Traditional Principal Component Analysis Research Articles

Machine-learning classification with additivity and diverse multifractal pathways in multiplicativity

Evidence of multifractal structures has spread to a wider set of physiological time series supporting the intricate interplay of biological and psychological functioning. These dynamics manifest as random multiplicative cascades, embodying nonlinear relationships characterized by recurring division, branching, and aggregation processes implicating noise across successive generations. This investigation focuses on how well the diversity of multifractal properties can be specific to the type of cascade relationship between generation (i.e., multiplicative, additive, or a mixture) as well as to the type of noise (i.e., including additive white Gaussian noise, fractional Gaussian noise, and various amalgamations) among 15 distinct types of binomial cascade processes. Cross-correlation analysis of multifractal spectral features confirms that these features capture nuanced aspects of cascading processes with minimal redundancy. Principal component analysis using 13 distinct multifractal spectral features shows that different cascade processes can manifest multifractal evidence of nonlinearity for distinct reasons. This transparency of multifractal spectral features to underlying cascade dynamics becomes less amenable to machine-learning strategies. Fully connected neural networks struggled to classify the 15 distinct types of cascade processes based on the respective multifractal spectral features (45.5% accuracy) yet demonstrated improved accuracy when addressing single categories of cross-generation relationships, that is, additive (91.6%), multiplicative (75.4%), or additomultiplicative (70.6%). While traditional principal component analysis reveals distinct loadings attributed to individual noise processes, multiplicative relationships between generations effectively make the constituent noise processes less discernible to neural networks. Neural networks may lack sufficient hierarchical depth required to effectively distinguish among nonadditive cascading processes, recommending either elaborating multifractal geometry or using alternate architectures for machine-learning classification of cascades with multiplicative relationships. Published by the American Physical Society 2024

Classification of Time–Frequency Maps of Guided Waves Using Foreground Extraction

Guided waves propagating in mechanical structures have proved to be an essential technique for applications, such as structural health monitoring. However, it is a well-known problem that when using non-stationary guided wave signals, dispersion, and high-order vibrational modes are excited, it becomes cumbersome to detect and identify relevant information. A typical method for the characterization of these non-stationary signals is based on time–frequency (TF) mapping techniques. This method produces 2D images, allowing the study of specific vibration modes and their evolution over time. However, this approach has low resolution, increases the size of the data, and introduces redundant information, making it difficult to extract relevant features for their accurate identification and classification. This paper presents a method for identifying discontinuities by analyzing the data in the TF maps of Lamb wave signals. Singular Value Decomposition (SVD) for low-rank optimization and then perform foreground feature extraction on the maps were proposed. These foreground features are then analyzed using Principal Component Analysis (PCA). Unlike traditional PCA, which operates on vectorized images, our approach focuses on the correlation between coordinates within the maps. This modification enhances feature detection and enables the classification of discontinuities within the maps. To evaluate unsupervised clustering of the dimensionally reduced data obtained from PCA, we experimentally tested our method using broadband Lamb waves with various vibrational modes interacting with different types of discontinuity patterns in a thin aluminum plate. A Support Vector Machine (SVM) classifier was then implemented for classification. The results of the experimental data yielded good classification effectiveness within reasonably low computational time despite the large matrixes of the TF maps used.

Exact and Approximation Algorithms for Sparse Principal Component Analysis

Sparse principal component analysis (SPCA) is designed to enhance the interpretability of traditional principal component analysis by optimally selecting a subset of features that comprise the first principal component. Given the NP-hard nature of SPCA, most current approaches resort to approximate solutions, typically achieved through tractable semidefinite programs or heuristic methods. To solve SPCA to optimality, we propose two exact mixed-integer semidefinite programs (MISDPs) and an arbitrarily equivalent mixed-integer linear program. The MISDPs allow us to design an effective branch-and-cut algorithm with closed-form cuts that do not need to solve dual problems. For the proposed mixed-integer formulations, we further derive the theoretical optimality gaps of their continuous relaxations. Besides, we apply the greedy and local search algorithms to solving SPCA and derive their first-known approximation ratios. Our numerical experiments reveal that the exact methods we developed can efficiently find optimal solutions for data sets containing hundreds of features. Furthermore, our approximation algorithms demonstrate both scalability and near-optimal performance when benchmarked on larger data sets, specifically those with thousands of features. History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms—Discrete. Funding: This research was supported in part by the Division of Civil, Mechanical and Manufacturing Innovation [Grant 224614], the Division of Computing and Communication Foundations [Grant 2246417], and the Office of Naval Research [Grant N00014-24-1-2066]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.0372 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2022.0372 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

Robust Principal Component Analysis Based on Fuzzy Local Information Reservation.

Principal Component Analysis (PCA) aims to acquire the principal component space containing the essential structure of data, instead of being used for mining and extracting the essential structure of data. In other words, the principal component space contains not only information related to the essential structure of data but also some unrelated information. This frequently occurs when the intrinsic dimensionality of data is unknown or when it has complex distribution characteristics such as multi-modalities, manifolds, etc. Therefore, it is unreasonable to identify noise and useful information based solely on reconstruction error. For this reason, PCA is unsuitable as a preprocessing technique for most applications, especially in noisy environment. To solve this problem, this paper proposes robust PCA based on fuzzy local information reservation (FLIPCA). By analyzing the impact of reconstruction error on sample discriminability, FLIPCA provides a theoretical basis for noise identification and processing. This not only greatly improves its robustness but also extends its applicability and effectiveness as a data preprocessing technique. Meanwhile, FLIPCA maintains consistent mathematical descriptions with traditional PCA while having few adjustable hyperparameters and low algorithmic complexity. Finally, we conducted comprehensive experiments on synthetic and real-world datasets, which substantiated the superiority of our proposed algorithm.

Supervised Dynamic PCA: Linear Dynamic Forecasting with Many Predictors

This paper proposes a novel dynamic forecasting method using a new supervised Principal Component Analysis (PCA) when a large number of predictors are available. The new supervised PCA provides an effective way to bridge the gap between predictors and the target variable of interest by scaling and combining the predictors and their lagged values, resulting in an effective dynamic forecasting. Unlike the traditional diffusion-index approach, which does not learn the relationships between the predictors and the target variable before conducting PCA, we first re-scale each predictor according to their significance in forecasting the targeted variable in a dynamic fashion, and a PCA is then applied to a re-scaled and additive panel, which establishes a connection between the predictability of the PCA factors and the target variable. We also propose to use penalized methods such as the LASSO to select the significant factors that have superior predictive power over the others. Theoretically, we show that our estimators are consistent and outperform the traditional methods in prediction under some mild conditions. We conduct extensive simulations to verify that the proposed method produces satisfactory forecasting results and outperforms most of the existing methods using the traditional PCA. An example of predicting U.S. macroeconomic variables using a large number of predictors showcases that our method fares better than most of the existing ones in applications.

A Novel Technique for Semantic Segmentation of Hyperspectral Images Using Multi-View Features

This research presents an innovative technique for semantic segmentation of Hyperspectral Image (HSI) while focusing on its dimensionality reduction. A unique technique is applied to three distinct HSI landcover datasets, Indian Pines, Pavia University, and Salinas Valley, acquired from diverse sensors. HSIs are inherently multi-view structures, causing redundancy and computation overload due to their high dimensionality. The technique utilizes Canonical Correlation Analysis (CCA) variants, Pairwise CCA (PCCA) and Multiple Set CCA (MCCA), to extract features from multiple views of the input image simultaneously. The performance of PCCA and MCCA is compared with the traditional Principal Component Analysis (PCA) on all datasets. The superior performance of CCA variants, particularly MCCA, is demonstrated in achieving higher Overall Accuracy (OA) for semantic segmentation compared to PCA. The research extends the analysis by integrating machine learning classifiers for per pixel prediction, demonstrating the effectiveness of the proposed techniques i.e., PCCA-SVM and MCCA-SVM.

Hybrid feature selection method for predicting software defect

To address the challenges associated with the abundance of features in software datasets, this study proposes a novel hybrid feature selection method that combines quantum particle swarm optimization (QPSO) and principal component analysis (PCA). The objective is to identify a subset of relevant features that can effectively contribute to the accuracy of a predictive model based on an artificial neural network (ANN). The quantum particle swarm optimization algorithm is employed to optimize the selection of features by simulating the behavior of quantum particles in a search space. This approach enhances the exploration and exploitation capabilities, allowing for a more effective identification of relevant features. Furthermore, principal component analysis is integrated into the hybrid method to reduce dimensionality and remove multicollinearity among features, thereby improving the efficiency of the feature selection process. The proposed hybrid method is applied to software defect datasets, where the selected subset of features is fed into an artificial neural network for defect prediction. The performance of the hybrid model is compared with traditional feature selection methods, standalone QPSO, and PCA. Experimental results demonstrate the effectiveness of the hybrid approach in achieving superior predictive accuracy while reducing the dimensionality of the dataset. The proposed approach not only enhances prediction accuracy but also provides a more interpretable and efficient subset of features for building robust defect prediction models.

Exploratory insights into prefrontal cortex activity in continuous glucose monitoring: findings from a portable wearable functional near-infrared spectroscopy system.

The escalating global prevalence of diabetes highlights an urgent need for advancements in continuous glucose monitoring (CGM) technologies that are non-invasive, accurate, and user-friendly. Here, we introduce a groundbreaking portable wearable functional near-infrared spectroscopy (fNIRS) system designed to monitor glucose levels by assessing prefrontal cortex (PFC) activity. Our study delineates the development and application of this novel fNIRS system, emphasizing its potential to revolutionize diabetes management by providing a non-invasive, real-time monitoring solution. Fifteen healthy university students participated in a controlled study, where we monitored their PFC activity and blood glucose levels under fasting and glucose-loaded conditions. Our findings reveal a significant correlation between PFC activity, as measured by our fNIRS system, and blood glucose levels, suggesting the feasibility of fNIRS technology for CGM. The portable nature of our system overcomes the mobility limitations of traditional setups, enabling continuous, real-time monitoring in everyday settings. We identified 10 critical features related to blood glucose levels from extensive fNIRS data and successfully correlated PFC function with blood glucose levels by constructing predictive models. Results show a positive association between fNIRS data and blood glucose levels, with the PFC exhibiting a clear response to blood glucose. Furthermore, the improved regressive rule principal component analysis (PCA) method outperforms traditional PCA in model prediction. We propose a model validation approach based on leave-one-out cross-validation, demonstrating the unique advantages of K-nearest neighbor (KNN) models. Comparative analysis with existing CGM methods reveals that our paper's KNN model exhibits lower RMSE and MARD at 0.11 and 8.96%, respectively, and the fNIRS data were highly significant positive correlation with actual blood glucose levels (r = 0.995, p < 0.000). This study provides valuable insights into the relationship between metabolic states and brain activity, laying the foundation for innovative CGM solutions. Our portable wearable fNIRS system represents a significant advancement in effective diabetes management, offering a promising alternative to current technologies and paving the way for future advancements in health monitoring and personalized medicine.

Efficiency of clustering methods and self-organizing maps of Adriatic sardines and anchovies regarding organochlorine and fatty acid burden.

The Adriatic Sea plays a crucial role as both a significant fishing ground and a thriving trading market for small pelagic edible fish. Recognized for their nutritional value, these fish are esteemed for their high protein content and abundance of polyunsaturated omega-3 and omega-6 fatty acids, making them a sought-after and healthful food choice. Nevertheless, pelagic species can also serve as a reservoir for lipophilic organochlorine pollutants, posing potential risks to human health. In this study, we compared traditional classification methods traditional principal component analysis (PCA) and Ward's clustering with an advanced self-organizing map (SOM) algorithm in determining distribution patterns of 24 organochlorines and 19 fatty acids in sardine and anchovy samples taken from the eastern Adriatic. The outcomes reveal the strengths and weaknesses of the three approaches (PCA, Ward's clustering, and SOM). However, it is evident that SOM has proven to be the most effective in offering detailed information and data visualization. Although sardines and anchovies exhibit similar distribution patterns for p,p'-DDE, PCB-28, PCB-138, PCB-153, PCB-118, and PCB-170, they differ in the concentrations of fatty acids such as stearic, palmitic, myristic, oleic, docosapentaenoic, and docosahexaenoic acid. Our findings supply valuable insights for environmental authorities and fish consumers concerning the potential risks associated with organochlorines in these two types of fish.

Nonunion scaphoid bone shape prediction using iterative kernel principal polynomial shape analysis.

The scaphoid is an important mechanical stabilizer for both the proximal and distal carpal columns. The precise estimation of the complete scaphoid bone based on partial bone geometric information is a crucial factor in the effective management of scaphoid nonunion. Statistical shape model (SSM) could be utilized to predict the complete scaphoid shape based on the defective scaphoid. However, traditional principal component analysis (PCA) based SSM is limited by its linearity and the inability to adjust the number of modes used for prediction. This study proposes an iterative kernel principal polynomial shape analysis (iKPPSA)-based SSM to predict the pre-morbid shape of the scaphoid, aiming at enhancing the accuracy as well as the robustness of the model. Sixty-five sets of scaphoid images were used to train SSM and nine sets of scaphoid images were used for validation. For each validation image set, three defect types (tubercle, proximal pole, and avascular necrosis) were virtually created. The predicted shapes of the scaphoid by PCA, PPSA, KPCA, and iKPPSA-based SSM were evaluated against the original shape in terms of mean error, Hausdorff distance error, and Dice coefficient. The proposed iKPPSA-based scaphoid SSM demonstrates significant robustness, with a generality of 0.264mm and a specificity of 0.260mm. It accounts for 99% of variability with the first seven principal modes of variation. Compared to the traditional PCA-based model, the iKPPSA-based scaphoid model prediction demonstrated superior performance for the proximal pole type fracture, with significant reductions of 25.2%, 24.7%, and 24.6% in mean error, Hausdorff distance, and root mean square error (RMSE), respectively, and a 0.35% improvement in Dice coefficient. This study showed that the iKPPSA-based SSM exploits the nonlinearity of data features and delivers high reconstruction accuracy. It can be effectively integrated into preoperative planning for scaphoid fracture management or morphology-based biomechanical modeling of the scaphoid.

Demonstrating the relevance of spatial-functional statistical analysis in marine ecological studies: The case of environmental variations in micronektonic layers

In this study, we conducted an analysis of a multifrequency acoustics dataset acquired from scientific echosounders in the West African water. Our objective was to explore the spatial arrangement of marine organism aggregations. We investigated various attributes of these intricate biological entities, such as thickness, relative density, and depth, in relation to their surroundings. These environmental conditions were represented at a fine scale using a towed multiparameter system. This study is closely intertwined with two key domains: Fisheries acoustics techniques and functional data analysis. Fisheries acoustics techniques facilitate the collection of high-resolution spatial and temporal data concerning marine organisms at various depths and spatial scales, all without causing any disturbance. On the other hand, spatial-functional data analysis is a statistical approach for examining data characterised by functional attributes distributed across a spatial domain. This analysis encompasses dimension reduction techniques, as well as supervised and unsupervised methods, which take into consideration spatial dependencies within extensive datasets.We began by applying multivariate statistical techniques and subsequently employed Functional Data Analysis (FDA). In the modeling section, we introduced the spatial dimension with the spatial coordinates as covariates in the General Additive Model (GAM) and Functional Generalized Spectral Additive Model (FGSAM) models, aiming to underscore its relevance in those contexts. In an exploratory phase, Multivariate Functional Principal Component Analysis provided detailed insights into the variations of parameters at different depths, a capability not offered by traditional Principal Component Analysis. When it came to regression tasks, we explored the interactions between descriptors of Sound Scattering Layers and key environmental variables, both with and without considering spatial dimensions. Our findings revealed significant distinctions between northern and southern Sound Scattering Layers, as well as between coastal and high-sea regions. The use of the spatial locations enhanced the performance of GAM and FGSAM, particularly in the case of salinity, reflecting the influence of water mixing and seawater temperature. The multifaceted effects of environmental variations on Sound Scattering Layers underscore the importance of spatial-functional statistical analysis in ecological studies involving complex, spatially functional objects. Beyond the scope of this specific case study, the application of functional data analysis shows promise for a wide array of ecological studies dealing with extensive spatial datasets.

Try with Simpler – An Evaluation of Improved Principal Component Analysis in Log-based Anomaly Detection

With the rapid development of deep learning (DL), the recent trend of log-based anomaly detection focuses on extracting semantic information from log events (i.e., templates of log messages) and designing more advanced DL models for anomaly detection. Indeed, the effectiveness of log-based anomaly detection can be improved, but these DL-based techniques further suffer from the limitations of more heavy dependency on training data (such as data quality or data labels) and higher costs in time and resources due to the complexity and scale of DL models, which hinder their practical use. On the contrary, the techniques based on traditional machine learning or data mining algorithms are less dependent on training data and more efficient, but produce worse effectiveness than DL-based techniques which is mainly caused by the problem of unseen log events (some log events in incoming log messages are unseen in training data) confirmed by our motivating study. Intuitively, if we can improve the effectiveness of traditional techniques to be comparable with advanced DL-based techniques, log-based anomaly detection can be more practical. Indeed, an existing study in the other area (i.e., linking questions posted on Stack Overflow) has pointed out that traditional techniques with some optimizations can indeed achieve comparable effectiveness with the state-of-the-art DL-based technique, indicating the feasibility of enhancing traditional log-based anomaly detection techniques to some degree. Inspired by the idea of “try-with-simpler”, we conducted the first empirical study to explore the potential of improving traditional techniques for more practical log-based anomaly detection. In this work, we optimized the traditional unsupervised PCA (Principal Component Analysis) technique by incorporating a lightweight semantic-based log representation in it, called SemPCA , and conducted an extensive study to investigate the potential of SemPCA for more practical log-based anomaly detection. By comparing seven log-based anomaly detection techniques (including four DL-based techniques, two traditional techniques, and SemPCA ) on both public and industrial datasets, our results show that SemPCA achieves comparable effectiveness as advanced supervised/semi-supervised DL-based techniques while being much more stable under insufficient training data and more efficient, demonstrating that the traditional technique can still excel after small but useful adaptation.

Exploring the impact of oil security attention on oil volatility: A new perspective

AbstractBy constructing a novel index, the oil security attention index, this paper uses the heterogeneous autoregressi (HAR)‐type and its extended models to study whether oil security attention can predict oil volatility. Based on the definition of the different dimensions of oil security and three‐pass regression filter (TPRF) dimension reduction technology, combined with Google search volume data of 23 keywords related to oil security, the oil security attention index is constructed. Considering the potential nonlinear relationship between attention and oil volatility, we incorporate asymmetric effects in the new extended HAR‐type models. The research findings show that the oil security attention index we propose can capture the volatility of West Texas Intermediate. The out‐of‐sample results indicate that the extended models have better predictive power, which confirms the asymmetric relationship between oil security attention and oil volatility. In the robustness analysis, we compare TPRF with traditional principal component analysis (PCA) and partial least squares (PLS), and show that the oil security attention index constructed using TPRF has more favourable information than PCA and PLS to capture the oil security attention of the public.

Time-slice dynamic prediction and multiway serial PCA for batch industrial process monitoring

This paper introduces an innovative method for batch industrial process monitoring and fault detection. By combining time-slice dynamic prediction with an enhanced adaptive multiway principal component analysis (PCA) technique, it aims to balance the trade-off between high fault detection rates and low false alarm rates in monitoring batch industrial data. The method extracts dynamic features from 3D batch data time slices and utilizes a serial PCA framework with variable control limits for real-time monitoring. Comparative evaluations against traditional adaptive multiway PCA and dynamic time-slice canonical correlation analysis approaches demonstrate its superior performance. A case study using a novel cold rolling mill simulation model underscores its effectiveness for batch industrial process monitoring and fault detection.

Fault detection and diagnosis for chemical processes using dynamic global–local preserving projections

AbstractMost traditional multivariate statistical monitoring methods require an assumption that the observation values at a certain moment and a past moment are statistically independent. However, in actual chemical and biological processes, the sample at a certain moment is often affected by the previous moment. Therefore, given the problem of more false alarms and poor detection ability based on the traditional principal component analysis, this article proposes a dynamic global–local preserving projections (DGLPP) algorithm. Unlike dynamic local preserving projections (DLPP) and dynamic principal component analysis (DPCA), DGLPP controls the global and local information retained in the dimensionality reduction data by introducing weight coefficients, which makes the algorithm applicable to more types of industrial processes. Moreover, new parameter determination methods are also proposed for improved detection and diagnosis. Through the improved contribution graph method, we can see the influence degree of each variable on the fault, to monitor and isolate the fault. Finally, by verifying the operation of the multivariable process and two practical cases, the results show that compared with DPCA, DLPP, and global local retained projection (GLPP) methods, the performance under this method has been significantly improved.

A Regularized High-Dimensional Positive Definite Covariance Estimator with High-Frequency Data

This paper proposes a novel large-dimensional positive definite covariance estimator for high-frequency data under a general factor model framework. We demonstrate an appealing connection between the proposed estimator and a weighted group least absolute shrinkage and selection operator (LASSO) penalized least-squares estimator. The proposed estimator improves on traditional principal component analysis by allowing for weak factors, whose signal strengths are weak relative to idiosyncratic components. Despite the presence of microstructure noises and asynchronous trading, the proposed estimator achieves guarded positive definiteness without sacrificing the convergence rate. To make our method fully operational, we provide an extended simultaneous alternating direction method of multipliers algorithm to solve the resultant constrained convex minimization problem efficiently. Empirically, we study the monthly high-frequency covariance structure of the stock constituents of the S&amp;P 500 index from 2008 to 2016, using all traded stocks from the NYSE, AMEX, and NASDAQ stock markets to construct the high-frequency Fama-French four and extended eleven economic factors. We further examine the out-of-sample performance of the proposed method through vast portfolio allocations, which deliver significantly reduced out-of-sample portfolio risk and enhanced Sharpe ratios. The success of our method supports the usefulness of machine learning techniques in finance. This paper was accepted by Agostino Capponi, finance. Funding: This work was supported by the Research Grants Council, University Grants Committee [Grants 11500119, 11505522, 11505721, and 21504818] and the National Natural Science Foundation of China (NSFC) Basic Scientific Center Project [Grant 71988101], entitled as “Econometric Modelling and Economic Policy Studies”, as well as NSFC [Grants 71803166 and 72173104]. Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2022.04138 .

Improved secure PCA and LDA algorithms for intelligent computing in IoT‐to‐cloud setting

AbstractThe rapid development of new technologies such as artificial intelligence and big data analysis requires the simultaneous development of cloud computing technology. The application of IoT‐to‐cloud setting has been fully applied in various industry sectors, such as sensor‐cloud system which is composed of wireless sensor network and cloud computing technology. With the increasing amount and types of collected data, companies need to reduce the dimension of massive data in cloud servers for obtaining data analysis reports rapidly. Due to frequent cloud server data leaks, companies must adequately protect the privacy of some confidential data. To this end, we designed a dimension reduction method for ciphertext data in the sensor‐cloud system based on the CKKS encryption scheme, principal component analysis (PCA) and linear discriminant analysis (LDA) dimension reduction algorithm. As data cannot be directly calculated using traditional PCA and LDA algorithm after encryption, we add some interactive operations and iterative calculations to replace some steps in traditional algorithms. Finally, we select the classification dataset IRIS which is commonly used in machine learning, and screen out the best encryption and calculation parameters, and efficiently realize the dimension reduction method of ciphertext data through a large number of experiments.

A novel fault detection scheme for a nonlinear dynamic process based on generalized non‐negative matrix projection‐maximum mean discrepancy: Application on the DAMADICS benchmark process

AbstractIn order to address the issue of minor fault detection in nonlinear dynamic processes, this paper proposes a fault detection method based on generalized non‐negative matrix projection‐maximum mean discrepancy (GNMP‐MMD). Firstly, the GNMP is employed to acquire the residual scores of the samples. Subsequently, a sliding window approach is integrated with MMD for real‐time monitoring of sample status within the residual subspace. In this study, GNMP is utilized to mitigate the impact of non‐Gaussianity in data distribution, while MMD serves to alleviate autocorrelation among samples. A numerical case and experimental data collected from the DAMADICS process are utilized to simulate and validate the proposed method. Compared to traditional principal component analysis (PCA), dynamic principal component analysis (DPCA), dynamic kernel principal component analysis (DKPCA), non‐negative matrix factorization (NMF), GNMP, and MMD, the experiment results clearly illustrate the feasibility of the proposed method.

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.

Error Evaluation Method of Capacitive Voltage Transformer Based on Improved Principal Component Analysis

The capacitive voltage transformer is an important data source for electricity trading and is easily influenced by environmental factors during operation, resulting in decreased metering accuracy. Because the voltage data does not satisfy the Gaussian distribution, the accuracy of the traditional principal component analysis method is poor when evaluating the error of capacitive voltage transformers. This paper proposes an improved principal component analysis method based on the local outlier factor. First, principal component analysis is utilized to separate the primary voltage fluctuation and error change. Then, a new statistic is established by using the local outlier factor instead of the traditional statistic as an evaluation standard, which reduces the missed diagnosis and misdiagnosis caused by the data distribution characteristics. The experimental results show that the improved method is better than the traditional method in terms of the detection rate of transformer anomaly detection, can effectively detect the abnormal change of transformer error and is more suitable for capacitive voltage transformers in operation.