Robust principal component analysis via truncated nuclear norm minimization

详细信息    查看全文

• 作者：Yan Zhang 张 艳 ; Jichang Guo 郭继昌 ; Jie Zhao 赵 洁…
• 关键词：truncated nuclear norm minimization (TNNM) ; robust principal component analysis (PCA) ; low ; rank ; alternating direction method
• 刊名：Journal of Shanghai Jiaotong University (Science)
• 出版年：2016
• 出版时间：October 2016
• 年：2016
• 卷：21
• 期：5
• 页码：576-583
• 全文大小：883 KB
• 刊物类别：Engineering
• 刊物主题：Electrical Engineering
  Life Sciences
  Architecture
  Chinese Library of Science
  
• 出版者：Shanghai Jiao Tong University Press
• ISSN：1995-8188
• 卷排序：21

文摘

Robust principal component analysis (PCA) is widely used in many applications, such as image processing, data mining and bioinformatics. The existing methods for solving the robust PCA are mostly based on nuclear norm minimization. Those methods simultaneously minimize all the singular values, and thus the rank cannot be well approximated in practice. We extend the idea of truncated nuclear norm regularization (TNNR) to the robust PCA and consider truncated nuclear norm minimization (TNNM) instead of nuclear norm minimization (NNM). This method only minimizes the smallest N − r singular values to preserve the low-rank components, where N is the number of singular values and r is the matrix rank. Moreover, we propose an effective way to determine r via the shrinkage operator. Then we develop an effective iterative algorithm based on the alternating direction method to solve this optimization problem. Experimental results demonstrate the efficiency and accuracy of the TNNM method. Moreover, this method is much more robust in terms of the rank of the reconstructed matrix and the sparsity of the error.