Robust Principal Component Analysis Method Research Articles

Financial Development and Subnational Export Performance: Evidence from the Indian States

The present study investigates the relationship between export performance and the level of financial development for 30 Indian states and union territories (UTs) from 2011–12 to 2020–21. The study first ranks the states and UTs on the parameters of financial development and physical infrastructure using the robust principal component analysis method. By applying the instrumental variable fixed effects panel data technique, the study observes that the level of financial development has a significant positive impact on the export performance of the states. The study also finds a positive effect of the availability of physical infrastructure, quality of governance and fiscal position on states’ export performance but does not observe a significant role of political stability in this context. The results suggest that export growth in the economically laggard and Himalayan states can come through policy interventions to improve financial development. In contrast, landlocked states need better physical infrastructure to facilitate easier production and transportation of export goods. The study lends new perspectives to the nascent literature on inter-regional disparities in India’s export performance and is expected to provide insights into improving the sub-national export performance of other developing countries as well. JEL Codes: F14, F36, F4

An Application of Robust Principal Component Analysis Methods for Anomaly Detection

Ensuring a secure network environment is crucial, especially with the increasing number of threats and attacks on digital systems. Implementing effective security measures, such as anomaly detection can help detect any abnormal traffic patterns. Several statistical and machine learning approaches are used to detect network anomalies including robust statistical methods. Robust methods can help identify abnormal traffic patterns and distinguish them from normal traffic accurately. In this study, a robust Principal Component Analysis (PCA) method called ROBPCA which is known for its extensive use in the literature of chemometrics and genetics is utilized for detecting network anomalies and compared with another robust PCA method called PCAGRID. The anomaly detection performances of these methods are evaluated by injecting synthetic traffic volume into a well-known traffic matrix. According to the application results, when the normal subspace is contaminated with large anomalies the ROBPCA method provides much better performance in detecting anomalies.

Improved quaternion robust principal component analysis for color image recovery

Numerous studies have demonstrated the potential of robust principal component analysis (RPCA) in image recovery. However, conventional RPCA methods for color image recovery apply RPCA independently to each color channel, which ignores the correlation information of the red, green and blue channels. To improve the performance of RPCA-based methods and draw inspiration from the success of quaternion representation in color image processing, we propose an improved quaternion RPCA (IQRPCA) method for color image recovery. The IQRPCA method treats all color channels holistically and considers the correlation information of different color channels naturally. In addition, we have developed a quaternion nuclear norm known as improved quaternion Cauchy nuclear norm, which produces an even more effective and robust approach to color image recovery task. Compared to the RPCA method in the quaternion setting, the IQRPCA method treats the singular values differently, which shows better recovery performance than competing methods. Furthermore, we provide a convergence analysis of the proposed method. Our experiments confirm the effectiveness of IQRPCA in the application of color image recovery.

Enhancing SAR Multipath Ghost Image Suppression for Complex Structures through Multi-Aspect Observation

When Synthetic Aperture Radar (SAR) observes complex structural targets such as oil tanks, it is easily interfered with by multipath signals, resulting in a large number of multipath ghost images in the SAR image, which seriously affect the image clarity. To address this problem, this paper proposes a multi-aspect multipath suppression method. This method observes complex structural targets from different azimuth angles to obtain a multi-aspect image sequence and then uses the difference in sequence features between the target image and the multipath ghost image with respect to aspect angle to separate them. This paper takes a floating-roof oil tank as an example to analyze the propagation path and the ghost image characteristics of multipath signals under different observation aspects. We conclude that the scattering center of the multipath ghost image changes with the radar observation aspect, whereas the scattering center of the target image does not. This paper uses the Robust Principal Component Analysis (RPCA) method to decompose the image sequence matrix into two parts: a sparse matrix and a low-rank matrix. The low-rank matrix represents the aspect-stable principal component in the image sequence; that is, the real scattering center. The sparse matrix represents the part of the image sequence that deviates from the principal component; that is, the signal that varies with aspect, mainly including multipath signals, sidelobes, anisotropic signals, etc. By reconstructing the low-rank matrix and the sparse matrix, respectively, we can obtain the image after multipath signal suppression and also the multipath ghost image. Both the target and the multipath signal provide useful information. The image after multipath signal suppression is useful for obtaining the structural information of the target, and the multipath ghost image is useful for analyzing the multipath phenomenon of the complex structure target. This paper conducts experimental verification using real airborne SAR data of an external floating roof oil tank and compares three methods: RPCA, PCA, and sub-aperture fusion method. The experiment shows that the RPCA method can better separate the target image and the multipath ghost image.

Mechanical Fault Diagnosis With Noisy Multisource Signals via Unified Pinball Loss Intuitionistic Fuzzy Support Tensor Machine

In this paper, a challenging and significant intelligent fault diagnosis task is investigated, in which multisource sensor signals with intense noise and outlier disturbances are jointly analyzed. Such a scenario has hardly been considered in industrial research. To this end, we develop a novel tensor-based nonlinear classifier called unified pinball loss intuitionistic fuzzy support tensor machine (UPIFSTM), which can successfully solve the above tasks and improve the performance of fault diagnosis in practical applications. First, the noisy multisource signals are converted into time-frequency images and reconstructed into tensor samples to mine the time domain, frequency domain features and coupled structure information in the spatial domain. Next, we design two nonlinear forms of nonmembership functions in the tensor space, and obtain an intuitionistic fuzzy score for each training sample to enhance the robustness of the model. Subsequently, pinball loss function is introduced to better handle noise sensitivity and resampling instability problems. Note that, we employ the tensor robust principal component analysis method to accurately recover the low-rank tensors corrupted by sparse noise from the original tensors. Finally, two numerical examples are presented to verify the feasibility and validity of the proposed method.

Cauchy robust principal component analysis with applications to high-dimensional data sets

Principal component analysis (PCA) is a standard dimensionality reduction technique used in various research and applied fields. From an algorithmic point of view, classical PCA can be formulated in terms of operations on a multivariate Gaussian likelihood. As a consequence of the implied Gaussian formulation, the principal components are not robust to outliers. In this paper, we propose a modified formulation, based on the use of a multivariate Cauchy likelihood instead of the Gaussian likelihood, which has the effect of robustifying the principal components. We present an algorithm to compute these robustified principal components. We additionally derive the relevant influence function of the first component and examine its theoretical properties. Simulation experiments on high-dimensional datasets demonstrate that the estimated principal components based on the Cauchy likelihood typically outperform, or are on a par with, existing robust PCA techniques. Moreover, the Cauchy PCA algorithm we have used has much lower computational cost in very high dimensional settings than the other public domain robust PCA methods we consider.

Discrete Robust Principal Component Analysis via Binary Weights Self-Learning.

Principal component analysis (PCA) is a typical unsupervised dimensionality reduction algorithm, and one of its important weaknesses is that the squared l2 -norm cannot overcome the influence of outliers. Existing robust PCA methods based on paradigm have the following two drawbacks. First, the objective function of PCA based on the l1 -norm has no rotational invariance and limited robustness to outliers, and its solution mostly uses a greedy search strategy, which is expensive. Second, the robust PCA based on the l2,1 -norm and the l2,p -norm is essential to learn probability weights for data, which only weakens the influence of outliers on the learning projection matrix and cannot be completely eliminated. Moreover, the ability to detect anomalies is also very poor. To solve these problems, we propose a novel discrete robust principal component analysis (DRPCA). Through self-learning binary weights, the influence of outliers on the projection matrix and data center estimation can be completely eliminated, and anomaly detection can be directly performed. In addition, an alternating iterative optimization algorithm is designed to solve the proposed problem and realize the automatic update of binary weights. Finally, our proposed model is successfully applied to anomaly detection applications, and experimental results demonstrate that the superiority of our proposed method compared with the state-of-the-art methods.

Tensor robust principal component analysis based on Bayesian Tucker decomposition for thermographic inspection

Thermographic inspection is considered an effective and promising nondestructive testing tool because of its intuitiveness, wide range and noncontact property. Despite this, the detection of weak defects and the recovery of their shape remain difficult, particularly when the surface being inspected is the opposite of the surface being drilled. This study proposes a new tensor robust principal component analysis method based on Bayesian Tucker decomposition to improve the spatial resolution of thermography. A hierarchical form of a generalized Student-t prior is imposed on the model parameters in the Bayesian framework so as to approximate the low-rank component related to the defect feature. Through variational Bayesian inference, all model parameters are adaptively estimated. Based on two experimental data, it appears that the proposed method is capable of improving the spatial resolution and detection accuracy of the thermographic inspection system.

An Unsupervised Image Denoising Method Using a Nonconvex Low-Rank Model with TV Regularization

In real-world scenarios, images may be affected by additional noise during compression and transmission, which interferes with postprocessing such as image segmentation and feature extraction. Image noise can also be induced by environmental variables and imperfections in the imaging equipment. Robust principal component analysis (RPCA), one of the traditional approaches for denoising images, suffers from a failure to efficiently use the background’s low-rank prior information, which lowers its effectiveness under complex noise backgrounds. In this paper, we propose a robust PCA method based on a nonconvex low-rank approximation and total variational regularization (TV) to model the image denoising problem in order to improve the denoising performance. Firstly, we use a nonconvex γ-norm to address the issue that the traditional nuclear norm penalizes large singular values excessively. The rank approximation is more accurate than the nuclear norm thanks to the elimination of matrix elements with substantial approximation errors to reduce the sparsity error. The method’s robustness is improved by utilizing the low sensitivity of the γ-norm to outliers. Secondly, we use the l1-norm to increase the sparsity of the foreground noise. The TV norm is used to improve the smoothness of the graph structure in accordance with the sparsity of the image in the gradient domain. The denoising effectiveness of the model is increased by employing the alternating direction multiplier strategy to locate the global optimal solution. It is important to note that our method does not require any labeled images, and its unsupervised denoising principle enables the generalization of the method to different scenarios for application. Our method can perform denoising experiments on images with different types of noise. Extensive experiments show that our method can fully preserve the edge structure information of the image, preserve important features of the image, and maintain excellent visual effects in terms of brightness smoothing.

Novel RPCA with nonconvex logarithm and truncated fraction norms for moving object detection

Recently, some successful applications used by robust principal component analysis (RPCA) have boosted the exploration of pattern recognition, especially for moving object detection. However, many representative RPCA methods, which aim to solve the problem of moving object detection, do not have better surrogate functions for approximating the sparse and low rank items of conventional RPCA, so they always miss some notable features of moving objects. This limitation has been motivating continuous research on RPCA. In this paper, a novel RPCA with nonconvex logarithm and truncated fraction norms (NLTFN) is proposed, which adopts a nonconvex logarithm norm and a truncated fraction norm to approximate the sparse and low rank items of conventional RPCA, respectively. Meanwhile, we extend the NLTFN to the other novel RPCA with robust nonconvex logarithm and truncated fraction norms (RNLTFN) method for enhancing the robustness against noise via introducing the noise item. Furthermore, the alternating direction method of multipliers (ADMM) is presented for solving our proposed NLTFN and RNLTFN methods effectively in this paper. At last, some experiments, which are conducted for videos with and without noise using different compared methods, finally demonstrate the better superiority and robustness of the proposed NLTFN and RNLTFN methods over other compared methods.

Highlight removal for endoscopic images based on accelerated adaptive non-convex RPCA decomposition

Objective:Highlights always occur in endoscopic images due to their special imaging environment. It not only increases the difficulty of observation and diagnosis from surgeons, but also influences the performance of Mixed/Augmented Reality techniques in surgery navigation.Methods:In this paper, we propose a novel accelerated adaptive non-convex robust principal component analysis method (AANC-RPCA) to remove highlights in endoscopic images. We first detect absolute highlight pixels of the enhanced endoscopic images with adaptive threshold segmentation. The quasi-convex function is proposed to approximate a new non-convex objective function. With detected highlight pixels and quasi-convex function, it introduces gradient to shrink sparse matrix and obtains a faster speed of convergence. Then we divide the image into multiple blocks and perform the parallel computation to enhance the efficiency. Finally, we design a weighted template that decays outward with dilation and linear filtering to reconstruct the endoscopic images. Our approach is almost independent of hyper-parameters and can achieve adaptive decomposition.Results:It has been verified on multiple types of endoscopic images through experiments and clinical blind tests. The results demonstrate that our method can obtain the best performance for the recovered images with more details in a shorter time (about 3–5 times).Conclusion:Coupled with the user study, both the quantitative and qualitative results indicate that our approach has the potential to be highly useful in endoscopy images. Compared with the existing highlight removal approaches, our method obtains the SOTA results and has the potential to be applied in the various medical processing processes.

Gross outlier removal and fault data recovery for SHM data of dynamic responses by an annihilating filter‐based Hankel‐structured robust PCA method

Gross outlier removal and fault data recovery for SHM data of dynamic responses by an annihilating filter‐based Hankel‐structured robust PCA method

Changed Detection Based on Patch Robust Principal Component Analysis

Change detection on retinal fundus image pairs mainly seeks to compare the important differences between a pair of images obtained at two different time points such as in anatomical structures or lesions. Illumination variation usually challenges the change detection methods in many cases. Robust principal component analysis (RPCA) takes intensity normalization and linear interpolation to greatly reduce the illumination variation between the continuous frames and then decomposes the image matrix to obtain the robust background model. The matrix-RPCA can obtain clear change regions, but when there are local bright spots on the image, the background model is vulnerable to illumination, and the change detection results are inaccurate. In this paper, a patch-based RPCA (P-RPCA) is proposed to detect the change of fundus image pairs, where a pair of fundus images is normalized and linearly interpolated to expand a low-rank image sequence; then, images are divided into many patches to obtain an image-patch matrix, and finally, the change regions are obtained by the low-rank decomposition. The proposed method is validated on a set of large lesion image pairs in clinical data. The area under curve (AUC) and mean average precision (mAP) of the method proposed in this paper are 0.9832 and 0.8641, respectively. For a group of small lesion image pairs with obvious local illumination changes in clinical data, the AUC and mAP obtained by the P-RPCA method are 0.9893 and 0.9401, respectively. The results show that the P-RPCA method is more robust to local illumination changes than the RPCA method, and has stronger performance in change detection than the RPCA method.

Data Recovery Technology Based on Subspace Clustering

High-dimensional data usually exist asymptotically in low-dimensional space. In this study, we mainly use tensor t-product as a tool to propose new algorithms in data clustering and recovery and verify them on classical data sets. This study defines the “singular values” of tensors, adopts a weighting strategy for the singular values, and proposes a tensor-weighted kernel norm minimization robust principal component analysis method, which is used to restore low-probability low-rank third-order tensor data. Experiments on synthetic data show that in the recovery of strictly low-rank data, the tensor method and weighting strategy can also obtain more accurate recovery when the rank is relatively large, which improves the volume of the rank. The proposed method combines the two and reflects its superiority through the restoration of 500 images under a small probability noise level.

Minimum regularized covariance determinant and principal component analysis-based method for the identification of high leverage points in high dimensional sparse data

ABSTRACT The main aim of this paper is to propose a novel method (RMD-MRCD-PCA) of identification of High Leverage Points (HLPs) in high-dimensional sparse data. It is to address the weakness of the Robust Mahalanobis Distance (RMD) method which is based on the Minimum Regularized Covariance Determinant (RMD-MRCD), which indicates a decrease in its performance as the number of independent variables (p) increases. The RMD-MRCD-PCA is developed by incorporating the Principal Component Analysis (PCA) in the MRCD algorithm whereby this robust approach shrinks the covariance matrix to make it invertible and thus, can be employed to compute the RMD for high dimensional data. A simulation study and two real data sets are used to illustrate the merit of our proposed method compared to the RMD-MRCD and Robust PCA (ROBPCA) methods. Findings show that the performance of the RMD-MRCD is similar to the performance of the RMD-MRCD-PCA for p close to 200. However, its performance tends to decrease when the number of p is more than 200 and worsens at p equals 700 and larger. On the other hand, the ROBPCA is not effective for less than 20% contamination as it suffers from serious swamping problems.

Missing and Corrupted Data Recovery in Wireless Sensor Networks Based on Weighted Robust Principal Component Analysis.

Although wireless sensor networks (WSNs) have been widely used, the existence of data loss and corruption caused by poor network conditions, sensor bandwidth, and node failure during transmission greatly affects the credibility of monitoring data. To solve this problem, this paper proposes a weighted robust principal component analysis method to recover the corrupted and missing data in WSNs. By decomposing the original data into a low-rank normal data matrix and a sparse abnormal matrix, the proposed method can identify the abnormal data and avoid the influence of corruption on the reconstruction of normal data. In addition, the low-rankness is constrained by weighted nuclear norm minimization instead of the nuclear norm minimization to preserve the major data components and ensure credible reconstruction data. An alternating direction method of multipliers algorithm is further developed to solve the resultant optimization problem. Experimental results demonstrate that the proposed method outperforms many state-of-the-art methods in terms of recovery accuracy in real WSNs.

Tensor-Based Robust Principal Component Analysis With Locality Preserving Graph and Frontal Slice Sparsity for Hyperspectral Image Classification

Tensor-based robust principal component analysis (PCA) methods are efficient to discover the low-rank part of a hyperspectral image for reducing redundant information and guarantee good classification results. However, current methods cannot remove noise adequately, and the residual noise remaining in the low-rank image limits the further improvement of classification performance. Thus, enhancing the robustness to noise is important and helpful for tensor-based robust PCA (RPCA) methods to process hyperspectral images. To this end, we propose a tensor-based RPCA method with a locality preserving graph and frontal slice sparsity (LPGTRPCA) for hyperspectral image classification. Specifically, a tensor <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$l_{2,2,1}$ </tex-math></inline-formula> norm that requires the frontal slice sparsity of a tensor is defined to extract the noise in the hyperspectral image from the frontal direction. What is more, a position-based Laplacian graph that preserves the local structures of a tensor according to the spatial position is designed for relieving the impact of the residual noise remaining in the low-rank image. Based on the tensor nuclear norm, the tensor <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$l_{2,2,1}$ </tex-math></inline-formula> norm, and the position-based Laplacian graph, LPGTRPCA efficiently separates the low-rank part with little noise from a raw hyperspectral image and achieves more robust classification results than current methods. LPGTRPCA is optimized by the alternative direction multiplier method (ADMM), and the convergence of solutions is experimentally demonstrated. In the experiments conducted on Indian Pines, Pavia University, and Salinas datasets, LPGTRPCA outperformed various state-of-the-art and classical tensor-based RPCA methods in terms of average class classification accuracy (AA), overall classification accuracy (OA), and kappa coefficient (KC).

Robust Self-Tuning Semiparametric PCA for Contaminated Elliptical Distribution

Principal component analysis (PCA) is one of the most popular dimension reduction methods. The usual PCA is known to be sensitive to the presence of outliers, and thus many robust PCA methods have been developed. Among them, the Tyler's M-estimator is shown to be the most robust scatter estimator under the elliptical distribution. However, when the underlying distribution is contaminated and deviates from ellipticity, Tyler's M-estimator might not work well. In this article, we apply the semiparametric theory to propose a robust semiparametric PCA. The merits of our proposal are twofold. First, it is robust to heavy-tailed elliptical distributions as well as robust to non-elliptical outliers. Second, it pairs well with a data-driven tuning procedure, which is based on active ratio and can adapt to different degrees of data outlyingness. Theoretical properties are derived, including the influence functions for various statistical functionals and asymptotic normality. Simulation studies and a data analysis demonstrate the superiority of our method.

Graph Convolution RPCA With Adaptive Graph.

Principal component analysis (PCA) is warmly welcomed in dimensionality reduction and its applications. Due to the high sensitivity of PCA to outliers, a series of PCA methods are proposed to enhance the robustness of PCA. Besides, the representation ability of the existing PCA methods has limitations as well. To enhance the robustness and representation ability of robust PCA, we elaborate a novel Graph Convolution Robust PCA method (GRPCA) to incorporate the manifold structure into PCA. It constructs a sparse graph based on the local connectivity structure of samples. Graph auto-encoder is utilized to solve the robust PCA problem under the low-rank and sparse constraints. With the dual-decoder, GRPCA learns the low-dimensional embeddings that reconstruct the manifold structure and low-rank approximation simultaneously. Furthermore, since the graph suffers from misconnection triggered by occlusions, the local connectivity structure of low-dimensional embeddings is utilized to modify the graph. Our proposed method excels in both the clustering of low-dimensional embeddings and the low-rank recovery. Lastly, extensive experiments conducted on six real-world datasets demonstrated the efficiency and superiority of the proposed GRPCA.

A data-driven approach to measuring epidemiological susceptibility risk around the world

Epidemic outbreaks are extreme events that become more frequent and severe, associated with large social and real costs. It is therefore important to assess whether countries are prepared to manage epidemiological risks. We use a fully data-driven approach to measure epidemiological susceptibility risk at the country level using time-varying information. We apply both principal component analysis (PCA) and dynamic factor model (DFM) to deal with the presence of strong cross-section dependence in the data. We conduct extensive in-sample model evaluations of 168 countries covering 17 indicators for the 2010–2019 period. The results show that the robust PCA method accounts for about 90% of total variability, whilst the DFM accounts for about 76% of the total variability. Our index could therefore provide the basis for developing risk assessments of epidemiological risk contagion. It could be also used by organizations to assess likely real consequences of epidemics with useful managerial implications.