Robust Principal Component Analysis Model Research Articles

Perbandingan Analisis Komponen Utama Robust Minimum Covarian Determinant dengan Least Trimmed Square pada Data Produk Domestik Regional Bruto

Regression analysis is a method to examine the relationship between variables and determine their influence. However, the problem of multicollinearity often arises in linear regression analysis and can cause interpretation problems. To handle multicollinearity, Principal Component Analysis (PCA) is used. However, this method has a weakness when the data contains outliers. Therefore, it was developed into robust PCA using the Minimum Covariance Determinant (MCD) method and the Least Trimmed Square (LTS) estimation method. This study uses Gross Regional Domestic Product data in Indonesia in 2020, which has problems with multicollinearity and outliers. This data is modeled using two robust PCA methods, namely MCD and LTS. The robust PCA model with MCD has an adjusted value of 87.87% and an MSE value of 0.0700. However, in the robust PCA regression model with LTS, the adjusted value is 98.93% and the MSE value is 0.0325. Thus, the effective method in handling multicollinearity and outliers is the LTS method because it shows better results.

Low-rank prior-based Fast-RPCA for clutter filtering and noise suppression in non-contrast ultrasound microvascular imaging

Accurate and real-time separation of blood signal from clutter and noise signals is a critical step in clinical non-contrast ultrasound microvascular imaging. Despite the widespread adoption of singular value decomposition (SVD) and robust principal component analysis (RPCA) for clutter filtering and noise suppression, the SVD’s sensitivity to threshold selection, along with the RPCA’s limitations in undersampling conditions and heavy computational burden often result in suboptimal performance in complex clinical applications. To address those challenges, this study presents a novel low-rank prior-based fast RPCA (LP-fRPCA) approach to enhance the adaptability and robustness of clutter filtering and noise suppression with reduced computational cost. A low-rank prior constraint is integrated into the non-convex RPCA model to achieve a robust and efficient approximation of clutter subspace, while an accelerated alternating projection iterative algorithm is developed to improve convergence speed and computational efficiency. The performance of the LP-fRPCA method was evaluated against SVD with a tissue/blood threshold (SVD1), SVD with both tissue/blood and blood/noise thresholds (SVD2), and the classical RPCA based on the alternating direction method of multipliers algorithm through phantom and in vivo non-contrast experiments on rabbit kidneys. In the slow flow phantom experiment of 0.2 mm/s, LP-fRPCA achieved an average increase in contrast ratio (CR) of 10.68 dB, 9.37 dB, and 8.66 dB compared to SVD1, SVD2, and RPCA, respectively. In the in vivo rabbit kidney experiment, the power Doppler results demonstrate that the LP-fRPCA method achieved a superior balance in the trade-off between insufficient clutter filtering and excessive suppression of blood flow. Additionally, LP-fRPCA significantly reduced the runtime of RPCA by up to 94-fold. Consequently, the LP-fRPCA method promises to be a potential tool for clinical non-contrast ultrasound microvascular imaging.

Three-dimensional seismic data reconstruction via partial sum of tensor nuclear norm minimization

AbstractRank-reduction has become a hotspot in seismic data reconstruction research in recent years. Traditional rank-reduction methods generally use the nuclear norm as a convex proxy for rank, but these methods overly penalize large singular values, leading to reconstruction results that deviate from the optimal solution. In this paper, we propose a tensor robust principal component analysis model with minimization of the partial sum of tensor nuclear norm for three-dimensional (3D) reconstruction of seismic data. The partial sum of tensor nuclear norm minimizes only the partial singular values and can approximate the rank function more accurately. TRPCA can accurately recover the 3D tensor corrupted by sparse errors, improving the accuracy of seismic data reconstruction. The experimental results of the simulated data and real data show that the reconstruction effect of the proposed method on the 3D seismic data is better than the compared methods.

Anomaly detection on OpenStack logs based on an improved robust principal component analysis model and its projection onto column space

AbstractWith the advent of technology and the development of more complex software systems, the size of logs generated by these systems has increasingly risen so that the anomaly detection for remediating common errors has been more difficult than ever. The cloud emergence in the information technology (IT) industry has led to the immigration of enterprises toward it, which has extended the application of cloud management stacks such as OpenStack. By using the OpenStack platform, users can access resource infrastructure and manage virtual machines (VMs). The anomaly detection in OpenStack logs is not realized conveniently due to the substantial size of logs, and it is required to automate this process. Since there is no appropriate open‐source dataset for OpenStack logs, we have generated 25,000 logs by injecting three types of anomalies to propose a more efficient technique in terms of performance and time in detecting anomalies in OpenStack logs relative to recent studies by proper OpenStack log parsing and analyzing these logs by data mining algorithms. To this end, compared to the previous research study, we could improve the anomaly detection performance in terms of F1 score, recall, and precision by 9%, 4%, and 14%, respectively, and decrease the running time relative to the log size by at least 30 s.

Evaluation of the metabolomic profile through 1H-NMR spectroscopy in ewes affected by postpartum hyperketonemia

Ketosis is one of the most important health problems in dairy sheep. The aim of this study was to evaluate the metabolic alterations in hyperketonemic (HYK) ewes. Forty-six adult Sardinian ewes were enrolled between 7 ± 3 days post-partum. Blood samples were collected from the jugular vein using Venosafe tubes containing clot activator from jugular vein after clinical examination. The concentration of β-hydroxybutyrate (BHB) was determined in serum and used to divide ewes into assign ewes into: Non-HYK (serum BHB < 0.80 mmol/L) and HYK (serum BHB ≥ 0.80 mmol/L) groups. Animal data and biochemical parameters of groups were examined with one-way ANOVA, and metabolite differences were tested using a t-test. A robust principal component analysis model and a heatmap were used to highlight common trends among metabolites. Over-representation analysis was performed to investigate metabolic pathways potentially altered in connection with BHB alterations. The metabolomic analysis identified 54 metabolites with 14 different between groups. These metabolites indicate altered ruminal microbial populations and fermentations; an interruption of the tricarboxylic acid cycle; initial lack of glucogenic substrates; mobilization of body reserves; the potential alteration of electron transport chain; influence on urea synthesis; alteration of nervous system, inflammatory response, and immune cell function.

Moving Object Detection in Dynamic Environment via Weighted Low-Rank Structured Sparse RPCA and Kalman Filtering

As a classical problem for computer vision, moving object detection (MOD) can be efficiently achieved by foreground and background separation. The Robust Principal Component Analysis (RPCA)-based method has been potentially utilized to solve the problem. However, the detection accuracy for RPCA-based method is limited for complex scenes with slow-motion. Besides, it is time consuming for the way to seek for background modeling based on solving a low-rank minimization problem, for which multiple frames of the videos are required as the input. Therefore, a real-time MOD framework (LSRPCA_KF) is proposed for the dynamic background, where a weighted low-rank and structured sparse RPCA algorithm is used to achieve background modeling for history data, while the online MOD is achieved by the background subtraction method and updated by the Kalman filter for every real time frame. Specifically, for the background model, a newly designed weight is incorporated to distinguish the significance of different singular values, and a structured sparse prior is added to penalty the spatial connection property of the moving object. Besides, the weighted low-rank and structured sparse RPCA model is efficiently solved by the Alternating Direction Method of Multipliers (ADMM) optimization algorithm. Experimental results demonstrated that better performance of our method with significantly reduced delay in processing and better detect the moving object has been achieved, especially for the dynamic background.

Infrared small target detection using kernel low-rank approximation and regularization terms for constraints

The robust detection of infrared (IR) small targets remains a challenging task. When targets are submerged in heavy clutter or disturbed by strong edge, it is difficult to extract targets and suppress background clutter simultaneously. In this paper, we present a kernel robust principal component analysis model for IR small target detection. Firstly, to overcome the interference of heavy clutter and strong edge, the kernel low-rank approximation is proposed to estimate the background component; Then, to further improve detection performance, the lp-norm is adopted to recover the sparse component, the total variation regularization is employed to smooth the background, and the graph Laplacian regularization is utilized as a sparse constraint to constrain the homogeneous target region. Finally, we derive an effective method to solve the proposed model based on the alternating direction method of multipliers. Experimental results not only show the proposed method can robustly and effectively detect IR small targets even when the targets are submerged in strong clutter or seriously disturbed by strong edge, but also confirm the proposed method is competitive with the state-of-the-art methods.

Hyperspectral Anomaly Detection Based on Improved RPCA with Non-Convex Regularization

The low-rank and sparse decomposition model has been favored by the majority of hyperspectral image anomaly detection personnel, especially the robust principal component analysis(RPCA) model, over recent years. However, in the RPCA model, ℓ0 operator minimization is an NP-hard problem, which is applicable in both low-rank and sparse items. A general approach is to relax the ℓ0 operator to ℓ1-norm in the traditional RPCA model, so as to approximately transform it to the convex optimization field. However, the solution obtained by convex optimization approximation often brings the problem of excessive punishment and inaccuracy. On this basis, we propose a non-convex regularized approximation model based on low-rank and sparse matrix decomposition (LRSNCR), which is closer to the original problem than RPCA. The WNNM and Capped ℓ2,1-norm are used to replace the low-rank item and sparse item of the matrix, respectively. Based on the proposed model, an effective optimization algorithm is then given. Finally, the experimental results on four real hyperspectral image datasets show that the proposed LRSNCR has better detection performance.

Multichannel SAR Moving Target Detection via RPCA-Net

Ground moving target indication (GMTI), as a challenging task for synthetic aperture radar (SAR) systems, keeps drawing considerable attention. Robust principal component analysis (RPCA) aiming at separating low-rank and sparse components has been successfully employed in SAR systems for GMTI recently. However, its practical application is limited by the heavy computational burden as well as the requirement of manual parameter modification. To cope with this problem, a fast and free of presetting parameters RPCA network (RPCA-Net) is proposed for SAR-GMTI under strong clutter background. In the proposed method, a novel RPCA model is first introduced, where not only the low-rank and sparse terms but also the errors in practical SAR systems are taken into account. Moreover, the low-rank factorization plus scaled gradient descent (ScaledGD) is also employed to acquire low-rank clutter background rather than singular value decomposition (SVD). Then, we parameterize our proposed RPCA model and unfold it as a feedforward neural network (FNN) to acquire the iterative parameters through backpropagation. Compared to the GMTI methods based on traditional RPCA models, our proposed RPCA-Net can provide a higher detection ability and faster convergence without presetting parameters empirically. Experiments on two groups of measured data collected by airborne SAR systems validate the superior performance of the proposed RPCA-Net.

Recovery of Corrupted Data in Wireless Sensor Networks Using Tensor Robust Principal Component Analysis

Due to the hardware and network conditions, data collected in Wireless Sensor Networks usually suffer from loss and corruption. Most existing research works mainly consider the reconstruction of missing data without data corruption. However, the inevitable data corruption poses a great challenge to guarantee the recovery accuracy. To address this problem, this letter proposes a data recovery method based on tensor singular value decomposition. Data collected by the spatial distributed sensor nodes in each time slot is arranged in matrix form instead of vector to further exploit the spatial correlation of the data. Therefore, data collected in consecutive time slots can form a three-way tensor. To avoid the influence of corruption on recovery accuracy, a Tensor Robust Principal Component Analysis model is developed to decompose the raw data tensor into a low-rank normal data tensor and a sparse error tensor. The recovery accuracy is further improved by incorporating total variation constraint. Computer experiments corroborate that the proposed method significantly outperforms the existing method in the recovery accuracy.

Moving Object Tracking via 3-D Total Variation in Remote-Sensing Videos

Tracking moving objects in remote-sensing videos is becoming increasingly important in remote-sensing analysis. This letter presents a novel object tracking method for remote-sensing videos. We start with using the traditional robust principal component analysis (RPCA) model to extract the moving object from the background. To describe the continuity of moving objects in spatial and temporal directions, we incorporate a 3-D total variation (3DTV) regularization into the RPCA model. Considering that the background is not static and the captured videos will contain noise because of the instability of the sensing camera, our proposed method introduces a certain part of the function to model the noise and capture the changes in background. Experimental results on real videos provided by 2016 IEEE GRSS Data Fusion Contest and 2020 Hyperspectral Object Tracking Challenge demonstrate the advantages of the moving object-tracking method via 3-D TV.

Predictive Approach to Perform Fault Detection in Electrical Submersible Pump Systems.

It has been a great challenge for the oil and gas industry to timely identify any electrical submersible pump (ESP) abnormal performance to avoid ESP failure. Given the high cost of the ESP failure, more and more real-time surveillance systems are applied to monitor ESP performance to generate alarms in the case of failures. This paper presents a robust principal component analysis (PCA) model to perform fault detection for ESP systems continuously. A three-dimensional plot of scores of principal components was used to observe different patterns during the stable and failure periods. 47 cases of actual failure events and 40 cases of stable operating events were tested on the robust PCA model to generate prediction results. The testing results demonstrate that the robust PCA model has managed to identify 20 failure events before the actual failure time out of the 47 failure cases and has successfully distinguished all the 40 stable operating wells. This study has concluded that PCA has the potential to be used as a monitoring platform to recognize dynamic change and therefore to predict the developing failures in the ESP system.

Video denoising and moving object detection by rank-1 and total variation regularization on robust principal component analysis framework

With the complexity of the video environment and the problem of possible noise during data transmission, traditional robust principal component analysis (RPCA) failed to obtain the lowest rank representation from corrupted data. A method of video denoising and an object detection algorithm based on the RPCA model with total variation and rank-1 constraint (TVR1-RPCA) is proposed; it employs the more refined prior representations for the static and dynamic components of the video sequences. The proposed method is based on RPCA under the framework of low-rank sparse decomposition; the rank-1 constraint is exploited to describe the strong low-rank property of the background layer, TV regularization is combined with l1 regularization to constrain the sparsity and spatial continuity of the foreground component, and l2 norm regularization is combined to constrain the noise to make up for the deficiencies of the existing RPCA model. In addition, an efficient algorithm based on the alternating direction method of multipliers is designed to solve the proposed video denoising and moving object detection issues. Our experiments on static and moving camera videos demonstrate that the proposed method is superior to the state-of-the-art methods in terms of denoising capability and detection accuracy.

Bayesian Robust Principal Component Analysis with Adaptive Singular Value Penalty

Robust principal component analysis (RPCA) has recently seen ubiquitous activity for dimensionality reduction in image processing, visualization and pattern recognition. Conventional RPCA methods model the low-rank component as regularizing each singular value equally. However, in numerous modern applications, each singular value has different physical meaning and should be treated differently. This is one of the main reasons why RPCA techniques cannot work well in dealing with many realistic problems. To solve this problem, a novel hierarchical Bayesian RPCA model with adaptive singular value penalty is proposed. This model enforces the low-rank constraint by introducing an adaptive penalty function on the singular values of the low-rank component. In particular, we impose a hierarchical Exponent-Gamma prior on the singular values of the low-rank component and the Beta-Bernoulli prior on sparsity indicators. The variational Bayesian framework and the Markov chain Monte Carlo-based Bayesian inference are considered for inferring the posteriors of all latent variables involved in low-rank and sparse components. Numerical experiments demonstrate the competitive performance of the proposed model on synthetic and real data.

Video Background/Foreground Separation Model Based on Non-Convex Rank Approximation RPCA and Superpixel Motion Detection

Traditional robust principal component analysis (RPCA) is very prone to voids in the process of background/foreground separation of complex scene videos and easy to misjudge the dynamic background as a moving target, which makes the separation effect unideal. In order to address this problem, this article introduces the super-pixel segmentation technique into the RPCA model. First, the Linear Spectral Clustering algorithm (LSC) is used to mark the super-pixel segmentation of the video sequence and a super-pixel grouping matrix is obtained. Then a new video background/foreground separation model is proposed based on the non-convex rank approximation RPCA and super-pixel motion detection (SPMD) technique. The Otsu algorithm is used to obtain the motion mask matrix and the augmented lagrange alternating direction method is used to solve the improved RPCA model. The results of numerical experiment show that the method proposed in this article has a higher accuracy in the detection of moving objects in dynamic background.

Cirrus Detection Based on Tensor Multi-Mode Expansion Sum Nuclear Norm in Infrared Imagery

Infrared small target detection systems are an important part of space infrared imaging satellites. However, small infrared target detection is often affected by cirrus false alarm sources with similar grayscales. In this article, an infrared cirrus detection method based on the tensor robust principal component analysis model (TRPCA) is proposed. The method treats multiple bands of remote sensing data as tensors, but classical tensor nuclear norms cannot represent the tensor rank well; therefore, we use tensor multi-mode expansion sum nuclear norm (TMESNN) to approximate the tensor rank better. First, a set of Landsat-8 data is transformed into a tensor model, and a TRPCA model is constructed by TMESNN and the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$L_{1} $ </tex-math></inline-formula> norm. Then, this model is solved by Ket augments and the alternating direction method of multipliers (ADMM). Finally, Mallat wavelet transform is used to supplement information and remove clutter, and the final detection result is obtained by adaptive threshold segmentation. Compared with other optimization-based methods, this method has better detection performance and accuracy.

Moving Object Detection Based on Non-Convex RPCA With Segmentation Constraint

Recently, robust principal component analysis (RPCA) has been widely used in the detection of moving objects. However, this method fails to effectively utilize the low-rank prior information of the background and the spatiotemporal continuity prior of the moving object, and the target extraction effect is often poor when dealing with large-scale complex scenes. To solve the above problems, a new non-convex rank approximate RPCA model based on segmentation constraint is proposed. Firstly, the model adopts the low-rank sparse decomposition method to divide the original video sequence into three parts: low-rank background, moving foreground and sparse noise. Then, a new non-convex function is proposed to better constrain the low-rank characteristic of the video background. Finally, based on the spatiotemporal continuity of the foreground object, the video is segmented by the super-pixel segmentation technology, so as to realize the constraint of the motion foreground region. The augmented Lagrange multiplier method is used to solve the model. Experimental results show that the proposed model can effectively improve the accuracy of moving object detection, and has better visual effect of foreground object detection than existed methods.

Robust principal component analysis using facial reduction

We introduce a novel approach for robust principal component analysis (RPCA) for a partially observed data matrix. The aim is to recover the data matrix as a sum of a low-rank matrix and a sparse matrix so as to eliminate erratic noise (outliers). This problem is known to be NP-hard in general. A classical approach to solving RPCA is to consider convex relaxations. One such heuristic involves the minimization of the (weighted) sum of a nuclear norm part, that promotes a low-rank component, with an ell _1 norm part, to promote a sparse component. This results in a well-structured convex problem that can be efficiently solved by modern first-order methods. However, first-order methods often yield low accuracy solutions. Moreover, the heuristic of using a norm consisting of a weighted sum of norms may lose some of the advantages that each norm had when used separately. In this paper, we propose a novel nonconvex and nonsmooth reformulation of the original NP-hard RPCA model. The new model adds a redundant semidefinite cone constraint and solves small subproblems using a PALM algorithm. Each subproblem results in an exposing vector for a facial reduction technique that is able to reduce the size significantly. This makes the problem amenable to efficient algorithms in order to obtain high-level accuracy. We include numerical results that confirm the efficacy of our approach.

Summary of Improvement and Research Based on Robust Principal Component Analysis Model

Moving object detection play an important role in the application of computer vision. In recent years, the proposal and improvement of robust principal component analysis has broad application prospects in intelligent video surveillance and other fields. In order to enable domestic and foreign researchers to deeply explore and apply the RPCA, this paper systematically reviews it. This paper summarizes the latest research progress, summarizes various RPCA models at home and abroad, and theoretically analyses their advantages and disadvantages. In this paper, different improved models are applied to video sequences of different scenes, and comparative experiments are carried out. Overall, the current improved algorithms can effectively remedy the shortcomings of the original RPCA method and improve the accuracy of moving object detection. However, some limitations of RPCA need to be further studied.

Robust principal component analysis: A factorization-based approach with linear complexity

Low-rankness has been widely observed in real world data and there is often a need to recover low-rank matrices in many machine learning and data mining problems. Robust principal component analysis (RPCA) has been used for such problems by separating the data into a low-rank and a sparse part. The convex approach to RPCA has been well studied due to its elegant properties in theory and many extensions have been developed. However, the state-of-the-art algorithms for the convex approach and their extensions are usually expensive in complexity due to the need for solving singular value decomposition (SVD) of large matrices. In this paper, we propose a novel RPCA model based on matrix tri-factorization, which only needs the computation of SVDs for very small matrices. Thus, this approach reduces the complexity of RPCA to be linear and makes it fully scalable. It also overcomes the drawback of the state-of-the-art scalable approach such as AltProj, which requires the precise knowledge of the true rank of the low-rank component. As a result, our method is about 4 times faster than AltProj. Our method can be used as a light-weight, scalable tool for RPCA in the absence of the precise value of the true rank.