Robust Principal Component Analysis Model Research Articles

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.

An Optimization Algorithm of Robust Principal Component Analysis and Its Application

With the rapid development of robust principal component analysis (RPCA), it has been widely used in signal processing, pattern recognition, computer vision and other fields. The RPCA model has characteristics of complete reconstruction of the original signal from the noise pollution, high-dimensional and high-order complex signals. In order to solve the problems of slow iteration speed and low recovery accuracy in typical algorithms, an improved robust principal component analysis (RPCA) algorithm is studied. Firstly, the idea of smooth approximate zero norm is introduced to build the objective optimization function, then the inertial momentum is used to optimize each iteration of the matrix recovery process, finally, the model parameters are optimized by the grid method. Through simulation and comparative analysis, the results show that the improved algorithm has high accuracy, fast processing speed and remarkable application effect in field of logging data processing.

An Improved Robust Principal Component Analysis Model for Anomalies Detection of Subway Passenger Flow

Subway is an important transportation means for residents, since it is always on schedule. However, some temporal management policies or unpredicted events may change passenger flow and then affect passengers requirement for punctuality. Thus, detecting anomaly event, mining its propagation law, and revealing its potential impact are important and helpful for improving management strategy; e.g., subway emergency management can predict flow change under the condition of knowing specific policy and estimate traffic impact brought by some big events such as vocal concerts and ball games. In this paper, we propose a novel anomalies detection method of subway passenger flow. In this method, an improved robust principal component analysis model is presented to detect anomalies; then ST-DBSCAN algorithm is used to group the station-level anomaly data on space-time dimensions to reveal the propagation law and potential impact of different anomaly events. The real flow data of Beijing subway are used for experiments. The experimental results show that the proposed method is effective for detecting anomalies of subway passenger flow in practices.

Joint Reconstruction and Anomaly Detection From Compressive Hyperspectral Images Using Mahalanobis Distance-Regularized Tensor RPCA

Anomaly detection plays an important role in remotely sensed hyperspectral image (HSI) processing. Recently, compressive sensing technology has been widely used in hyperspectral imaging. However, the reconstruction from compressive HSI and detection are commonly completed independently, which will reduce the processing’s efficiency and accuracy. In this paper, we propose a framework for hyperspectral compressive sensing with anomaly detection which reconstruct the HSI and detect the anomalies simultaneously. In the proposed method, the HSI is composed of the background and anomaly parts in the tensor robust principal component analysis model. To characterize the low-dimensional structure of the background, a novel tensor nuclear norm is used to constrain the background tensor. As the anomaly part is formed by a few anomalous spectra, the anomaly part is assumed to be a tuber-wise sparse tensor. In addition, to enhance the separation of the background and anomaly, we minimize the sum of Mahalanobis distance of the background pixels. Experiments on four HSIs demonstrate that the proposed method outperforms several state-of-the-art methods on both reconstruction and anomaly detection accuracies.

Background recovery via motion-based robust principal component analysis with matrix factorization

Background recovery is a key technique in video analysis, but it still suffers from many challenges, such as camouflage, lighting changes, and diverse types of image noise. Robust principal component analysis (RPCA), which aims to recover a low-rank matrix and a sparse matrix, is a general framework for background recovery. The nuclear norm is widely used as a convex surrogate for the rank function in RPCA, which requires computing the singular value decomposition (SVD), a task that is increasingly costly as matrix sizes and ranks increase. However, matrix factorization greatly reduces the dimension of the matrix for which the SVD must be computed. Motion information has been shown to improve low-rank matrix recovery in RPCA, but this method still finds it difficult to handle original video data sets because of its batch-mode formulation and implementation. Hence, in this paper, we propose a motion-assisted RPCA model with matrix factorization (FM-RPCA) for background recovery. Moreover, an efficient linear alternating direction method of multipliers with a matrix factorization (FL-ADM) algorithm is designed for solving the proposed FM-RPCA model. Experimental results illustrate that the method provides stable results and is more efficient than the current state-of-the-art algorithms.

Infrared Patch-Tensor Model With Weighted Tensor Nuclear Norm for Small Target Detection in a Single Frame

The robust and efficient detection of infrared small target is a key technique for infrared search and track systems. Several robust principal component analysis (RPCA)-based methods have been developed recently, which have achieved the state-of-the-art performance. However, there are still two drawbacks: 1) the false alarm ratio would raise under the heavy background clutters and noises and 2) these methods are usually time-consuming and not suitable for real-time processing. To solve this problem, an infrared patch-tensor (IPT) model based on weighted tensor nuclear norm is proposed in this paper. First, the infrared image is transformed into the IPT. Considering the sum of nuclear norms adopted in the IPT model is not the convex envelope of the tensor rank, and the solution is substantially suboptimal. The tensor nuclear norm is adopted to recover the underlying low-rank background tensor and sparse target tensor, and the computation complexity can be reduced dramatically with the help of the tensor Singular Value Decomposition. Moreover, to further suppress the background clutters, a weight tensor is incorporated with tensor nuclear norm to preserve the background edges better. Then, the separation between target and background is formulated as a convex weighted tensor RPCA model. Finally, the proposed model can be solved by the alternating direction method of multipliers. Extensive experiments demonstrate that the proposed model outperforms the other state-of-the-arts in terms of performance and efficiency.

A partially isochronous splitting algorithm for three-block separable convex minimization problems

During the last decade, the state-of-the-art alternating direction method of multipliers (ADMM) has successfully been used to solve many two-block separable convex minimization problems arising from several applied areas such as signal/image processing and statistical and machine learning. It however remains an interesting problem of how to implement ADMM to three-block separable convex minimization problems as required by the situation where many objective functions in the above-mentioned areas are actually more conveniently decomposed to the sum of three convex functions, due also to the observation that the straightforward extension of ADMM from the two-block case to the three-block case is apparently not convergent. In this paper, we shall introduce a new algorithm that is called a partially isochronous splitting algorithm (PISA) in order to implement ADMM for the three-block separable model. The main idea of our algorithm is to incorporate only one proximal term into the last subproblem of the extended ADMM so that the resulting algorithm maximally inherits the promising properties of ADMM. A remarkable superiority over the extended ADMM is that we can simultaneously solve two of the subproblems, thereby taking advantages of the separable structure and parallel architectures. Theoretically, we will establish the global convergence of our algorithm under standard conditions, and also the O(1/t) rate of convergence in both ergodic and nonergodic senses, where t is the iteration counter. The computational competitiveness of our algorithm is shown by numerical experiments on an application to the well-tested robust principal component analysis model.

Moving Target Detection via Efficient ATI-GoDec Approach for Multichannel SAR System

Clutter suppression and ground moving target indication (GMTI) are challenging tasks for multichannel synthetic aperture radar (MC-SAR) systems. In recent years, robust principal component analysis (RPCA), such as the augmented Lagrange multiplier method (ALM) and go decomposition (GoDec) algorithm, has drawn considerable attention for its excellent performance in distinguishing the different parts from a set of correlative database. In this letter, an efficient along-track interferometry GoDec (ATI-GoDec) approach is proposed for GMTI in MC-SAR systems under a strong clutter background. The proposed method can be separated into two sections: the predetection and the postdetection. The predetection by an efficient ATI RPCA method can decrease missing targets, and postdetection with a novel magnitude and phase (M&P) detection has the ability to reduce the false targets. As a result, the proposed method can provide a more robust performance by a comparison to the traditional ATI detection. It can also widen the tolerant values of the preset cardinality and decrease the probability of false alarm compared with the conventional GoDec algorithm. Moreover, the proposed method only takes several iterations to reach the convergence by solving the optimization problem of the RPCA model, which makes it more efficient than the previous RPCA methods. The results by applying the proposed method into a set of real SAR data are consistent with the analysis presented in this letter.

Detection of varied defects in diverse fabric images via modified RPCA with noise term and defect prior

Purpose – The purpose of this paper is to present a novel method for fabric defect detection. Design/methodology/approach – The method based on joint low-rank and spare matrix recovery, since patterned fabric is manufactured by a set of predefined symmetry rules, and it can be seen as the superposition of sparse defective regions and low-rank defect-free regions. A robust principal component analysis model with a noise term is designed to handle fabric images with diverse patterns robustly. The authors also estimate a defect prior and use it to guide the matrix recovery process for accurate extraction of various fabric defects. Findings – Experiments on plain and twill, dot-, box- and star-patterned fabric images with various defects demonstrate that the method is more efficient and robust than previous methods. Originality/value – The authors present a RPCA-based model for fabric defects detection, and show how to incorporate defect prior to improve the detection results. The authors also show that more robust detection and less running time can be obtained by introducing a noise term into the model.

Predicting Drug-Target Interactions With Multi-Information Fusion.

Identifying potential associations between drugs and targets is a critical prerequisite for modern drug discovery and repurposing. However, predicting these associations is difficult because of the limitations of existing computational methods. Most models only consider chemical structures and protein sequences, and other models are oversimplified. Moreover, datasets used for analysis contain only true-positive interactions, and experimentally validated negative samples are unavailable. To overcome these limitations, we developed a semi-supervised based learning framework called NormMulInf through collaborative filtering theory by using labeled and unlabeled interaction information. The proposed method initially determines similarity measures, such as similarities among samples and local correlations among the labels of the samples, by integrating biological information. The similarity information is then integrated into a robust principal component analysis model, which is solved using augmented Lagrange multipliers. Experimental results on four classes of drug-target interaction networks suggest that the proposed approach can accurately classify and predict drug-target interactions. Part of the predicted interactions are reported in public databases. The proposed method can also predict possible targets for new drugs and can be used to determine whether atropine may interact with alpha1B- and beta1- adrenergic receptors. Furthermore, the developed technique identifies potential drugs for new targets and can be used to assess whether olanzapine and propiomazine may target 5HT2B. Finally, the proposed method can potentially address limitations on studies of multitarget drugs and multidrug targets.

Robust 2D principal component analysis: a structured sparsity regularized approach.

Principal component analysis (PCA) is widely used to extract features and reduce dimensionality in various computer vision and image/video processing tasks. Conventional approaches either lack robustness to outliers and corrupted data or are designed for one-dimensional signals. To address this problem, we propose a robust PCA model for two-dimensional images incorporating structured sparse priors, referred to as structured sparse 2D-PCA. This robust model considers the prior of structured and grouped pixel values in two dimensions. As the proposed formulation is jointly nonconvex and nonsmooth, which is difficult to tackle by joint optimization, we develop a two-stage alternating minimization approach to solve the problem. This approach iteratively learns the projection matrices by bidirectional decomposition and utilizes the proximal method to obtain the structured sparse outliers. By considering the structured sparsity prior, the proposed model becomes less sensitive to noisy data and outliers in two dimensions. Moreover, the computational cost indicates that the robust two-dimensional model is capable of processing quarter common intermediate format video in real time, as well as handling large-size images and videos, which is often intractable with other robust PCA approaches that involve image-to-vector conversion. Experimental results on robust face reconstruction, video background subtraction data set, and real-world videos show the effectiveness of the proposed model compared with conventional 2D-PCA and other robust PCA algorithms.

Application of classical statistics, logratio transformation and multifractal approaches to delineate geochemical anomalies in the Zarshuran gold district, NW Iran

The aim of this study is to discriminate the geochemical anomalies in the Zarshuran district, NW Iran, using different geochemical methods and present a more useful method where anomalous areas better coincide with the geological features. For this methods of delineation, geochemical anomalies were compared using geological features, occupied area of anomalies respect to the total study area, and field observations. Frequency based analysis such as mean+2SDEV and median+2MAD and concentration–area (C–A) multifractal methods were adopted for estimating thresholds and separating geochemical anomalies in uni-element data, as well as multi-element ones. Threshold values obtained from mean+2SDEV and median+2MAD, from original point geochemical data, are smaller than those of the pixel values; this may be due to the stronger variance of pixel values. In addition, the C–A multifractal method, as a useful tool to identify weak geochemical anomalies, was applied for defining the threshold values. Robust principal component analysis (RPCA) methods coupled with isometric log-ratio (ilr) transformations were utilized to open the geochemical data in order to reduce the effects of the data closure problem. The 20-quantile intervals decomposed anomaly maps from PC1 were obtained from the classical PCA, robust PCA showed that the upper quintile (>80 quintile) of classical PCA covers a larger area (32.54%) than the robust PCA (18.16%), and as a result, the robust PCA displayed smaller areas and has good spatial associations with outcrops of hydrothermal Au–As mineralization in this area; coincident with the known Zarshuran former mining area (ore field), Zarshuran unit, Ghaldagh silicified limestone occurrence and newly explored works confirmed by field observation. Although the C–A model shows a smaller area (8.06%), this anomaly location is limited to the Zarshuran old mining area with no new exploration targets. Comparison of the models indicates that the RPCA model is not only beneficial to further Au exploration in the study area, but also provides a meaningful geological study to the community of the compositional data analysis.

Visual Characterization and Diversity Quantification of Chemical Libraries: 1. Creation of Delimited Reference Chemical Subspaces

High-throughput screening (HTS) is a well-established technology which can test up to several million compounds in a few weeks. Despite these appealing capabilities, available resources and high costs may limit the number of molecules screened, making diversity analysis a method of choice to design and prioritize screening libraries. With a constantly increasing number of molecules available for screening, chemical space has become a key concept for visualizing, analyzing, and comparing chemical libraries. In this first article, we present a new method to build delimited reference chemical subspaces (DRCS). A set of 16 million screening compounds from 73 chemical providers has been gathered, resulting in a database of 6.63 million standardized and unique molecules. These molecules have been used to create three DRCS using three different sets of chemical descriptors. A robust principal component analysis model for each space has been obtained, whereby molecules are projected in a reduced two-dimensional viewable space. The specificity of our approach is that each reduced space has been delimited by a representative contour encompassing a very large proportion of molecules and reflecting its overall shape. The methodology is illustrated by mapping and comparing various chemical libraries. Several tools used in these studies are made freely available, thus enabling any user to compute DRCS matching specific requirements.