Principal Component Analysis (PCA) is a widely used technique for data analysis and dimensionality reduction, but its sensitivity to feature scale and outliers limits its applicability. Robust Principal Component Anal...Principal Component Analysis (PCA) is a widely used technique for data analysis and dimensionality reduction, but its sensitivity to feature scale and outliers limits its applicability. Robust Principal Component Analysis (RPCA) addresses these limitations by decomposing data into a low-rank matrix capturing the underlying structure and a sparse matrix identifying outliers, enhancing robustness against noise and outliers. This paper introduces a novel RPCA variant, Robust PCA Integrating Sparse and Low-rank Priors (RPCA-SL). Each prior targets a specific aspect of the data’s underlying structure and their combination allows for a more nuanced and accurate separation of the main data components from outliers and noise. Then RPCA-SL is solved by employing a proximal gradient algorithm for improved anomaly detection and data decomposition. Experimental results on simulation and real data demonstrate significant advancements.展开更多
Discriminating internal layers by radio echo sounding is important in analyzing the thickness and ice deposits in the Antarctic ice sheet.The signal processing method of synthesis aperture radar(SAR)has been widely us...Discriminating internal layers by radio echo sounding is important in analyzing the thickness and ice deposits in the Antarctic ice sheet.The signal processing method of synthesis aperture radar(SAR)has been widely used for improving the signal to noise ratio(SNR)and discriminating internal layers by radio echo sounding data of ice sheets.This method is not efficient when we use edge detection operators to obtain accurate information of the layers,especially the ice-bed interface.This paper presents a new image processing method via a combined robust principal component analysis-total variation(RPCA-TV)approach for discriminating internal layers of ice sheets by radio echo sounding data.The RPCA-based method is adopted to project the high-dimensional observations to low-dimensional subspace structure to accelerate the operation of the TV-based method,which is used to discriminate the internal layers.The efficiency of the presented method has been tested on simulation data and the dataset of the Institute of Electronics,Chinese Academy of Sciences,collected during CHINARE 28.The results show that the new method is more efficient than the previous method in discriminating internal layers of ice sheets by radio echo sounding data.展开更多
The principal component analysis （PCA） algorithm is widely applied in a diverse range of fields for performance assessment, fault detection, and diagnosis. However, in the presence of noise and gross errors, the non...The principal component analysis （PCA） algorithm is widely applied in a diverse range of fields for performance assessment, fault detection, and diagnosis. However, in the presence of noise and gross errors, the nonlinear PCA （NLPCA） using autoassociative bottle-neck neural networks is so sensitive that the obtained model differs significantly from the underlying system. In this paper, a robust version of NLPCA is introduced by replacing the generally used error criterion mean squared error with a mean log squared error. This is followed by a concise analysis of the corresponding training method. A novel multivariate statistical process monitoring （MSPM） scheme incorporating the proposed robust NLPCA technique is then investigated and its efficiency is assessed through application to an industrial fluidized catalytic cracking plant. The results demonstrate that, compared with NLPCA, the proposed approach can effectively reduce the number of false alarms and is, hence, expected to better monitor real-world processes.展开更多
The existing recommendation algorithms have lower robustness in facing of shilling attacks. Considering this problem, we present a robust recommendation algorithm based on kernel principal component analysis and fuzzy...The existing recommendation algorithms have lower robustness in facing of shilling attacks. Considering this problem, we present a robust recommendation algorithm based on kernel principal component analysis and fuzzy c-means clustering. Firstly, we use kernel principal component analysis method to reduce the dimensionality of the original rating matrix, which can extract the effective features of users and items. Then, according to the dimension-reduced rating matrix and the high correlation characteristic between attack profiles, we use fuzzy c-means clustering method to cluster user profiles, which can realize the effective separation of genuine profiles and attack profiles. Finally, we construct an indicator function based on the attack detection results to decrease the influence of attack profiles on the recommendation, and incorporate it into the matrix factorization technology to design the corresponding robust recommendation algorithm. Experiment results indicate that the proposed algorithm is superior to the existing methods in both recommendation accuracy and robustness.展开更多
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 ...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.展开更多
Gauge duality theory was originated by Preund （1987）, and was recently further investigated by Friedlander et al. （2014）. When solving some matrix optimization problems via gauge dual, one is usually able to avoid...Gauge duality theory was originated by Preund （1987）, and was recently further investigated by Friedlander et al. （2014）. When solving some matrix optimization problems via gauge dual, one is usually able to avoid full matrix decompositions such as singular value and/or eigenvalue decompositions. In such an approach, a gauge dual problem is solved in the first stage, and then an optimal solution to the primal problem can be recovered from the dual optimal solution obtained in the first stage. Recently, this theory has been applied to a class of semidefinite programming （SDP） problems with promising numerical results by Friedlander and Mac^to （2016）. We establish some theoretical results on applying the gauge duality theory to robust principal component analysis （PCA） and general SDP. For each problem, we present its gauge dual problem, characterize the optimality conditions for the primal-dual gauge pair, and validate a way to recover a primal optimal solution from a dual one. These results are extensions of Friedlander and Macedo （2016） from nuclear norm regularization to robust PCA and from a special class of SDP which requires the coefficient matrix in the linear objective to be positive definite to SDP problems without this restriction. Our results provide further understanding in the potential advantages and disadvantages of the gauge duality theory.展开更多
图像融合中,多数边缘保持滤波器在优化过程中会损坏细节和纹理信息,并且噪声也会严重影响融合结果,使得融合结果之间出现边界模糊和细节丢失问题。提出了一种基于RPCA(Robus principal compo-nent association)算法的红外光和可见光图...图像融合中,多数边缘保持滤波器在优化过程中会损坏细节和纹理信息,并且噪声也会严重影响融合结果,使得融合结果之间出现边界模糊和细节丢失问题。提出了一种基于RPCA(Robus principal compo-nent association)算法的红外光和可见光图像融合方法,可有效提高图象清晰度和视觉信息的保真度。首先,利用鲁棒主成分分析(RPCA)分解源图像为低秩部分和稀疏部分,并运用相对全变分和平均能量法对两者进行处理,最后通过NSCT逆变换获得融合图像。实验结果表明,与其他方法相比,该方法所得融合图像的平均梯度、空间频率、边缘强度、互信息量均有提升,提升量级分别为10.6%到72.6%、15%到60.2%、9.7%到69.6%,22.7%到229.7%。展开更多
近年来,鲁棒主成分分析法(Robust Principal Component Analysis,RPCA)被广泛应用到运动目标检测中,但该类方法未能有效利用运动目标的时空连续性先验,容易将动态背景误判为运动目标,且背景恢复精度不高.为此提出一种基于全变分-核回归...近年来,鲁棒主成分分析法(Robust Principal Component Analysis,RPCA)被广泛应用到运动目标检测中,但该类方法未能有效利用运动目标的时空连续性先验,容易将动态背景误判为运动目标,且背景恢复精度不高.为此提出一种基于全变分-核回归的RPCA运动目标检测方法.该方法以RPCA为基础,利用3维全变分模型增强前景的时空连续性,去除动态背景干扰,得到清晰完整的前景.同时,利用基于扩散张量的核回归对背景的时空相关性建模,去除噪声干扰,从而精确恢复背景.在多组公开数据集上的实验结果表明,该方法在动态背景、光照变化等复杂场景中能够较为精确地检测出运动目标和恢复背景.展开更多
为了实现在监控视频中对人体运动目标的准确提取,针对传统的三帧差分法在运动目标提取过程中容易出现"空洞"现象,提出了一种鲁棒主成分分析(robust principal component analysis,RPCA)与三帧差分相融合的运动目标检测算法。...为了实现在监控视频中对人体运动目标的准确提取,针对传统的三帧差分法在运动目标提取过程中容易出现"空洞"现象,提出了一种鲁棒主成分分析(robust principal component analysis,RPCA)与三帧差分相融合的运动目标检测算法。算法通过将RPCA提取的视频当前帧的背景作为三帧差分法的中间帧与视频当前帧的前一帧和视频当前帧分别进行邻间差分,使得三帧差分法在运动目标检测过程中避免了背景像素点所带来的影响,消除了"空洞"现象。仿真结果表明该算法在完整性和准确性方面要优于其他三种传统运动目标检测算法,可以在复杂背景环境中实现准确的运动目标提取。展开更多
文摘Principal Component Analysis (PCA) is a widely used technique for data analysis and dimensionality reduction, but its sensitivity to feature scale and outliers limits its applicability. Robust Principal Component Analysis (RPCA) addresses these limitations by decomposing data into a low-rank matrix capturing the underlying structure and a sparse matrix identifying outliers, enhancing robustness against noise and outliers. This paper introduces a novel RPCA variant, Robust PCA Integrating Sparse and Low-rank Priors (RPCA-SL). Each prior targets a specific aspect of the data’s underlying structure and their combination allows for a more nuanced and accurate separation of the main data components from outliers and noise. Then RPCA-SL is solved by employing a proximal gradient algorithm for improved anomaly detection and data decomposition. Experimental results on simulation and real data demonstrate significant advancements.
基金supported by the National Hi-Tech Research and Development Program of China("863"Project)(Grant No.2011AA040202)the National Natural Science Foundation of China(Grant No.40976114)
文摘Discriminating internal layers by radio echo sounding is important in analyzing the thickness and ice deposits in the Antarctic ice sheet.The signal processing method of synthesis aperture radar(SAR)has been widely used for improving the signal to noise ratio(SNR)and discriminating internal layers by radio echo sounding data of ice sheets.This method is not efficient when we use edge detection operators to obtain accurate information of the layers,especially the ice-bed interface.This paper presents a new image processing method via a combined robust principal component analysis-total variation(RPCA-TV)approach for discriminating internal layers of ice sheets by radio echo sounding data.The RPCA-based method is adopted to project the high-dimensional observations to low-dimensional subspace structure to accelerate the operation of the TV-based method,which is used to discriminate the internal layers.The efficiency of the presented method has been tested on simulation data and the dataset of the Institute of Electronics,Chinese Academy of Sciences,collected during CHINARE 28.The results show that the new method is more efficient than the previous method in discriminating internal layers of ice sheets by radio echo sounding data.
基金Supported by the National High-Tech Research and Development (863) Program of China (No. 2001AA413320)
文摘The principal component analysis （PCA） algorithm is widely applied in a diverse range of fields for performance assessment, fault detection, and diagnosis. However, in the presence of noise and gross errors, the nonlinear PCA （NLPCA） using autoassociative bottle-neck neural networks is so sensitive that the obtained model differs significantly from the underlying system. In this paper, a robust version of NLPCA is introduced by replacing the generally used error criterion mean squared error with a mean log squared error. This is followed by a concise analysis of the corresponding training method. A novel multivariate statistical process monitoring （MSPM） scheme incorporating the proposed robust NLPCA technique is then investigated and its efficiency is assessed through application to an industrial fluidized catalytic cracking plant. The results demonstrate that, compared with NLPCA, the proposed approach can effectively reduce the number of false alarms and is, hence, expected to better monitor real-world processes.
基金Supported by the Scientific Research Foundation of Liaoning Provincial Education Department(L2015240)the National Natural Science Foundation of China(61379116,61503169)the Joint Fund of the Science and Technology Department of Liaoning Province(20170540448)
文摘The existing recommendation algorithms have lower robustness in facing of shilling attacks. Considering this problem, we present a robust recommendation algorithm based on kernel principal component analysis and fuzzy c-means clustering. Firstly, we use kernel principal component analysis method to reduce the dimensionality of the original rating matrix, which can extract the effective features of users and items. Then, according to the dimension-reduced rating matrix and the high correlation characteristic between attack profiles, we use fuzzy c-means clustering method to cluster user profiles, which can realize the effective separation of genuine profiles and attack profiles. Finally, we construct an indicator function based on the attack detection results to decrease the influence of attack profiles on the recommendation, and incorporate it into the matrix factorization technology to design the corresponding robust recommendation algorithm. Experiment results indicate that the proposed algorithm is superior to the existing methods in both recommendation accuracy and robustness.
基金the Doctoral Program of Higher Education of China(No.20120032110034)
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.
基金supported by Hong Kong Research Grants Council General Research Fund (Grant No. 14205314)National Natural Science Foundation of China (Grant No. 11371192)
文摘Gauge duality theory was originated by Preund （1987）, and was recently further investigated by Friedlander et al. （2014）. When solving some matrix optimization problems via gauge dual, one is usually able to avoid full matrix decompositions such as singular value and/or eigenvalue decompositions. In such an approach, a gauge dual problem is solved in the first stage, and then an optimal solution to the primal problem can be recovered from the dual optimal solution obtained in the first stage. Recently, this theory has been applied to a class of semidefinite programming （SDP） problems with promising numerical results by Friedlander and Mac^to （2016）. We establish some theoretical results on applying the gauge duality theory to robust principal component analysis （PCA） and general SDP. For each problem, we present its gauge dual problem, characterize the optimality conditions for the primal-dual gauge pair, and validate a way to recover a primal optimal solution from a dual one. These results are extensions of Friedlander and Macedo （2016） from nuclear norm regularization to robust PCA and from a special class of SDP which requires the coefficient matrix in the linear objective to be positive definite to SDP problems without this restriction. Our results provide further understanding in the potential advantages and disadvantages of the gauge duality theory.
文摘图像融合中,多数边缘保持滤波器在优化过程中会损坏细节和纹理信息,并且噪声也会严重影响融合结果,使得融合结果之间出现边界模糊和细节丢失问题。提出了一种基于RPCA(Robus principal compo-nent association)算法的红外光和可见光图像融合方法,可有效提高图象清晰度和视觉信息的保真度。首先,利用鲁棒主成分分析(RPCA)分解源图像为低秩部分和稀疏部分,并运用相对全变分和平均能量法对两者进行处理,最后通过NSCT逆变换获得融合图像。实验结果表明,与其他方法相比,该方法所得融合图像的平均梯度、空间频率、边缘强度、互信息量均有提升,提升量级分别为10.6%到72.6%、15%到60.2%、9.7%到69.6%,22.7%到229.7%。
文摘近年来,鲁棒主成分分析法(Robust Principal Component Analysis,RPCA)被广泛应用到运动目标检测中,但该类方法未能有效利用运动目标的时空连续性先验,容易将动态背景误判为运动目标,且背景恢复精度不高.为此提出一种基于全变分-核回归的RPCA运动目标检测方法.该方法以RPCA为基础,利用3维全变分模型增强前景的时空连续性,去除动态背景干扰,得到清晰完整的前景.同时,利用基于扩散张量的核回归对背景的时空相关性建模,去除噪声干扰,从而精确恢复背景.在多组公开数据集上的实验结果表明,该方法在动态背景、光照变化等复杂场景中能够较为精确地检测出运动目标和恢复背景.
文摘为了实现在监控视频中对人体运动目标的准确提取,针对传统的三帧差分法在运动目标提取过程中容易出现"空洞"现象,提出了一种鲁棒主成分分析(robust principal component analysis,RPCA)与三帧差分相融合的运动目标检测算法。算法通过将RPCA提取的视频当前帧的背景作为三帧差分法的中间帧与视频当前帧的前一帧和视频当前帧分别进行邻间差分,使得三帧差分法在运动目标检测过程中避免了背景像素点所带来的影响,消除了"空洞"现象。仿真结果表明该算法在完整性和准确性方面要优于其他三种传统运动目标检测算法,可以在复杂背景环境中实现准确的运动目标提取。
