Principal Component Analysis Approach Research Articles

Comparisons of Different Representative Species Selection Schemes for Reduced-Order Modeling and Chemistry Acceleration of Complex Hydrocarbon Fuels

The simulation of engine combustion processes, such as autoignition, an important process in the co-optimization of fuel-engine design, can be computationally expensive due to the large number of thermo-chemical scalars needed to describe the full chemical system. Yet, the inherent correlations between the different chemical species during oxidation can significantly reduce the complexity of representing this system. One strategy is to select a subset of representative species that accurately captures the combustion process at a fraction of the computational cost of the full system. In this study, we compare the performance of four different techniques to select these species. They include the two-step principal component analysis (PCA) approach, directed relation graphs (DRGs), the global pathway selection (GPS) approach, and the manifold-informed species selection method. A parametric study of the representative species selection is carried out on data from the simulation of homogeneous and perfectly stirred reactors by investigating seven cumulative variances and 47 different cut-off percentages for the two-step PCA, and 65 and 51 thresholds for the DRGs and GPS, respectively. Results show that these selection methods capture key important species that can accurately describe the chemical system and track each stage of oxidation. The two-step PCA is sensitive to the cumulative variance, and DRGs and GPS are sensitive to the choice of target variables. By selecting key representative species and reducing the number of thermo-chemical scalars, these three methods can be used to develop computationally efficient hybrid chemistry schemes.

Comparison of linear and nonlinear modeling approaches to develop an abundance index based on voyage and market data for a data-limited fishery

IntroductionWorldwide coastal fish resources face severe threats from fisheries overexploitation. However, the evaluation of abundance trends in most coastal fisheries is constrained by limited data. This study took blackmouth croaker (Atrobucca nibe), a stock depleted by coastal trawl fishery in southwestern Taiwan, as an example to showcase the development of a relative abundance index from data-limited fishery (only landing data were available).MethodsThis study employed unique data sourcing from voyage data recorders (VDRs) to estimate fishing effort (in combination with landing data to estimate the catch per unit effort, CPUE) that demonstrated the potential application in global data-limited fisheries and assessed alternative approaches for predictors of fishery-targeting practices to condition effort for producing more accurate metrics of relative abundance. The nominal CPUE was standardized using three statistical models: generalized linear model, generalized additive model (GAM), and vector-autoregressive spatiotemporal models (VASTs) with two treatments of each of the four effects: environmental (sea temperature, salinity, density of mixing layer, seafloor temperature, and chlorophyll), vessel, spatial, and targeting effects. A total of 15 models were designed and compared for these effects, and their explanatory power (EP) was evaluated using cross-validation R2 and other metrics.Results and discussionResults indicated that the targeting effect exerted the most significant influence on standardization and was suggested to be addressed through the principal component analysis (PCA) approach. Both vessel and spatial effects demonstrated considerable influence, whereas the environmental effect exhibited a limited impact, possibly due to the small fishing area in this study. Regarding models’ EP, given the nonlinear nature of the PCA algorithm and environmental data, the study highlighted the superiority of the GAM over linear-based models. However, incorporating nonlinear features in VAST (M15) makes it the most effective model in terms of predictive power in this study. Concerning the stock status, despite variations in relative CPUE trends among major models, a general declining trend since 2015 signals the potential decline of the blackmouth stock and urges fishery managers to consider further design of management measures.

Assessing the effectiveness of spatial PCA on SVM-based decoding of EEG data

Principal component analysis (PCA) has been widely employed for dimensionality reduction prior to multivariate pattern classification (decoding) in EEG research. The goal of the present study was to provide an evaluation of the effectiveness of PCA on decoding accuracy (using support vector machines) across a broad range of experimental paradigms. We evaluated several different PCA variations, including group-based and subject-based component decomposition and the application of Varimax rotation or no rotation. We also varied the numbers of PCs that were retained for the decoding analysis. We evaluated the resulting decoding accuracy for seven common event-related potential components (N170, mismatch negativity, N2pc, P3b, N400, lateralized readiness potential, and error-related negativity). We also examined more challenging decoding tasks, including decoding of face identity, facial expression, stimulus location, and stimulus orientation. The datasets also varied in the number and density of electrode sites. Our findings indicated that none of the PCA approaches consistently improved decoding performance related to no PCA, and the application of PCA frequently reduced decoding performance. Researchers should therefore be cautious about using PCA prior to decoding EEG data from similar experimental paradigms, populations, and recording setups.

Optimization of parameters and formulation of numerical model employing GRA–PCA and RSM approach for friction stir welded Ti–6Al–4V alloy joints

In this work, an endeavour was made to determine the impact of the tool’s shoulder diameter, pin profile, rotational and traverse speeds on the mechanical properties of the friction stir welded namely Ti–6Al–4 V alloy joints. A total of 21 experiments were carried out based on the central composite design (CCD) concept of response surface methodology (RSM). A quadratic regression based numerical model was formulated to ascertain the relationship amidst the parameters of FSW process and the mechanical properties of the fabricated Ti alloy joints. Analysis of variance (ANOVA) was employed to confirm the importance of parameters and their interactive impacts. Optimized process parameter combinations were ascertained by grey relation based analysis (GRA) was coupled together with principal component analysis (PCA), a hybrid based approach. Single score of GRG based response was determined and GRG scores were ranked for all experiments. 1st rank was attained by the experiment no. 20 possessing a GRG score of 2.9989. Optimized values of 25 mm shoulder diameter having a taper cylindrical pin geometry employed at a tool traverse speed of 40 mm min−1, rotational speed of 1400 rpm resulted in the generation of flaw free Ti alloy joint possessing a largest tensile strength of 809.8 MPa, yield strength of 778.7 MPa and percentage of elongation of 6.9%. SEM based fractography of Ti alloy joint specimens announced that taper cylindrical pin geometry along with 25 m shoulder diameter of employed tool have an inevitable part in generating frictional heat in ideal volumes and a perfect stirring action during FSW process.

Classical vs. neural network-based PCA approaches for lossy image compression: Similarities and differences

The paper describes three lossy data compression techniques based on the principal component analysis (PCA), which are compared using the image compression task. The presented approach uses both classical PCA method based on the eigen-decomposition of the image data covariance matrix and two different neural network structures. The first neural structure is a two-layer feed-forward network with supervised learning acting as the so-called autoencoder, and the second one is a single-layered network with an unsupervised learning method commonly known as the generalized Hebbian algorithm. For each compression method mentioned above, the influence of the number of image segments (frames) and the number of eigenvalues/eigenvectors on the compression ratio and the image quality are examined using three different gray-scale test images. The paper also addresses a vital implementation issue regarding selecting appropriate data types to represent the compressed data. The paper’s main conclusion is that the classical PCA method outperforms its neural counterparts, both in terms of the decompressed image quality and the time required to perform the compression procedure. The positive aspect of using neural networks as a tool for PCA-based lossy data compression is that they do not require calculating the correlation matrix explicitly and thus can be used in online data acquisition schemes.

Enhancing NILM classification via robust principal component analysis dimension reduction

Non-intrusive load monitoring (NILM) techniques estimate the consumption of individual appliances in a household or facility, based on aggregated reading from a centralized meter. Usually, NILM techniques are shown to be improved when various power features and additional power quality parameters are included. However, adding power features leads to increased time complexity which is a disadvantage to real-time operation. Previous attempt to operate a principal component analysis (PCA) method to reduce the dimension of the problem managed to improve the run time but with considerably low accuracy. To this end, we utilize a robust PCA approach, to mitigate the influence of outliers in the data as a measure for improved performance. The proposed procedure achieves extraordinary results with accuracy over 96% for 600 hours long record of power quality measurements of the consumption of seven appliances from the standard AMPds dataset.

Clusterization of Behavioral and Psychological Symptoms of Dementia as Assessed by Neuropsychiatric Inventory: A Case Against the Use of Principal Component Analysis.

The term Behavioral and Psychological Symptoms of Dementia (BPSD) covers a group of phenomenologically and medically distinct symptoms that rarely occur in isolation. Their therapy represents a major unmet medical need across dementias of different types, including Alzheimer's disease. Understanding of the symptom occurrence and their clusterization can inform clinical drug development and use of existing and future BPSD treatments. The primary aim of the present study was to investigate the ability of a commonly used principal component analysis to identify BPSD patterns as assessed by Neuropsychiatric Inventory (NPI). NPI scores from the Aging, Demographics, and Memory Study (ADAMS) were used to characterize reported occurrence of individual symptoms and their combinations. Based on this information, we have designed and conducted a simulation experiment to compare Principal Component analysis (PCA) and zero-inflated PCA (ZI PCA) by their ability to reveal true symptom associations. Exploratory analysis of the ADAMS database revealed overlapping multivariate distributions of NPI symptom scores. Simulation experiments have indicated that PCA and ZI PCA cannot handle data with multiple overlapping patterns. Although the principal component analysis approach is commonly applied to NPI scores, it is at risk to reveal BPSD clusters that are a statistical phenomenon rather than symptom associations occurring in clinical practice. We recommend the thorough characterization of multivariate distributions before subjecting any dataset to Principal Component Analysis.

A framework for optimizing environmental covariates to support model interpretability in digital soil mapping

A common practice in digital soil mapping (DSM) is to incorporate many environmental covariates into a machine-learning algorithm to predict the spatial patterns of soil attributes. Variance inflation factor (VIF), principal component analysis (PCA), and recursive feature elimination (RFE) are three statistical methods that can be used to reduce the number of covariates. This study aims 1) to compare VIF and PCA approaches; 2) to identify an approach to determine the minimum number of covariates in DSM to ensure model parsimony using RFE after using VIF; and 3) to examine methods to interpret the impact of covariates on the variability of the predicted soil properties. The study area was the province of British Columbia (BC), Canada. This study used legacy data for four soil properties to make digital soil maps: soil organic carbon (SOC%), pH, clay%, and coarse fragment (CF%). Seven models were made for each soil property to determine the influence on validation results by using a different number of covariates produced by various methods on validation results. The results showed that the number of covariates could be reduced from 70 to 4 to 12 with only a little or no difference in concordance correlation coefficient (CCC) validation results. The CCC results of pH models using 70 and 7 covariates were both 0.74, and for other soil properties, this difference was negligible. The validation results obtained from PCA models showed that the performance of PCA in reducing the number of covariates was not as effective as when using VIF. Moreover, this study showed that covariates related to precipitation were the most important for modeling SOC%, soil pH, and clay%. Topographic covariates were the most influential covariates for modeling soil CF%. This study emphasizes the potential benefits of combining various data reduction methods to achieve optimal outcomes and generate the most parsimonious and interpretable models.

Unveiling antioxidant capacity of standardized chitosan-tripolyphosphate microcapsules containing polyphenol-rich extract of Portulaca oleraceae

The medicinal plant Portulaca oleraceae has a long history of usage in traditional medicine. Plant extracts have several interesting pharmacological effects but have some drawbacks that can be addressed via capsulation with chitosan. This work set out to do just that tally up the antioxidant effects of a polyphenol-rich P. olerace extract and see how capsulation affected them. The reflux extraction and response surface methodology (RSM) were carried out to optimize the phenolic and flavonoid content of P. oleraceae extract. Additionally, high-resolution mass spectrometry was employed to determine the secondary metabolite present in the extract. The microcapsules of extract-loaded chitosan were prepared using the ionic gelation method and characterized in terms of size, encapsulation efficiency (EE), and morphology of microcapsules. Fourier transform infrared (FTIR) was used to observe the successful production of microcapsules with a principal component analysis (PCA) approach. The antioxidant activity of microcapsules was established using the radical scavenging method. According to RSM, the highest amounts of TPC and TFC were obtained at 72.894 % ethanol, 2.031 h, and 57.384 °C. The compounds were employed from the optimized extract of P. oleraceae including phenolics and flavonoids. The microcapsules were secured with a %EE of 43.56 ± 2.31 %. The characteristics of microcapsules were approved for the obtained product's successful synthesis according to the PCA. The microcapsules have antioxidant activity in a concentration-dependent manner (p < 0.0001). The findings of this study underscored the benefits of employing chitosan as a nanocarrier for extract, offering a promising approach to enhance plant-derived therapies.

Identification of spermatogenesis in individual seminiferous tubules and testicular tissue of adult normal and busulfan-treated mice employing Raman spectroscopy and principal component analysis

The present study aims to identify spermatogenesis in testicular seminiferous tubules (ST) and testicular tissue of adult normal and busulfan-treated mice utilizing PCA and Raman spectroscopy. Raman measurements were conducted on single tubules and testes samples from adult and immature mice, comparing them with those from busulfan-treated adult mice, with validation through histological examination. The analysis revealed a higher signal variability (30 %–40 % at the peaks), prompting scrutiny of individual Raman spectra as a means of spermatogenesis measurement. However, principal component analysis (PCA) demonstrated significant cluster separation between the ST of mature and immature mice. Similar investigations were performed to compare ST from normal mature mice and those from busulfan-treated (BS-treated) mature mice, revealing substantial separation along PC1 and PC2 for all comparison sets. Additionally, comparing testicular samples from mature and immature mice revealed distinct separation in PCA. The study concludes that the combined approach of PCA and Raman spectroscopy proves to be a noninvasive and potentially valuable method for identifying spermatogenesis in seminiferous tubules and testicular samples.

Development of in-country logistics performance index for emerging economies: a case of Indian states

PurposeLogistics sector is recognized as one of the core enablers of the economic development of a nation. However, inefficiency in logistics operations impedes the achievement of intended targets by increasing the cost of doing business. Also, it is difficult to improve the efficiency of a country’s logistics operations without a metric for evaluating and understanding logistics capabilities and efficiency. Therefore, the present study has developed In-country Logistics Performance Index (ILP Index) to propose a benchmarking tool to measure the in-country logistics competitiveness, particularly in the setting of emerging economies, i.e. India.Design/methodology/approachThis study has developed a unified index using principal component analysis and quintile approach. In addition, the proposed index relies on several dimensions that are developed and illustrated using quantitative secondary panel data.FindingsThe findings of this study reveal that the quality of infrastructure, economy, and telecommunications are the three most important dimensions that may significantly support the growth of the transportation and logistics sector. The results reveal that Gujarat, Tamil Nadu, and Maharashtra are the top performers whereas, Bihar, Jharkhand, and Jammu and Kashmir scores the least due to the insufficient logistics infrastructure as compared to other Indian states.Originality/valueGiven the extensive focus on international-level logistics index (like World Bank’s LPI) in the existing literature, this study intends to develop in-country logistics index to evaluate the logistics capabilities at the regional and state level. In addition, unlike prior studies, this study utilizes quantitative secondary data to eliminate cognitive and opinion bias. Moreover, this benchmarking tool would assist decision-makers in idealizing standard practices toward sustainable logistics operations. Additionally, the ILP index could serve the international investors in crucial decision-making, as it provides valuable insights into a country’s logistics readiness, influencing their investment choices and trade preferences. Finally, the proposed approach is adaptable to measuring the overall performance of any other industry/economy.

Application of polyphenolic compound-based HPLC fingerprint in Chinese golden camellias (Camellia sect. Chrysantha)

Chinese golden camellias (Camellia sect. Chrysantha) are traditional substitute tea with medicinal and food properties. The development of fingerprinting techniques specific to Chinese golden camellias may provide a new means of reliably assessing the quality of tea and traditional medicine. Herein, 32 total specimens were collected in Southern China and used to establish a polyphenolic compound-based high-performance liquid chromatography (HPLC) signature profile. The established chromatographic fingerprints were subjected to similarity, hierarchical clustering analysis (HCA), together with principal component analysis (PCA) evaluations, and the uncertainty and reliability for such HPLC fingerprints were also evaluated. Similarity values for C. sect. Chrysantha samples ranged from 0.721 to 0.969 relative to the reference chromatographic fingerprint (RFP). HCA and PCA approaches were performed to classify 13 specimens of C. sect. Chrysantha from different species and regions into four categories that respectively contained 7, 1, 2, and 3 specimens. In this HPLC fingerprint, peak 11 was authenticated as rutin, while peaks 2, 4, 6, 7, 9, 12 and 13 were tentatively characterized via liquid chromatography-high-resolution mass spectrometry (LC-HRMS) as corresponding with other polyphenolic agents. Credibility analyses indicated that the macroscopic qualitative and quantitative reliability values for C. fascicularis RFP were greater than 0.9500. Taken together, statistical analyses thus confirmed that this HPLC fingerprinting strategy can be reliably used to classify and assess the quality of C. sect. Chrysantha specimens. And the qualitative and quantitative reliability analysis and systematic quantitative fingerprint methods are promising tools for future efforts to ensure the quality of C. fascicularis.

Kinship relationship of Uroteuthis chinensis in the waters of western Kalimantan and northern Java based on morphometric characters and genetic structure

Uroteuthis chinensis was a squid species with a wide distribution and rapid reproduction. It was commonly found in the waters of western Kalimantan and northern Java, which were the highest squid fishing grounds in Indonesia. Exploitation of U. chinensis in these waters was intensive and increasing, which might have affected the sustainability of U. chinensis squid resources. Therefore, proper and responsible management was needed to maintain the sustainability of this squid resource. For exploitation to be sustainable and optimal, management based on stock units of the managed resources was required. Therefore, information was needed on the stock units of U. chinensis squid in the western waters of Kalimantan and northern Java. Currently, the Indonesian government has separated the management of these two interconnected waters. The method used was to analyze 12 morphometric characters and genetic structures with COI and Rhodopsin markers. Sampling locations included the Sungailiat and Pontianak, for the waters of western Kalimantan, Jakarta, Pekalongan, and Lamongan for the waters of northern Java. Morphometric data were analyzed using Principal Component Analysis (PCA) and Discriminant Analysis (DA) approaches. Genetic analysis (COI and Rhodopsin) included genetic diversity, AMOVA, and haplotype distribution. The results of the morphometric analysis showed that the 12 morphometric size characters in this study showed a close relationship between the five U. chinensis sample populations. Genetic variation between populations and FST values on COI and Rhodopsin showed very low values; P-values also showed results that were not significantly different between populations. The haplotype distribution of both COI and Rhodopsin showed almost the same composition in both observed waters. The results of these analyses suggested that U. chinensis species in both waters showed indications of connectivity and close kinship or could be regarded as a single stock. Therefore, collaborative management across fisheries management areas in both waters (western Kalimantan and northern Java) was required.

Detection and estimation of adulterated gasoline fuel in India using FTIR-ATR spectroscopy with chemometric methods

In this work, Fourier Transform Infrared Attenuated Total Reflectance (FTIR-ATR) spectroscopy was combined with multivariate techniques, such as Principal Component Analysis (PCA), Soft Independent Modelling of Class Analogy (SIMCA), and Partial Least Squares Discriminant Analysis (PLS-DA), to classify and quantify the gasoline adulteration with kerosene. The Calibration models of Kerosene blended on gasoline fuel of 12 standard samples (2–24% v/v) were prepared. The chemometric tools were used to compare 142 samples from Mizoram and 12 samples from neighbouring states. The PCA and SIMCA approaches did not detect adulteration. The PLS-DA classification model found 7 samples were adulterated, with excellent specificity and sensitivity. The PLS regression model had the ability to predict adulterant concentrations with prediction errors less than 2% for all adulterants. The predicted concentration range of the PLS-R model is 0.3–13 % v/v, with high significant values of R-Square (0.996) and RMSE (0.405).

Good governance and natural resource management in oil and gas resource-rich countries: A machine learning approach

Good governance and performance in managing oil and gas resources is an area of growing interest in resource-rich countries in the global economy. Countries with higher good governance indexes are expected to be more successful in managing natural resources. This study uses machine learning to investigate the good governance role in oil and gas resource management in 55 countries in 2017. Although our primary focus is on the oil- and gas-rich countries, the findings can be applied to other resource-rich countries. Using the Principal Components Analysis and K-clustering approach, countries are clustered into six groups based on good governance data. The result shows that only the four developed countries (i.e., 7% of the sample countries including Norway, UK, Canada, and US) show a high level of good governance. However, the other countries, including 82% of the sample, mainly indicate a low level of good governance. Since this majority wholly includes developing countries, the results not only confirm the resource curse hypothesis but also reveal the association between good governance and natural resource management. In addition, the results indicate that the countries in the same cluster of good governance are located in the neighboring regions, implying the effects of various cultural, social, historical, traditional, and trade factors. These countries should manage the resource revenue in a transparent and adequately taxed framework while increasing economic diversity and complexity. Furthermore, they should enhance regional cooperation and knowledge sharing by considering the spatial and geographical flows and effects to improve good governance.

A Survey on Factors Preventing the Adoption of Automated Software Testing: A Principal Component Analysis Approach

Automated software testing is a crucial yet resource-intensive aspect of software development. This burden on resources affects widespread adoption, with expertise and cost being the primary challenges preventing adoption. This paper focuses on automated testing driven by manually created test cases, acknowledging its advantages while critically analysing its implications across various development stages that are affecting its adoption. Additionally, it analyses the differences in perception between those in nontechnical and technical roles, where nontechnical roles (e.g., management) predominantly strive to reduce costs and delivery time, whereas technical roles are often driven by quality and completeness. This study investigates the difference in attitudes toward automated testing (AtAT), specifically focusing on why it is not adopted. This article presents a survey conducted among software industry professionals that spans various roles to determine common trends and draw conclusions. A two-stage approach is presented, comprising a comprehensive descriptive analysis and the use of Principal Component Analysis. In total, 81 participants received a series of 22 questions, and their responses were compared against job role types and experience levels. In summary, six key findings are presented that cover expertise, time, cost, tools and techniques, utilisation, organisation, and capacity.

Innovative teaching strategies: A principal component analysis

The paper investigated the degree of innovative teaching practices by secondary school teachers in the Vhembe District, South Africa, using a principal component analysis approach. Innovative teaching strategies refer to creative and efficient actions and performances that teachers use in the selection of materials, techniques, and learner assessments to encourage and develop learner creativity (Yu et al., 2021). Innovative teachers are those whose teaching methods differ from the conventional patterns of knowledge-transfer teaching and teacher-centred teaching. They solve educational problems in novel ways using new technologies and theoretical frameworks while guiding learners in deep learning and creativity (Tan et al., 2022). The objective of the study was to examine the innovative teaching strategies implemented by teachers in rural secondary schools to improve learner performance. A descriptive case study was employed in the paper, which was based on a quantitative research design. Using probability sampling approaches, 338 secondary school teachers were sampled. Data was collected through questionnaires and was analysed using descriptive statistical methods. The variables were reduced from 30 to 9 clusters using principal component analysis with varimax rotation. Clusters were termed stakeholders’ engagement, school and classroom practices, learner support, collaboration, professionalism, technology, relationships, diversity, and expertise.

Exploration of grid energy efficiency influencing factors by applying principal component analysis approach

Abstract This paper focuses on the problem of power losses in the transmission, transformation, distribution and marketing segments of the power system, and explores how to effectively improve the energy efficiency of the power grid to optimize the cost management of the power grid. The article uses principal component analysis to accurately diagnose the energy efficiency status of the grid, and analyzes the multiple factors affecting grid losses and their degree of influence. It is found that the total loss in 10km transmission line when wind power access reaches 328kw, and the complete loss of wind power access is higher than photovoltaic access under the condition of different line lengths, which are 315kw, 321kw, and 328kw, respectively. In the use of iron transmission line, the average loss at the current of 400A is 89.600W, which is higher than using aluminum alloy material by 66.200 W. If energy-efficient aluminum alloy fittings are fully utilized in transmission lines, the average annual power saving can be up to 301,368 kWh. The study shows that it is crucial to analyze the factors affecting the energy efficiency of power grids during the planning and construction stage of the power grids.

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.

A dimension reduction approach for loss valuation in credit risk modeling

This paper addresses the “curse of dimensionality” in the loss valuation of credit risk models. A dimension reduction methodology based on the Bayesian filter and smoother is proposed. This methodology is designed to achieve a fast and accurate loss valuation algorithm in credit risk modeling, but it can also be extended to valuation models of other risk types. The proposed methodology is generic, robust and can easily be implemented. Moreover, the accuracy of the proposed methodology in the estimation of expected loss and value-at-risk (VaR) is illustrated by numerical experiments. The results suggest that, compared to the currently most used Principal Component Analysis (PCA) approach, the proposed methodology provides more accurate estimation of expected loss and VaR of a loss distribution.