• Communications for Statistical Applications and Methods
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• v.31 no.2
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• pp.235-246
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• 2024

In high-dimensional data analysis, sufficient dimension reduction (SDR) has been considered as an attractive tool for reducing the dimensionality of predictors while preserving regression information. The principal support vector machine (PSVM) (Li et al., 2011) offers a unified approach for both linear and nonlinear SDR. This article comprehensively explores a variety of SDR methods based on the PSVM, which we call principal machines (PM) for SDR. The PM achieves SDR by solving a sequence of convex optimizations akin to popular supervised learning methods, such as the support vector machine, logistic regression, and quantile regression, to name a few. This makes the PM straightforward to handle and extend in both theoretical and computational aspects, as we will see throughout this article.

• The Korean Journal of Applied Statistics
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• v.30 no.1
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• pp.135-145
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• 2017

Principal component analysis (PCA) describes the variation of multivariate data in terms of a set of uncorrelated variables. Since each principal component is a linear combination of all variables and the loadings are typically non-zero, it is difficult to interpret the derived principal components. Sparse principal component analysis (SPCA) is a specialized technique using the elastic net penalty function to produce sparse loadings in principal component analysis. When data are structured by groups of variables, it is desirable to select variables in a grouped manner. In this paper, we propose a new PCA method to improve variable selection performance when variables are grouped, which not only selects important groups but also removes unimportant variables within identified groups. To incorporate group information into model fitting, we consider a hierarchical lasso penalty instead of the elastic net penalty in SPCA. Real data analyses demonstrate the performance and usefulness of the proposed method.

• Hwankyungkyoyuk
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• v.15 no.1
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• pp.31-50
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• 2002

The purpose of this study were the effects of principal related factors on the choice of the subject of environmental education in curriculum of middle and high school. We select 495 middle and high schools from 3 district of Chungbuk, Daejeon and Incheon. And, we send the questionnaires to the principals and withrowed answer questionnaire of 313(63.2%) from them. From the analysis of questionnaire, we obtained the reliability coefficient cronbach alpha value(0.8684). The results of this research as fallows : the principal factors that had chosen the subject of environmental education have significantly higher knowledge, recognition, attitude and practice than that not choiced on the subject of environmental education(p=0.000). The correlation between principal's attitude on the choice of the subject of environmental education and choice state of school was significantly higher than the other factors, and it's correlation coefficient was 0.328(p<0.01). Principal's attitude factor on the choice of the subject of environmental education have a great influence on his practice factor of them, and standard regression coefficient was 0.642(p<0.001). We found that principal's attitude factor on the choice of the subject of environmental education to have a great influence on the choice state of school in view of the results so far achieved.

• KOREAN JOURNAL OF CROP SCIENCE
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• v.50 no.1
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• pp.60-66
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• 2005

Pod shape of twenty soybean (Glycine max L. Merrill) genotypes was evaluated quantitatively by image analysis using elliptic Fourier descriptors and their principal components. The closed contour of each pod projection was extracted, and 80 elliptic Fourier coefficients were calculated for each contour. The Fourier coefficients were standardized so that they were invariant of size, rotation, shift, and chain code starting point. Then, the principal components on the standardized Fourier coefficients were evaluated. The cumulative contribution at the fifth principal component was higher than $95\%$, indicating that the first, second, third, fourth, and fifth principal components represented the aspect ratio of the pod, the location of the pod centroid, the sharpness of the two pod tips and the roundness of the base in the pod contour, respectively. Analysis of variance revealed significant genotypic differences in these principal components and seed number per pod. As the principal components for pod shape varied continuously, pod shape might be controlled by polygenes. It was concluded that principal component scores based on elliptic Fourier descriptors yield seemed to be useful in quantitative parameters not only for evaluating soybean pod shape in a soybean breeding program but also for describing pod shape for evaluating soybean germplasm.

• Journal of the Korean Statistical Society
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• v.25 no.1
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• pp.67-80
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• 1996

Factor analysis is a multivariate technique for describing the in-terrelationship among many variables in terms of a few underlying but unobservable random variables called factors. There are various approaches for this factor analysis. In particular, principal factor analysis is one of the most popular methods. This follows the mathematical algorithm of the principal component analysis based on the singular value decomposition. But it is known that the singular value decomposition is not resistant, i.e., it is very sensitive to small changes in the input data. In this article, using the resistant singular value decomposition of Choi and Huh (1994), we derive a resistant principal factor analysis relatively little influenced by notable observations.

• The Pure and Applied Mathematics
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• v.30 no.4
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• pp.397-406
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• 2023

Let R be a commutative ring with identity, X be an indeterminate over R, and R[X] be the polynomial ring over R. In this paper, we study when R[X] is a radically principal ideal ring. We also study the t-operation analog of a radically principal ideal domain, which is said to be t-compactly packed. Among them, we show that if R is an integrally closed domain, then R[X] is t-compactly packed if and only if R is t-compactly packed and every prime ideal Q of R[X] with Q ∩ R = (0) is radically principal.

• The Journal of the Acoustical Society of Korea
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• v.15 no.1
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• pp.23-33
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• 1996

In this paper we point out that if the classical principal domain for bispectra is utilized to determine a second-order Volterra model's output, such and output will be incomplete. This deficiency is associated with the periodic nature of the DFT. For this reason, the objective of this paper is to present an "extended" principal domain for Volterra kernels which leads to an improved estimate of the nonlinear system's response. In order to define the extended principal domain, we derive a new discrete frequency-domain Volterra model from a discrete time-domain Volterra model utilizing 2-dimensional DFT and the relationship between the quadratic component of the Volterra model and a square filter. The effect of the extended domain on the model output is interpreted in terms of the periodicity of DFT. Through computer simulations, we demonstrate the effects of the extended principal domain on the Volterra modeling. The simulation results indicate that the extended principal domain plays and important role in computing Volterra model outputs and estimating Volterra model coefficients.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.24 no.5
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• pp.1013-1022
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• 2014

Correlation Power Analysis (CPA) is a type of Side-Channel Analysis (SCA) that extracts the secret key using the correlation coefficient both side-channel information leakage by cryptography device and intermediate value of algorithms. Attack performance of the CPA is affected by noise and temporal synchronization of power consumption leaked. In the recent years, various researches about the signal processing have been presented to improve the performance of power analysis. Among these signal processing techniques, compression techniques of the signal based on Principal Component Analysis (PCA) has been presented. Selection of the principal components is an important issue in signal compression based on PCA. Because selection of the principal component will affect the performance of the analysis. In this paper, we present a method of selecting the principal component by using the correlation of the principal components and the power consumption is high and a CPA technique based on the principal component that utilizes the feature that the principal component has different. Also, we prove the performance of our method by carrying out the experiment.

• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.12
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• pp.3372-3381
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• 1995

An equilibrium analysis was carried out to determine principal species of heavy metals in waste incineration and their behaviors with variation of temperature, chlorine concentration, excess air ratio, and C/H ratio. The waste was assumed as a compound of hydrocarbon fuel, chlorine, and metals. Calculated results showed that the most important parameter to determine the principal species was temperature. Chlorine concentration also affected on mole fractions of the principal species. Generally principal species at high temperature were chlorides while there were some metals of which principal species were oxides. At low temperature mole fractions of the principal species increased, but at high temperature mole fractions of some metal species decreased. C/H ratio of the hydrocarbon fuel and excess air ratio had little effect on mole fractions of the metal species, compared to the temperature and chlorine concentration.

• Communications for Statistical Applications and Methods
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• v.18 no.6
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• pp.761-770
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• 2011

Robust principal components regression is suggested to deal with both the multicollinearity and outlier problem. A main aspect of the robust principal components regression is the selection of an optimal set of principal components. Instead of the eigenvalue of the sample covariance matrix, a selection criterion is developed based on the condition index of the minimum volume ellipsoid estimator which is highly robust against leverage points. In addition, the least trimmed squares estimation is employed to cope with regression outliers. Monte Carlo simulation results indicate that the proposed criterion is superior to existing ones.