• Communications for Statistical Applications and Methods
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• v.28 no.2
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• pp.135-150
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• 2021

We propose principal differential analysis based classification methods. Computations of squared multiple correlation function (RSQ) and principal differential analysis (PDA) scores are reviewed; in addition, we combine principal differential analysis results with the logistic regression for binary classification. In the numerical study, we compare the principal differential analysis based classification methods with functional principal component analysis based classification. Various scenarios are considered in a simulation study, and principal differential analysis based classification methods classify the functional data well. Gene expression data is considered for real data analysis. We observe that the PDA score based method also performs well.

• Communications for Statistical Applications and Methods
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• v.20 no.3
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• pp.175-184
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• 2013

Kernel principal component analysis(PCA) maps observations in nonlinear feature space to a reduced dimensional plane of principal components. We do not need to specify the feature space explicitly because the procedure uses the kernel trick. In this paper, we propose a graphical scheme to represent variables in the kernel principal component analysis. In addition, we propose an index for individual variables to measure the importance in the principal component plane.

• Journal of the Korean Geotechnical Society
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• v.26 no.10
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• pp.69-79
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• 2010

To detect abnormal events in slopes, Principal Component Analysis (PCA) is applied to the slope that was collapsed during monitoring. Principal component analysis is a kind of statical methods and is called non-parametric modeling. In this analysis, principal component score indicates an abnormal behavior of slope. In an abnormal event, principal component score is relatively higher or lower compared to a normal situation so that there is a big score change in the case of abnormal. The results confirm that the abnormal events and collapses of slope were detected by using principal component analysis. It could be possible to predict quantitatively the slope behavior and abnormal events using principal component analysis.

• Communications for Statistical Applications and Methods
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• v.11 no.1
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• pp.49-58
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• 2004

In this talk we proposed an asymptotic test for dimensionality in the latent variable model for probabilistic principal component analysis with missing values at random. Proposed algorithm is a sequential likelihood ratio test for an appropriate Normal latent variable model for the principal component analysis. Modified EM-algorithm is used to find MLE for the model parameters. Results from simulations and real data sets give us promising evidences that the proposed method is useful in finding necessary number of components in the principal component analysis with missing values at random.

• Journal of the Korean Mathematical Society
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• v.57 no.2
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• pp.401-414
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• 2020

It is computationally expensive to compute principal components from scratch at every update or downdate when new data arrive and existing data are truncated from the data matrix frequently. To overcome this limitations, incremental principal component analysis is considered. Specifically, we present a sliding window based efficient incremental principal component computation from a covariance matrix which comprises of two procedures; simultaneous update and downdate of principal components, followed by the rank-one matrix update. Additionally we track the accurate decomposition error and the adaptive numerical rank. Experiments show that the proposed algorithm enables a faster execution speed and no-meaningful decomposition error differences compared to typical incremental principal component analysis algorithms, thereby maintaining a good approximation for the principal components.

• Korean Journal of Veterinary Research
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• v.53 no.1
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• pp.7-10
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• 2013

A study was conducted to determine the interdependence among the conformation traits of 28 "Pallaresa" cows using principal component analysis. Originally 21 body linear measurements were obtained, from which eight traits are subsequently eliminated. From the principal components analysis, with raw varimax rotation of the transformation matrix, two principal components were extracted, which accounted for 65.8% of the total variance. The first principal component alone explained 51.6% of the variation, and tended to describe general size, while the second principal component had its loadings for back-sternal diameter. The two extracted principal components, which are traits related to dorsal heights and back-sternal diameter, could be considered in selection programs.

• Journal of Life Science
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• v.13 no.3
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• pp.343-348
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• 2003

This study was conducted to get basic information on the Korean local corn line collected from Busan City and Kyungnam Province, a total of 49 lines were selected and assessed by the principal component analysis method. In the result of principal component analysis for 7 characteristics, 67.4% and 86.3% of total variation could be appreciated by the first two and first four principal components, respectively. Contribution of characteristics to principal component was high at upper principal components and low at lower principal components. Biological meaning of principal component and plant types corresponding to the each principal component were explained clearly by the correlation coefficient between principal component and characteristics. The first principal component appeared to correspond to the size of plant and ear, and the duration of vegetative growing period. The second principal component appeared to correspond to the number of ear and tiller. But the meaning of the third and fourth principal components were not clear.

• Communications for Statistical Applications and Methods
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• v.10 no.3
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• pp.1057-1068
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• 2003

Results of using principal component analysis prior to cluster analysis are compared with results from applying agglomerative clustering algorithm alone. The retrieval ability of the agglomerative clustering algorithm is improved by using principal components prior to cluster analysis in some situations. On the other hand, the loss in retrieval ability for the agglomerative clustering algorithms decreases, as the number of informative variables increases, where the informative variables are the variables that have distinct information(or, necessary information) compared to other variables.

• Journal of the Korean Data and Information Science Society
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• v.24 no.3
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• pp.533-541
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• 2013

In this study, a simple principal component analysis using Lasso is proposed. This method consists of two steps. The first step is to compute principal components by the principal component analysis. The second step is to regress each principal component on the original data matrix by Lasso regression method. Each of new principal components is computed as the linear combination of original data matrix using the scaled estimated Lasso regression coefficient as the coefficients of the combination. This method leads to easily interpretable principal components with more 0 coefficients by the properties of Lasso regression models. This is because the estimator of the regression of each principal component on the original data matrix is the corresponding eigenvector. This method is applied to real and simulated data sets with the help of an R package for Lasso regression and its usefulness is demonstrated.

• Journal of the Korean Data and Information Science Society
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• v.14 no.3
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• pp.623-630
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• 2003

Recently, Tanaka(1988) derived two influence functions related to an eigenvalue problem $(A-\lambda_sI)\upsilon_s=0$ of real symmetric matrix A and used them for sensitivity analysis in principal component analysis. In this paper, we deal with the perturbation expansions up to quadratic terms of the same functions and discuss the application to sensitivity analysis in principal component regression analysis(PCRA). Numerical example is given to show how the approximation improves with the quadratic term.