其 RPCA 应用()
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《计算机技术与发展》[ISSN:1006-6977/CN:61-1281/TN]

卷:
27
期数:
2017年12期
页码:
71-76
栏目:
智能、算法、系统工程
出版日期:
2017-12-10

文章信息/Info

Title:
A New Method for Solving Nuclear Norm with Random Matrix and Its Application in Robust Principal Component Analysis
文章编号:
1673-629X(2017)12-0071-06
作者:
王 臻; 杨 敏
南京邮电大学 自动化学院,江苏 南京 210023
Author(s):
WANG Zhen; YANG Min
College of Automation,Nanjing University of Posts and Telecommunications,Nanjing 210023,China
关键词:
稳健主成分分析; 交替方向法; 标准随机 k -SVD; 快速随机 k -SVD
Keywords:
RPCA; ADM; prototype randomized k -SVD; faster randomized k -SVD
分类号:
TP391
DOI:
10.3969/ j. issn.1673-629X.2017.12.016
文献标志码:
A
摘要:
RPCA(稳健主成分分析)从原始观测数据中恢复低秩成分和稀疏成分。 RPCA 常用交替方向法迭代求解,算法的效率取决于核范数优化求解,即 SVD 分解。 而 RPCA 在计算机视觉应用中,图像和视频等巨大的数据量为大规模数据SVD 分解带来了很大困难。 采用随机矩阵算法对 SVD 分解进行改进,分别为计数缩略算法、标准随机 k -SVD 算法和快速随机 k -SVD 算法。 主要是对原有大规模数据矩阵进行降维随机采样,使用随机投影算法得到原数据矩阵的一个近似,对这个近似矩阵进行 QR 分解,得到对应的酉矩阵。 对酉矩阵进行相关操作,得到与原矩阵 SVD 相似的结果。算法的时间效率和存储空间得到极大改善。 基于单张图像和视频前景检测等仿真实验,表明所提方法大大提高了 RPCA 迭代优化求解的效率。
Abstract:
 RPCA (Robust Principal Component Analysis) recovers sparse and low rank components from the original observation data. It commonly uses ADM (Alternate Direction Method) for iterative solving,the efficiency of which depends on the nuclear norm optimization solution,that is SVD. The application of RPCA in computer vision,large amounts of data from images and video make it difficult for large-scale data SVD. Therefore,a random matrix algorithm is adopted to improve the SVD,respectively the algorithm of count sketch, the prototype randomized k -SVD and the faster randomized k -SVD. Its main idea is to reduce the size of the original large-scale data matrix and sample randomly. Using the random projection algorithm to obtain an approximation of the original matrix,and operating QR decomposition of this approximate matrix,the unitary matrix corresponding to it is obtained,and then the results which is similar to the SVD can be achieved through correlated operation of unitary matrix. The time and space of the algorithm have been greatly optimized.Simulation based on single image and video foreground detection shows that the proposed method can greatly improve the efficiency of RPCA iterative optimization.

相似文献/References:

[1]张孟资,张立强.交替方向法在小波域图像修复中的应用[J].计算机技术与发展,2013,(10):235.
　ZHANG Meng-zi[],ZHANG Li-qiang[].Application of Alternating Direction Method in Wavelet Domain Image Inpainting[J].Computer Technology and Development,2013,(12):235.
[2]姚刚,杨敏. 稀疏子空间聚类的惩罚参数自调整交替方向法[J].计算机技术与发展,2014,24(11):131.
　YAO Gang,YANG Min. Alternating Direction Method of Self-adjusting Penalty Parameters of Sparse Subspace Clustering[J].Computer Technology and Development,2014,24(12):131.

更新日期/Last Update: 2018-03-06