Robust principal component analysis?: Recovering low-rank matrices from sparse errors

2010 ◽  
Author(s):  
Emmanuel Candes ◽  
Xiaodong Li ◽  
Yi Ma ◽  
John Wright
Keyword(s):  
Principal Component Analysis ◽  
Principal Component ◽  
Component Analysis ◽  
Low Rank ◽  
Robust Principal Component Analysis

scholarly journals Differentially Expressed Genes Extracted by the Tensor Robust Principal Component Analysis (TRPCA) Method

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-13 ◽  
Author(s):  
Yue Hu ◽  
Jin-Xing Liu ◽  
Ying-Lian Gao ◽  
Sheng-Jun Li ◽  
Juan Wang
Keyword(s):  
Principal Component Analysis ◽  
Differentially Expressed Genes ◽  
Principal Component ◽  
Component Analysis ◽  
Differentially Expressed ◽  
Low Rank ◽  
Cancer Gene ◽  
Sequencing Data ◽  
Robust Principal Component Analysis ◽  
The Matrix

In the big data era, sequencing technology has produced a large number of biological sequencing data. Different views of the cancer genome data provide sufficient complementary information to explore genetic activity. The identification of differentially expressed genes from multiview cancer gene data is of great importance in cancer diagnosis and treatment. In this paper, we propose a novel method for identifying differentially expressed genes based on tensor robust principal component analysis (TRPCA), which extends the matrix method to the processing of multiway data. To identify differentially expressed genes, the plan is carried out as follows. First, multiview data containing cancer gene expression data from different sources are prepared. Second, the original tensor is decomposed into a sum of a low-rank tensor and a sparse tensor using TRPCA. Third, the differentially expressed genes are considered to be sparse perturbed signals and then identified based on the sparse tensor. Fourth, the differentially expressed genes are evaluated using Gene Ontology and Gene Cards tools. The validity of the TRPCA method was tested using two sets of multiview data. The experimental results showed that our method is superior to the representative methods in efficiency and accuracy aspects.

Low-rank tensor train for tensor robust principal component analysis

2020 ◽  
Vol 367 ◽  
pp. 124783 ◽  
Author(s):  
Jing-Hua Yang ◽  
Xi-Le Zhao ◽  
Teng-Yu Ji ◽  
Tian-Hui Ma ◽  
Ting-Zhu Huang
Keyword(s):  
Principal Component Analysis ◽  
Principal Component ◽  
Component Analysis ◽  
Low Rank ◽  
Robust Principal Component Analysis ◽  
Rank Tensor

scholarly journals Tensor Robust Principal Component Analysis via Non-Convex Low Rank Approximation

2019 ◽  
Vol 9 (7) ◽  
pp. 1411 ◽  
Author(s):  
Shuting Cai ◽  
Qilun Luo ◽  
Ming Yang ◽  
Wen Li ◽  
Mingqing Xiao
Keyword(s):  
Principal Component Analysis ◽  
Critical Role ◽  
Principal Component ◽  
Component Analysis ◽  
Current Approach ◽  
Low Rank ◽  
Tensor Rank ◽  
Robust Principal Component Analysis ◽  
Augmented Lagrange Multiplier ◽  
Convex Regularization

Tensor Robust Principal Component Analysis (TRPCA) plays a critical role in handling high multi-dimensional data sets, aiming to recover the low-rank and sparse components both accurately and efficiently. In this paper, different from current approach, we developed a new t-Gamma tensor quasi-norm as a non-convex regularization to approximate the low-rank component. Compared to various convex regularization, this new configuration not only can better capture the tensor rank but also provides a simplified approach. An optimization process is conducted via tensor singular decomposition and an efficient augmented Lagrange multiplier algorithm is established. Extensive experimental results demonstrate that our new approach outperforms current state-of-the-art algorithms in terms of accuracy and efficiency.

Non-Line-of-Sight Positioning Algorithm Based on Robust Principal Component Analysis

2014 ◽  
Vol 998-999 ◽  
pp. 889-893
Author(s):  
Zhu Lin Xiong ◽  
Ce Lun Liu ◽  
Wei Du ◽  
Ze Bin Xie
Keyword(s):  
Principal Component Analysis ◽  
Mobile Station ◽  
Principal Component ◽  
Component Analysis ◽  
Low Rank ◽  
Line Of Sight ◽  
Time Of Arrival ◽  
Robust Principal Component Analysis ◽  
Error Matrix ◽  
Non Line Of Sight

Non-Line-of-Sight (NLOS) propagation problems badly degrade the accuracy of wireless mobile positioning algorithms, which incurs a large positive bias in the Time-of-Arrival (TOA) measurements. Under several assumptions, the Hankel matrix of TOA data can be decomposed into a low-rank distance matrix and a sparse error matrix. This paper utilizes the robust principal component analysis (RPCA) method to solve the decomposition problem. After estimating the distance, the positioning problem can use existing Line-of-Sight (LOS) based algorithms to calculate the coordinate of the mobile station (MS). Simulation results show our method outperforms other existing NLOS positioning methods and the RPCA based matrix decomposition process can eliminate NLOS effect efficiently.

scholarly journals A Novel Robust Principal Component Analysis Algorithm of Nonconvex Rank Approximation

2020 ◽  
Vol 2020 ◽  
pp. 1-17
Author(s):  
E. Zhu ◽  
M. Xu ◽  
D. Pi
Keyword(s):  
Principal Component Analysis ◽  
Principal Component ◽  
Component Analysis ◽  
Low Rank ◽  
Robust Principal Component Analysis ◽  
Approximation Function ◽  
Rank Matrix ◽  
Rank Approximation ◽  
Low Rank Matrix ◽  
Novel Model

Noise exhibits low rank or no sparsity in the low-rank matrix recovery, and the nuclear norm is not an accurate rank approximation of low-rank matrix. In the present study, to solve the mentioned problem, a novel nonconvex approximation function of the low-rank matrix was proposed. Subsequently, based on the nonconvex rank approximation function, a novel model of robust principal component analysis was proposed. Such model was solved with the alternating direction method, and its convergence was verified theoretically. Subsequently, the background separation experiments were performed on the Wallflower and SBMnet datasets. Furthermore, the effectiveness of the novel model was verified by numerical experiments.

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