Robust Principal Component Analysis Research Articles

The art of centering without centering for robust principal component analysis

The art of centering without centering for robust principal component analysis

High-dimensional robust principal component analysis and its applications

Principal component analysis method is one of the most widely used statistical procedures for data dimension reduction. The traditional principal component analysis method is sensitive to outliers since it is based on the sample covariance matrix. Meanwhile, the deviation of the principal component analysis based on the Minimum Covariance Determinant (MCD) estimation is significantly increased as the data dimension increases. In this paper, we propose a high-dimensional robust principal component analysis based on the Rocke estimator. Simulation studies and a real data analysis illustrate that the finite sample performance of the proposed method is significantly better than those of the existing methods.

The Improved Wavelet Denoising Scheme Based on Robust Principal Component Analysis for Distributed Fiber Acoustic Sensor

The Improved Wavelet Denoising Scheme Based on Robust Principal Component Analysis for Distributed Fiber Acoustic Sensor

Tensor recovery based on rank adaptive and non-convex methods

The growing popularity of tensor singular value decomposition (T-SVD) in tensor recovery problems and the N-tubal rank can be applied to higher order tensors. However, this method faces new challenges as it does not fully use the rank prior information of tensors and lacks non-convex relaxation methods. Thus, this paper applies a new non-convex function, called Minimax Logarithmic Concave Penalty (MLCP), based on the N-tubal rank method. Two MLCP models based on N-tubal rank are introduced for solving low-rank tensor completion (LRTC) and tensor robust principal component analysis (TRPCA) problems, along with corresponding solving algorithms. The effectiveness and superiority of these models are demonstrated through experiments on real datasets.

ITRPCA: a new model for computational drug repositioning based on improved tensor robust principal component analysis.

Background: Drug repositioning is considered a promising drug development strategy with the goal of discovering new uses for existing drugs. Compared with the experimental screening for drug discovery, computational drug repositioning offers lower cost and higher efficiency and, hence, has become a hot issue in bioinformatics. However, there are sparse samples, multi-source information, and even some noises, which makes it difficult to accurately identify potential drug-associated indications. Methods: In this article, we propose a new scheme with improved tensor robust principal component analysis (ITRPCA) in multi-source data to predict promising drug-disease associations. First, we use a weighted k-nearest neighbor (WKNN) approach to increase the overall density of the drug-disease association matrix that will assist in prediction. Second, a drug tensor with five frontal slices and a disease tensor with two frontal slices are constructed using multi-similarity matrices and an updated association matrix. The two target tensors naturally integrate multiple sources of data from the drug-side aspect and the disease-side aspect, respectively. Third, ITRPCA is employed to isolate the low-rank tensor and noise information in the tensor. In this step, an additional range constraint is incorporated to ensure that all the predicted entry values of a low-rank tensor are within the specific interval. Finally, we focus on identifying promising drug indications by analyzing drug-disease association pairs derived from the low-rank drug and low-rank disease tensors. Results: We evaluate the effectiveness of the ITRPCA method by comparing it with five prominent existing drug repositioning methods. This evaluation is carried out using 10-fold cross-validation and independent testing experiments. Our numerical results show that ITRPCA not only yields higher prediction accuracy but also exhibits remarkable computational efficiency. Furthermore, case studies demonstrate the practical effectiveness of our method.

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.

Identification of carbonate cave reservoirs using wavelet reconstruction and WLRPCA based background modeling

Carbonate cave reservoirs are controlled by large strike-slip fault, which are home to incredibly rich oil and gas resources and hold immense exploration potential. The effective identification of these reservoirs using geophysical methods is quite important, but often challenging due to low signal-to-noise ratio and strong background reflection shielding of raw seismic data. In order to fully exploit the information of carbonate reservoirs contained in seismic data and improve the interpretation accuracy, we involve the innovative use of wavelet reconstruction and background modeling techniques to enhance the identification accuracy of carbonate cave reservoirs based on post-stack seismic data. The wavelet reconstruction in the first step mitigate the impact of noise and background reflection, allowing us to reveal the bead-like reflections hidden underneath strong interference energy. Then, we propose a background modeling method based on the weighted logarithmic robust principal component analysis (WLRPCA) technique in the second part to further eliminate background and noise signals. Compared with traditional principal component analysis (PCA) and robust principal component analysis (RPCA), WLRPCA exhibits superior recognition accuracy and noise immunity in the background modeling process, which effectively separates the target reflection from interference reflection and provides a favorable data basis for subsequent reservoir identification. Finally, a comprehensive attribute analysis is conducted on the processed seismic data, which confirms that the sweetness is the most effective attribute in detecting cave reservoirs. The proposed method has been successfully applied to both synthetic data and real data from an oil field in northern China, demonstrating their feasibility and effectiveness in identifying carbonate cave reservoirs.

Sparse discriminant PCA based on contrastive learning and class-specificity distribution

Much mathematical effort has been devoted to developing Principal Component Analysis (PCA), which is the most popular feature extraction method. To suppress the negative effect of noise on PCA performance, there have been extensive studies and applications of a large number of robust PCAs achieving outstanding results. However, existing methods suffer from at least two shortcomings: (1) They expressed PCA as a reconstruction model measured by Euclidean distance, which only considers the relationship between the data and its reconstruction and ignores the differences between different data points; (2) They did not consider the class-specificity distribution information contained in the data itself, thus lacking discriminative properties. To overcome the above problems, we propose a Sparse Discriminant Principal Components Analysis (SDPCA) model based on contrastive learning and class-specificity distribution. Specifically, we use contrastive learning to measure the relationship between samples and their reconstructions, which fully takes the discriminative information between data into account in PCA. In order to make the extracted low-dimensional features profoundly reflect the class-specificity distribution of the data, we minimize the squared ℓ1,2-norm of the low-dimensional embedding. In addition, to reduce the effects of redundant features and noise and to improve the interpretability of PCA at the same time, we impose sparsity constraints on the projection matrix using the squared ℓ1,2-norm. Our experimental results on different types of benchmark databases demonstrate that our model has state-of-the-art performance.

Spatial Overlay Analysis of Geochemical Singularity Index α-Value of Porphyry Cu Deposit in Gangdese Metallogenic Belt, Tibet, Western China

The statistical modeling with ILR-RPCA-back CLR has two problems when dealing with the closure effect of geochemical data. Firstly, after performing isometric logratio (ilr) transformation, robust principal component analysis (RPCA) is employed for processing. The double-plot diagram illustrates that the element sequence transformation occurs in the first and second principal components, while the unique principal component remains unattainable. Secondly, by transforming both the score and load into the centered logratio (CLR) space using the U matrix, it is possible to obtain a score result that corresponds to the original order of elements according to the CLR = ILR·U formula. However, for obtaining a load result that corresponds to the original order of elements, an alternative formula “CLR = UT·ILR” must be used instead. In order to determine the optimal element assemblage for porphyry copper deposits, this study conducted statistical analysis on mineral assemblages from discovered deposits in the Gangdese metallogenic belt and identified Cu, Mo, Au, Ag, W, and Bi as key elements associated with porphyry copper deposits. Subsequently, by analyzing the singularities of the composite elements, the spatial overlay of the combined element is carried out, and concentration-area (C-A) fractal filtering is applied to identify the anomaly and background areas. To facilitate comparison, we conducted an analysis of various mineral and ore deposit types, revealing the following findings: (1) Combination elements exhibit superior recognition capability than single elements in porphyry copper deposits; (2) Skarn-type copper deposits unrelated to porphyry show a high degree of dissimilarity compared to those related to porphyry; (3) this method offers advantages over the single element method in evaluating porphyry gold deposits by reducing anomaly levels and initial investment during the evaluation stage for porphyry copper anomalies; (4) However, this method has limited ability in distinguishing between porphyry copper and molybdenum deposits.

Identifying potential small molecule-miRNA associations via Robust PCA based on γ-norm regularization.

Dysregulation of microRNAs (miRNAs) is closely associated with refractory human diseases, and the identification of potential associations between small molecule (SM) drugs and miRNAs can provide valuable insights for clinical treatment. Existing computational techniques for inferring potential associations suffer from limitations in terms of accuracy and efficiency. To address these challenges, we devise a novel predictive model called RPCA$\Gamma $NR, in which we propose a new Robust principal component analysis (PCA) framework based on $\gamma $-norm and $l_{2,1}$-norm regularization and design an Augmented Lagrange Multiplier method to optimize it, thereby deriving the association scores. The Gaussian Interaction Profile Kernel Similarity is calculated to capture the similarity information of SMs and miRNAs in known associations. Through extensive evaluation, including Cross Validation Experiments, Independent Validation Experiment, Efficiency Analysis, Ablation Experiment, Matrix Sparsity Analysis, and Case Studies, RPCA$\Gamma $NR outperforms state-of-the-art models concerning accuracy, efficiency and robustness. In conclusion, RPCA$\Gamma $NR can significantly streamline the process of determining SM-miRNA associations, thus contributing to advancements in drug development and disease treatment.

Background initialization in video data using singular value decomposition and robust principal component analysis

Background initialization is used in video processing applications to extract a scene without the foreground scene. In recent times, the issue of background initialization has gained researchers’ attention in different fields such as video surveillance, video segmentation, computational photography, and so on. The initialization of the background is affected due to different complex dissimilarities such as shadow, intermittent movement, illumination, camera jitter, and clutter. To overcome the aforementioned issues, this paper proposes a decomposition using the combination of the Singular Value Decomposition (SVD) and Robust Principal Component Analysis (RPCA) for Singular Spectrum Analysis (SSA) to perform an effective background initialization. The incorporation of RPCA in SVD is used to overcome the issues related to non-Gaussian noise and it also uses an effective structural knowledge of the video input i.e. sparse and low rank matrix which improves the Peak-Signal-to-Noise-Ratio (PSNR) of the background image. The SBI dataset was used to analyze the performances of SSA-SVDRPCA. The SSA-SVDRPCA is analyzed using MultiScale Structural Similarity Index (MSSSIM), Average gray-level error (AGE), Percentage of clustered error pixels (pCEPS), Percentage of error pixels (pEPs), and PSNR. The existing approaches such as Background Initialization Singular Spectrum Analysis (BISSA) and Quaternion-based Dynamic Mode Decomposition (Q-DMD) are used to compare with the SSA-SVDRPCA method. The PSNR of the SSA-SVDRPCA for Board class is 30.39 dB which is higher than the BISSA and Q-DMD.

Robust implementation of foreground extraction and vessel segmentation for X-ray coronary angiography image sequence

The extraction of contrast-filled vessels from X-ray coronary angiography (XCA) image sequence has important clinical significance for intuitively diagnosis and therapy. In this study, the XCA image sequence is regarded as a 3D tensor input, the vessel layer is regarded as a sparse tensor, and the background layer is regarded as a low-rank tensor. Using tensor nuclear norm (TNN) minimization, a novel method for vessel layer extraction based on tensor robust principal component analysis (TRPCA) is proposed. Furthermore, considering the irregular movement of vessels and the low-frequency dynamic disturbance of surrounding irrelevant tissues, the total variation (TV) regularized spatial–temporal constraint is introduced to smooth the foreground layer. Subsequently, for vessel layer images with uneven contrast distribution, a two-stage region growing (TSRG) method is utilized for vessel enhancement and segmentation. A global threshold method is used as the preprocessing to obtain main branches, and the Radon-Like features (RLF) filter is used to enhance and connect broken minor segments. The final binary vessel mask is constructed by combining the two intermediate results. The visibility of TV-TRPCA algorithm for foreground extraction is evaluated on clinical XCA image sequences and third-party dataset, which can effectively improve the performance of commonly used vessel segmentation algorithms. Based on TV-TRPCA, the accuracy of TSRG algorithm for vessel segmentation is further evaluated. Both qualitative and quantitative results validate the superiority of the proposed method over existing state-of-the-art approaches.

Multifactorial characterization of nutritional and quality profiles of organically-sweetened Kunun-zaki beverage

Increased risk of non-communicable diseases (NCDs) such obesity, Type-2 diabetes, cardiovascular illnesses, and dental health issues has been associated with excessive added-sugar consumption. The objective of this study was to develop Kunun-zaki - a non-carbonated, non-alcoholic, cereal-based fermented beverage, using natural plant-based sweeteners Thaumatococcus daniellii (Miracle fruits) and Dioscoreophyllum cumminsii (Serendipity berry) in place of table sugar at various concentrations (1.0 – 5.0 g/100 mL). The beverages' quality characteristics, nutritional, antinutrients, minerals and sensory profiles were determined. With regard to the majority of the variables examined, the main factors and interaction effects were significant (p < 0.05). Beverage sweetened with both fruits showed improved physical characteristics and quality indicators, and they also retained more micronutrients (vitamins and minerals). Although at tolerable level, alkaloids and tannins, however, were somewhat more prevalent these organically-sweetened samples, whereas phytates were more in sucrose ones. Application of robust (R2 > 0.80) Principal Component Analysis (PCA) and Orthogonal Projection to Latent Structure Discriminant Analysis (OPLS-DA) clearly partitioned all the desirable physicochemical and sensory attributes of the beverages mainly between miracle fruits and serendipity-sweetened Kunun-zaki, with just overall consumer acceptability favoring the sucrose-sweetened beverage. Hence, these further reiterate the superiority of these organic sweeteners over common table sugar in the formulation of Kunun-zaki and their potential expanded application in food systems.

Guaranteed Tensor Recovery Fused Low-rankness and Smoothness.

Tensor recovery is a fundamental problem in tensor research field. It generally requires to explore intrinsic prior structures underlying tensor data, and formulate them as certain forms of regularization terms for guiding a sound estimate of the restored tensor. Recent researches have made significant progress by adopting two insightful tensor priors, i.e., global low-rankness (L) and local smoothness (S), which are always encoded as a sum of two separate regularizers into recovery models. However, unlike the primary theoretical developments on low-rank tensor recovery, these joint "L+S" models have no theoretical exact-recovery guarantees yet, making the methods lack reliability in real practice. To this crucial issue, in this work, we build a unique regularizer termed as tensor correlated total variation (t-CTV), which essentially encodes both L and S priors of a tensor simultaneously. Especially, by equipping t-CTV into the recovery models, we can rigorously prove the exact recovery guarantees for two typical tensor recovery tasks, i.e., tensor completion and tensor robust principal component analysis. To the best of our knowledge, this should be the first exact-recovery results among all related "L+S" methods for tensor recovery. We further propose ADMM algorithms with fine convergence to solve the proposed models. Significant recovery accuracy improvements are observed in extensive experiments. Typically, our method achieves a workable performance when the missing rate is extremely large, e.g., 99.5%, for the color image inpainting task, while all its peers totally fail in such a challenging case. Code is released at https://github.com/wanghailin97.

TwSense: Highly Robust Through-the-Wall Human Detection Method Based on COTS Wi-Fi Device

With the popularization of Wi-Fi router devices, the application of device-free sensing has garnered significant attention due to its potential to make our lives more convenient. Wi-Fi signal-based through-the-wall human detection offers practical applications, such as emergency rescue and elderly monitoring. However, the accuracy of through-the-wall human detection is hindered by signal attenuation caused by wall materials and multiple propagation paths of interference. Therefore, through-the-wall human detection presents a substantial challenge. In this paper, we proposed a highly robust through-the-wall human detection method based on a commercial Wi-Fi device (TwSense). To mitigate interference from wall materials and other environmental factors, we employed the robust principal component analysis (OR-PCA) method to extract the target signal of Channel State Information (CSI). Subsequently, we segmented the action-induced Doppler shift feature image using the K-means clustering method. The features of the images were extracted using the Histogram of Oriented Gradients (HOG) algorithm. Finally, these features were fed into an SVM classifier (G-SVM) optimized by a grid search algorithm for action classification and recognition, thereby enhancing human detection accuracy. We evaluated the robustness of the entire system. The experimental results demonstrated that TwSense achieved the highest accuracy of 96%.

Diagnosis and staging of cervical cancer using label-free surface-enhanced Raman spectroscopy and BWRPCA-TLNN model

This paper presents a label-free and highly accurate classification serum analytical platform, which will be used to identify cervical cancer at different stages. In detail, the microarray chip fabricated based on the ordered Ag-AuNRs substrate was prepared to measure the surface-enhanced Raman scattering (SERS) spectra of serum of healthy subjects and cervical cancer patients (Ⅰ, Ⅱ, Ⅲ, and Ⅳ), and then a binary weight robust principal component analysis (BWRPCA)-two-layer nearest neighbor (TLNN) model was designed as the diagnosis and recognition model of SERS spectra. The results revealed that the microarray chip can realize rapid, sensitive, high-throughput detection of SERS spectra of serum. The BWRPCA-TLNN successfully differentiated the SERS spectra and accurately captured the key characteristics for classification. The established BWRPCA-TLNN model achieved an excellent classification accuracy of 91.2 %, a diagnostic sensitivity of over 84.0 % and a specificity of over 97.0 %. This exploratory work demonstrated that SERS combined with BWRPCA-TLNN as a diagnostic screening method has potential for improving cervical cancer detection and screening.

An Efficient Outlier Detection Using Isolation Forest Based on Robust Scaling and Principal Component Analysis for the Prediction of Anxiety Disorder

An Efficient Outlier Detection Using Isolation Forest Based on Robust Scaling and Principal Component Analysis for the Prediction of Anxiety Disorder

Multispectral and hyperspectral image fusion based on low-rank unfolding network

Recently, deep unfolding networks (DUNs) have been applied to the fusion of low spatial resolution hyperspectral (LR HS) and high spatial resolution multispectral (HR MS) images and achieved satisfactory high spatial resolution hyperspectral (HR HS) images. However, the low-rank and sparse priors in these networks are not exploited sufficiently. In this paper, we establish an LR HS and HR MS image fusion model based on robust principal component analysis (RPCA), which simultaneously captures the low-rank and sparse properties in HS images. Then, the fusion model is optimized with the alternating direction method of multipliers (ADMM). To make full use of the representation capacity of DUNs, we unfold the derived ADMM algorithm as a network, named low-rank unfolding network (LRU-Net). Specifically, each iteration in ADMM is unfolded as one stage in LRU-Net, in which the low-rank and sparse priors are learned by singular value thresholding (SVT) and sparse module, respectively. Finally, all features from all stages are integrated to produce the desired HR HS image. Three benchmark datasets were chosen for comparison to demonstrate the effectiveness of the proposed LRU-Net. The experimental results demonstrate that LRU-Net performs better in terms of both qualitative and quantitative results compared to state-of-the-art fusion methods. The source code is publicly available at https://github.com/RSMagneto/LRU-Net.

Towards Reduced Order Models via Robust Proper Orthogonal Decomposition to capture personalised aortic haemodynamics

Data driven, reduced order modelling has shown promise in tackling the challenges associated with computational and experimental haemodynamic models. In this work, we focus on the use of Reduced Order Models (ROMs) to reconstruct velocity fields in a patient-specific dissected aorta, with the objective being to compare the ROMs obtained from Robust Proper Orthogonal Decomposition (RPOD) to those obtained from the traditional Proper Orthogonal Decomposition (POD). POD and RPOD are applied to in vitro, haemodynamic data acquired by Particle Image Velocimetry and compare the decomposed flows to those derived from Computational Fluid Dynamics (CFD) data for the same geometry and flow conditions. In this work, PIV and CFD results act as surrogates for clinical haemodynamic data e.g. MR, helping to demonstrate the potential use of ROMS in real clinical scenarios. The flow is reconstructed using different numbers of POD modes and the flow features obtained throughout the cardiac cycle are compared to the original Full Order Models (FOMs).Robust Principal Component Analysis (RPCA), the first step of RPOD, has been found to enhance the quality of PIV data, allowing POD to capture most of the kinetic energy of the flow in just two modes similar to the numerical data that are free from measurement noise. The reconstruction errors differ along the cardiac cycle with diastolic flows requiring more modes for accurate reconstruction. In general, modes 1–10 are found sufficient to represent the flow field. The results demonstrate that the coherent structures that characterise this aortic dissection flow are described by the first few POD modes suggesting that it is possible to represent the macroscale behaviour of aortic flow in a low-dimensional space; thus significantly simplifying the problem, and allowing for more computationally efficient flow simulations or machine learning based flow predictions that can pave the way for translation of such models to the clinic.

Effect of Sichuan Pepper (Zanthoxylum genus) Addition on Flavor Profile in Fermented Ciba Chili (Capsicum genus) Using GC-IMS Combined with E-Nose and E-Tongue.

This study examined the flavor profiles of fermented Ciba chili, comparing samples with Sichuan pepper (HJ) to those without Sichuan pepper (CK), using three analytical techniques: E-tongue, E-nose, and gas chromatography-ion mobility spectrometry (GC-IMS). The results obtained from the E-tongue and E-nose exhibited a clear difference in taste and flavor between CK and HJ. In detail, CK mainly exhibited a sour flavor profile, whereas HJ displayed an intricate and rich flavor. The HS-GC-IMS results identified a total of 60 compounds in the samples, with terpenes, alcohols, and esters being the primary volatile flavor compounds. Additionally, Zanthoxylum was found to significantly enhance the concentration of these compounds in fermented Ciba chili. Through robust principal component analysis (rPCA), 17 distinct flavor compounds were selected. Correlation analysis revealed that most terpenes exhibited positive correlations with LY2/LG, LY2/gCT1, LY2/Gct, LY2/G, LY2/Gh, and terpenes were found in higher concentrations in HJ. This study contributes a theoretical basis and provides data support for optimizing the fermentation process and elucidating the underlying mechanism of characteristic aroma formation in Ciba chili after fermentation.