• Title/Summary/Keyword: principal components analysis

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AN EFFICIENT ALGORITHM FOR SLIDING WINDOW BASED INCREMENTAL PRINCIPAL COMPONENTS ANALYSIS

  • Lee, Geunseop
    • 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.

A Determination Method of Representative Points in the Space of Principal Components for Generation of Representative Cases (대표 인체 모델 생성을 위한 주성분 공간의 대표점 결정 기법 개발)

  • Jung, Kihyo
    • Journal of the Ergonomics Society of Korea
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    • v.37 no.3
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    • pp.291-300
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    • 2018
  • Objective: This study developed a determination method of representative points in the space of principal components to generate representative cases for anthropometric design and digital human simulation. Background: The advanced generation method using principal component analysis can create a group of representative cases that statistically accommodate a designated percentage of design target users. However, a specific determination method of representative points to generate representative cases has not been proposed in existing studies. Method: This study proposed a determination method of representative points on an n-dimensional ellipse formed in the space of principal components. The proposed method determined representative points on each principal component and on the combination of principal components using an optimization model. The performance of proposed method was evaluated by generating representative cases for anthropometric design and digital human simulation of airplane cockpit. Results: The proposed method selected eight representative points on an ellipse formed to accommodate 95% of design target users in the space of two principal components. The selected points represented one overall small user, two small users with different body proportion, two medium users with different body proportion, two large users with different body proportion, and one overall large user. Conclusion: The proposed method properly determined representative points on an ellipse in principal components. Application: The proposed method can be used to generate representative cases using principal component analysis for anthropometric design and digital human simulation.

Genetic Diversity of Soybean Pod Shape Based on Elliptic Fourier Descriptors

  • Truong Ngon T.;Gwag Jae-Gyun;Park Yong-Jin;Lee Suk-Ha
    • 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.

Application of varimax rotated principal component analysis in quantifying some zoometrical traits of a relict cow

  • Pares-Casanova, P.M.;Sinfreu, I.;Villalba, D.
    • 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.

Assessment and Classification of Korean Indigenous Corn Lines by Application of Principal Component Analysis (주성분분석에 의한 재래종 옥수수의 해석)

  • 이인섭;박종옥
    • 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.

A Taxonomy of Korean Isopyroideae (Ranunculaceae)

  • Lee, Nam-Sook;Yeau, Sung-Hee
    • Animal cells and systems
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    • v.2 no.4
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    • pp.439-449
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    • 1998
  • To discuss the taxonomic dispositions of Korean Isopyroideae (Ranunculaceae) taxa, principal components analysis and cluster analysis were performed using quantitative and qualitative morphological characters. The principal components analysis revealed that the size and number of ovule, ovary width, ratio of style length/ovary length, filament length, sepal size, style length, leaf size, and ovary length are important characters to distinguish Korean Isopyroideae taxa. The cluster and principal components analyses based on both quantitative and quantitative characters demonstrate that lsopyrum mandshuricum is more closely related to Enemion raddeanum than to Semiaquilegia adoxoides. Even though Enemion s not separated from Isopyrum by uantitative characters, they are distinguished by qualitative characters, suggesting that our taxa, Enemion, Semiaquilegia, Isopyrum and Aquilegia, should be recognized in Korean Isopyroideae. In addition, cluster analyses suggest that S. adoxoides could be separated from Aquilegia buergeriana var, oxysepala.

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A New Deletion Criterion of Principal Components Regression with Orientations of the Parameters

  • Lee, Won-Woo
    • Journal of the Korean Statistical Society
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    • v.16 no.2
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    • pp.55-70
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    • 1987
  • The principal components regression is one of the substitues for least squares method when there exists multicollinearity in the multiple linear regression model. It is observed graphically that the performance of the principal components regression is strongly dependent upon the values of the parameters. Accordingly, a new deletion criterion which determines proper principal components to be deleted from the analysis is developed and its usefulness is checked by simulations.

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Simple principal component analysis using Lasso (라소를 이용한 간편한 주성분분석)

  • Park, Cheolyong
    • 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.

New EM algorithm for Principal Component Analysis (주성분 분석을 위한 새로운 EM 알고리듬)

  • 안종훈;오종훈
    • Proceedings of the Korean Information Science Society Conference
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    • pp.529-531
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    • 2001
  • We present an expectation-maximization algorithm for principal component analysis via orthogonalization. The algorithm finds actual principal components, whereas previously proposed EM algorithms can only find principal subspace. New algorithm is simple and more efficient thant probabilistic PCA specially in noiseless cases. Conventional PCA needs computation of inverse of the covariance matrices, which makes the algorithm prohibitively expensive when the dimensions of data space is large. This EM algorithm is very powerful for high dimensional data when only a few principal components are needed.

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Procedure for the Selection of Principal Components in Principal Components Regression (주성분회귀분석에서 주성분선정을 위한 새로운 방법)

  • Kim, Bu-Yong;Shin, Myung-Hee
    • The Korean Journal of Applied Statistics
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    • v.23 no.5
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    • pp.967-975
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    • 2010
  • Since the least squares estimation is not appropriate when multicollinearity exists among the regressors of the linear regression model, the principal components regression is used to deal with the multicollinearity problem. This article suggests a new procedure for the selection of suitable principal components. The procedure is based on the condition index instead of the eigenvalue. The principal components corresponding to the indices are removed from the model if any condition indices are larger than the upper limit of the cutoff value. On the other hand, the corresponding principal components are included if any condition indices are smaller than the lower limit. The forward inclusion method is employed to select proper principal components if any condition indices are between the upper limit and the lower limit. The limits are obtained from the linear model which is constructed on the basis of the conjoint analysis. The procedure is evaluated by Monte Carlo simulation in terms of the mean square error of estimator. The simulation results indicate that the proposed procedure is superior to the existing methods.