Reduction of the Multivariate Input Dimension Using Principal Component Analysis

Background Availability of numerous oil deposits with a wide variety of the conditions of occurrence, reservoir properties and physical-chemical properties of fluids makes important the need of grouping of development objects and identification of relatively uniform groups by certain criteria. Grouping allows to define similarities and differences between deposits in determining development objects, and to substantiate systems of development. Analysis of large data sets on objects characterized by the measured or estimated parameters is labor-intensive, requiring a lot of time and effort, so there is a question of dimension reduction, i.e. of reducing the original data set to a smaller number of parameters, and grouping of objects into relatively uniform groups. Here the parameters can be selected from the original ones or obtained by calculation and conversion (with the least loss of information about the objects under study). An effective tool of analysis that can help in this matter is the method of principal component analysis. Aims and Objectives Apply the method of principal component analysis to reduce the number of parameters which define objects of study, so that to find effective ways to develop new oil and gas deposits, and fast and correct solution of practical problems through the use of gained summary experience and assessment of similarities and differences of oil and gas reservoirs by combinations of geological-field attributes. Methods The problem of ranking oil deposits in Western Siberia, is solved by the method of principal component analysis, which is a linear transformation of features in a new set of «independent» random values, which are arranged in descending order of their variances, and the main components are determined by the eigenvectors of the correlation matrix obtained based on input parameters characterizing the objects under investigation. Having selected the components that comprise the bulk of the variances, one can calculate them for different types of objects and classify by clusterable points. Grouping of objects of research was carried out using built-in functions of computer statistics programs (a system of statistical analysis Statistica, analytical applications for Microsoft Excel XLStat). The same calculation was performed on the basis of the theory of mathematical statistics. The calculation results coincided. Results The method of principal component analysis allowed selection from the original data set comprising 50 research objects characterized by 12 parameters of six relatively uniform groups using only 4 factors (principal components) which, however, contain much more information than the individual parameters. As a result of the carried out analysis data were systematized and the dimension of the initial population (transition from multidimensional space to the four-dimensional) was reduced, with no significant loss of information about research objects. Conclusion Based on the proposed algorithm, and relatively uniform groups obtained there is a possibility for inclusion of new deposits into one of these groups and selection of the nearest to it analogous object, that will simplify the design of development system and identify ways and means of improving system’s effectiveness.

The development of artificial neural networks is related to statistical and biometric analysis which is one of the applications that can require artificial neural network models. Recognition of facial patterns is an important part of identifying a person. The face can be divided into areas such as the nose, eyes and mouth. Face pattern recognition is a research area that can be applied to the principal component analysis (PCA) method. The training process carried out by the eigenface calculation uses PCA and the results of this study show that facial pattern recognition based on the proportion of memorization and generalization for the use of the method without PCA is better than facial pattern recognition using PCA. Pattern recognition without using the PCA method, the level of memorization and generalization reaches 100% at the 40th iteration and 0.0099 error with a learning rate and momentum of 0.8, while facial pattern recognition using the PCA method, the memorization and generalization level reaches 100% in the iteration. to -1000 and error 0.00103 with learning rate and momentum 0.9.

Systematic principal component analysis (PCA) methods are presented in this paper for reliable islanding detection for power systems with significant penetration of distributed generations (DGs), where synchrophasors, recorded by phasor measurement units, are used for system monitoring. Existing islanding detection methods, such as rate-of-change-of-frequency and vector shift are fast for processing local information; however, with the growth in installed capacity of DGs, they suffer from several drawbacks. Incumbent genset islanding detection cannot distinguish a system-wide disturbance from an islanding event, leading to maloperation. The problem is even more significant when the grid does not have sufficient inertia to limit frequency divergences in the system fault/stress due to the high penetration of DGs. To tackle such problems, this paper introduces PCA methods for islanding detection. A simple control chart is established for intuitive visualization of the transients. A recursive PCA scheme is proposed as a reliable extension of the PCA method to reduce the false alarms for time-varying process. To further reduce the computational burden, the approximate linear dependence condition errors are calculated to update the associated PCA model. The proposed PCA and RPCA methods are verified by detecting abnormal transients occurring in the U.K. utility network.

ABSTRACTThis study presents an integrated approach, based on data envelopment analysis (DEA) and principal component analysis (PCA) methods, to evaluate the influence of Six Sigma deployment on key job characteristics in an automotive industry. The job characteristics are defined as satisfaction, stress, and security. A standard questionnaire is designed and distributed among the employees at the company's production site, who were affected by the implementation of Six Sigma. DEA and PCA methods are applied to measure the performance of the sub-groups of employees in the company. Consequently, the most efficient and inefficient sub-groups are determined. According to the findings of this investigation, it was perceived that the implementation of Six Sigma has had the greatest impact on job satisfaction. Additionally, a design of experiment was carried out to recognize the most effective job factor, which was identified to be the overall working conditions for the related case study. This is the first study that integrates DEA and PCA toward identifying and optimizing job characteristics in terms of Six Sigma implementation. The approach, employed in this study, can be easily used in the other manufacturing systems, in order to assist them to identify and improve their key job characteristics.

This paper presents a novel Gabor-based kernel Principal Component Analysis (PCA) method by integrating the Gabor wavelet representation of face images and the kernel PCA method for face recognition. Gabor wavelets first derive desirable facial features characterized by spatial frequency, spatial locality, and orientation selectivity to cope with the variations due to illumination and facial expression changes. The kernel PCA method is then extended to include fractional power polynomial models for enhanced face recognition performance. A fractional power polynomial, however, does not necessarily define a kernel function, as it might not define a positive semidefinite Gram matrix. Note that the sigmoid kernels, one of the three classes of widely used kernel functions (polynomial kernels, Gaussian kernels, and sigmoid kernels), do not actually define a positive semidefinite Gram matrix either. Nevertheless, the sigmoid kernels have been successfully used in practice, such as in building support vector machines. In order to derive real kernel PCA features, we apply only those kernel PCA eigenvectors that are associated with positive eigenvalues. The feasibility of the Gabor-based kernel PCA method with fractional power polynomial models has been successfully tested on both frontal and pose-angled face recognition, using two data sets from the FERET database and the CMU PIE database, respectively. The FERET data set contains 600 frontal face images of 200 subjects, while the PIE data set consists of 680 images across five poses (left and right profiles, left and right half profiles, and frontal view) with two different facial expressions (neutral and smiling) of 68 subjects. The effectiveness of the Gabor-based kernel PCA method with fractional power polynomial models is shown in terms of both absolute performance indices and comparative performance against the PCA method, the kernel PCA method with polynomial kernels, the kernel PCA method with fractional power polynomial models, the Gabor wavelet-based PCA method, and the Gabor wavelet-based kernel PCA method with polynomial kernels.

Introduction: Saffron is one of the most important economic plants in the Khorasan province. Awareness of soil quality in agricultural lands is essential for the best management of lands and for obtaining maximum economic benefit. In general, plant growth is a function of environmental factors especially chemical and physical properties of soil (20). It has been demonstrated that there was a positive and high correlation between soil organic matter and saffron yield. Increasing the yield of saffron due to organic matter is probably due to soil nutrient, especially phosphorous and nitrogen and also improvement of soil physical quality (6, 28, 29). The yield of saffron in soils with high nitrogen as a result of vegetative growth is high (8). Shahandeh (6) found that most of the variation of saffron yield depends on soil properties. Due to the economic importance of saffron and the role of soil properties on saffron yield, this research was conducted to find the relationship between saffron yield and some soil physical and chemical properties, and to determine the contribution of soil properties that have the greatest impact on saffron yield in the Ghayenat area. Materials and Methods: This research was performed in 30 saffron fields (30 soil samples) of the Ghayenat area (longitude 59° 10΄ 10.37˝ - 59° 11΄ 38.41˝ and latitude 33° 43΄ 35.08˝ - 33΄ 44΄ 02.78˝), which is located in the Khrasan province of Iran. In this research, 21 soil properties were regarded as the total data set (TDS). Then the principal component analysis (PCA) was used to determine the most important soil properties affecting saffron yield as a minimum data set (MDS) and the stepwise regression to estimate saffron yield. To estimate the yield of saffron in stepwise regression method, saffron yield was considered as a dependent variable and soil physical and chemical properties were considered to be independent variables. Results and Discussion: According to the PCA method, among the 21 studied properties, 7 out of them including calcium, iron, zinc contents, sand, calcium carbonate equivalent percent, mean weight diameter of aggregates (MWD) and manganese (Mn) had the higher Eigenvalues. Therefore, the above properties were introduced as the most important soil properties in saffron fields. Calcium carbonate had the negative effect on the availability of micro-nutrients (26). Christensen et al. (15) found that by increasing the calcium carbonate in soil due to high pH and formation of insoluble components, the uptake of micro-nutrients is especially limited. The results of stepwise regression method (equation 1) showed that soil acidity (pH), zinc content, bulk density, MWD, iron content, salinity (EC), organic carbon and available potassium in soil were the most important properties that affect the yield of saffron, so that the determination coefficient (R2) of the regression model was high (Table 2) and it can explain 74% of the variation of saffron yield. Y = 6924.51 – 1187.31 pH – 89.65 EC + 71.6 Fe – 826.02 Zn + 471.55 OC, + 5490.96 K + 1353.56 BD + 752.82 MWD (1) where Y: saffron yield (kgha-1), pH: soil acidity, EC: electoral conductivity (dSm-1), Fe: iron concentration (mgkg-1), Zn: zinc concentration (mgkg-1), OC: organic carbon (%), K: soil potassium (%), BD: soil bulk density (Mgm-3), and MWD: mean weight diameter of aggregates (MM). Based on the absolute values of standard s in the regression model (Table 3), pH value and then after Zn concentration had the most effect on saffron yield. In general, responses of different plants to soil pH is varied, and saffron grows satisfactory in pH = 7.8 (5). Soil pH influences the uptake of soil nutrients by plants (15), so that this parameter had the most effect on saffron yield and by increasing the soil pH, the yield of saffron decreases. According to the regression model, Zn concentration was the second parameter in saffron yield. Zn has the important role in structure of plant enzymes (30). After these 2 parameters, Bd, MWD, Fe concentration, EC, Organic carbon and K concentration in soil had more effect on saffron yield (Table 3). Conclusion: According to both PCA and regression methods, the concentration of iron and zinc and MWD were determined as the important and effective soil properties on saffron yield in the Ghayenat area. In addition, soil pH in stepwise regression method and calcium carbonate in PCA method were determined as the effective properties on saffron yield. Therefore, it is suggested that the parameters of Zn, Fe, and MWD along with soil pH and calcium carbonate which were regarded individually in two methods, were considered as the most soil properties in saffron yield.

Mangroves are coastal plants influenced by tidal cycles. One of the regions in South Sumatra Province with a mangrove ecosystem is Sembilang National Park. As a national park, this location is strategically positioned for research related to mangrove species. The utilization of the Principal Component Analysis (PCA) method is considered to enhance the capabilities of remote sensing data in mangrove mapping. However, its application has been limited to the mangrove level. The research objective is to identify mangrove species in Sembilang National Park using the PCA method by leveraging Landsat-8 image data acquired on September 9, 2019. Mangrove distribution is obtained through the Mangrove Vegetation Index (MVI) and vector data from Global Mangrove Watch. The image is then overlaid with field species data to obtain species spectral patterns. Additionally, the correlation between spectral band values and eigenvalues (PC) is analyzed to detect parameters correlated with eigenvalues. The research results show that PC values correlate with mangrove species and can be used for mangrove species identification. This is demonstrated by Bruguiera Gymnorrhiza species with canopy coverage of 60.8% and 62.46% at ST7 and ST8 having the same PC values, while mangroves with canopy coverage of 62.5% in different species have different PC values. Moreover, the PCA method can indicate two crucial factors in identifying mangrove species, namely vegetation and soil factors. Mangrove merupakan tumbuhan pesisir yang dipengaruhi oleh pasang surut. Salah satu wilayah di Provinsi Sumatera Selatan yang memiliki ekosistem mangrove adalah Taman Nasional Sembilang. Sebagai taman nasional, lokasi ini sangat strategis untuk dilakukan penelitian terkait spesies mangrove. Pemanfaatan metode principal component analysis (PCA) dinilai mampu meningkatkan kemampuan data penginderaan jauh dalam pemetaan mangrove. Namun selama ini, pemanfaatan terbatas pada level mangrove. Adapun tujuan penelitian adalah mengidentifikasi spesies mangrove di Taman Nasional Sembilang menggunakan metode PCA dengan memanfaatkan data citra Landsat-8 yang diakusisi pada 09 September 2019. Sebaran mangrove diperoleh melalui indeks vegetasi mangrove (MVI) dan data vektor dari Global Mangrove Watch. Citra tersebut kemudian di overlay dengan data spesies lapangan untuk mendapatkan pola spektral species. Selain itu, korelasi nilai spektral band dan eigen (PC) dianalisis untuk mendeteksi parameter yang berkorelasi dengan nilai eigen. Hasil penelitian menunjukkan nilai PC memiliki korelasi dengan spesies mangrove dan dapat digunakan untuk mengidentifikasi spesies mangrove. Hal ini ditunjukkan spesies Bruguiera Gymnorrhiza dengan tutupan kanopi 60,8% dan 62,46% pada ST7 dan ST8 memiliki nilai PC yang sama serta mangrove dengan besaran tutupan kanopi 62,5% pada spesies nilai PC berbeda. Selain itu, metode PCA mampu menunjukkan dua faktor penting dalam mengidentifikasi spesies mangrove, yaitu faktor vegetasi dan tanah.

Building energy management system(BEMS) in order to save the energy used in the operation stage of buildings has been actively introduced recently and it is recommended to apply BEMS to various certification system, but, there is a real situation such as low utilization level of comparison of energy savings and monitoring function oriented simple statistical processing. In this study, by using the principal component analysis(PCA) method that is able to analyze whether failure in repeater of measuring sensor for the chiller measurement data in the actual building where BEMS is operating, failures that exist in BEMS data were detected. PCA method is the most widely used method of adjusting the data and could detect a fault and improve the performance of diagnosis of low-dimensional description of data generated by the PCA method using multivariate statistics such as the Hotelling <TEX>$T^2$</TEX> statistics and Q-statistics to monitor the industrial system. It is found that because the end of operation time before replacing the sensor and Q-statistics beyond Q-Thresholds has been appeared to the same sample position, the failure of the sensor can be detected by PCA method using the stored BEMS data.

Biometric recognition systems or human identification are very important in security access for identification and verification systems. The biometric recognition system can be used as an identification system based on the characteristics possessed by the body part of each individual. The soles of the feet can be used for identification because the soles of the feet have certain and unique characteristics which include major lines, protrusions, small dots, single points, and textures. The introduction of biometrics in babies is still conventional, which is a standard operating procedure such as attaching bracelets on baby's feet and imprinting or inking on the soles of baby's feet which are affixed to paper and are very vulnerable to the risk of damage or loss of data, there is a need for a system that can store data automatically digital and able to do the baby identification process. The Principal Component Analysis method is used for the extraction process of the characteristics of the baby's feet. The classification uses the K-Nearest Neighbor (K-NN) method with the euclidean distance approach. Tests were carried using 120 images of baby feet, there are 20 classes, each class contains 3 images of the right foot and 3 images of the foot of the left foot, and a dataset of 280 training images. The highest accuracy result obtained in system testing is 91% with a computation time of 5.63 seconds using the Principal Component Analysis method with the K-Nearest Neighbor (K-NN) classification.Keywords: Footprint, Feature Extraction, Principal Component Analysis, K-Nearest Neighbor.

Satellite microwave emission mixed with signals from active sensors is referred to as radio-frequency interference (RFI). RFI affects greatly the quality of data and retrieval products from space-borne microwave radiometry. An accurate RFI detection will not only enhance geophysical retrievals over land but also provide evidence of the much-needed protection of the microwave frequency band for satellite remote sensing technologies. It is difficult to detect RFI from space-borne microwave radiometer data over winter land, because RFI signals are usually mixed with snow in mid-high latitudes. A modified principal component analysis (PCA) method is proposed in this paper for detecting microwave low frequency RFI signals. Only three original variables, one RFI index (sensitive to RFI signal) and two scattering indices (sensitive to snow scattering), are included in the vector for principal component analysis in this modified method instead of the nine or seven RFI index original variables used in a normal PCA algorithm. The principal component with higher correlation and contribution to the original RFI index is the RFI-related principal component. In the absence of a reliable validation data set of the “true” RFI, the consistency in the identified RFI distribution obtained from this method compared to other independent methods, such as the spectral difference method, the normalized PCA method, and the double PCA method, give confidence to the RFI signals’ identification over land. The simple and reliable modified PCA method could successfully detect RFI not only in summer but also in winter AMSR-E data.

Head-related transfer function (HRTF) plays an important role in the construction of 3D auditory display. This paper presents an individual HRTF modeling method using deep neural networks based on spatial principal component analysis. The HRTFs are represented by a small set of spatial principal components combined with frequency and individual-dependent weights. By estimating the spatial principal components using deep neural networks and mapping the corresponding weights to a quantity of anthropometric parameters, we predict individual HRTFs in arbitrary spatial directions. The objective and subjective experiments evaluate the HRTFs generated by the proposed method, the principal component analysis (PCA) method, and the generic method. The results show that the HRTFs generated by the proposed method and PCA method perform better than the generic method. For most frequencies the spectral distortion of the proposed method is significantly smaller than the PCA method in the high frequencies but significantly larger in the low frequencies. The evaluation of the localization model shows the PCA method is better than the proposed method. The subjective localization experiments show that the PCA and the proposed methods have similar performances in most conditions. Both the objective and subjective experiments show that the proposed method can predict HRTFs in arbitrary spatial directions.

In this paper, the online correction model predictive control (MPC) strategy is presented for partial differential equation (PDE) unknown spatially-distributed systems (SDSs). The low-dimensional MIMO models are obtained using principal component analysis (PCA) method from the high-dimensional spatio-temporal data. Though the linear low-dimensional model is easy for control design, it is a linear approximation for nonlinear SDSs. Thus, the MPC strategy is proposed based on the online correction low-dimensional models, where the state at a previous time is used to correct the output of low-dimensional models and the spatial output is correct by the average deviation of the historical data. The simulations demonstrated show the accuracy and efficiency of the proposed methodologies.

A 3D object can be recovered from scanned point data, which requires accurate estimating normal directions of the object surface from the cloud data. Many point cloud processing algorithms rely on the accurate normal as input to generate an accurate 3D surface model. The neighborhood of a data point in its smooth region can be well approximated by a plane. However, the neighborhood of a feature point employed for the normal estimation is isotropic which would enclose points belonging to different surface patches across the sharp feature. In this paper, isotropic neighborhoods are segmented to search anisotropic neighborhoods for the accurate normal estimation. Normals and candidate feature points are first estimated by the principal component analysis (PCA) method. Neighborhoods of the feature point are then mapped into a Gaussian image. A k-means clustering algorithm is then used for the Gaussian image to identify an anisotropic sub-neighborhood for the data point. The normal of the candidate feature point is finally estimated by the anisotropic neighborhood with the PCA method. The proposed method can accurately estimate normal directions while preserving sharp features of the object surface. Applications have demonstrated the effectiveness of the proposed method.

Correlation between independent variables in multiple linear regression model called multicollinearity. One of the assumptions of multiple linear regression free from multicollinearity problem. Principal Component Analysis (PCA) method in this study aims to overcome the existence of multicollinearity in multiple linear regression and know the dominant factor to the research. PCA method has the advantage of clearing the correlation without losing the original variable. Case study a risk factor that affects the incidence of pneumonia infants in East Java 2014. This non reactive research because uses publication data of health profil of East Java. Result of this research multicollinearity problem in research data when detected by VIF/tolerance method. Variable of vitamin A coverage, measles immunization coverage and health service coverage are the variables that observed multicollinearity. A multicollinearity solution produces (F1) or new variable(coverage of vitamin A, immunization measles and health service), reduction of three variables that multicollinearity to not multicollinearity with VIF value of 1.608 &lt; 10. Results of this study also proves the weakness of PCA method in analyzing the significance. PCA method shows the most influencing factors on the incidence of pneumonia of children under five year. Dominant factor in this research coverage of infant health services covering, coverage of vitamin A and coverage of measles immunization. Coverage factor of health services has a coefficient matrix value of 0.890 or 89% more influential than other factor.

New approach to establish an object reference frame for dental arch in computer-aided surgical simulation