• Communications for Statistical Applications and Methods
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• 제22권2호
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• pp.173-180
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• 2015

We propose a selection procedure of principal components in principal component regression. Our method selects principal components using variable selection procedures instead of a small subset of major principal components in principal component regression. Our procedure consists of two steps to improve estimation and prediction. First, we reduce the number of principal components using the conventional principal component regression to yield the set of candidate principal components and then select principal components among the candidate set using sparse regression techniques. The performance of our proposals is demonstrated numerically and compared with the typical dimension reduction approaches (including principal component regression and partial least square regression) using synthetic and real datasets.

• Journal of the Korean Statistical Society
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• 제16권2호
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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.

• 대한수학회지
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• 제57권2호
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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.

• Journal of the Korean Data and Information Science Society
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• 제8권2호
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• pp.127-134
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• 1997

A method is proposed for the choice of the number of principal components in principal component regression based on the predicted error sum of squares. To do this, we approximately evaluate that statistic using a linear approximation based on the perturbation expansion. In this paper, we apply the proposed method to various data sets and discuss some properties in choosing the number of principal components in principal component regression.

• Journal of the Korean Data and Information Science Society
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• 제10권1호
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• pp.163-172
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• 1999

We propose a cross-validatory method for the choice of the number of principal components in principal component regression based on the magnitudes of correlations with y. There are two different manners in choosing principal components, one is the order of eigenvalues(Shin and Moon, 1997) and the other is that of correlations with y. We apply our method to various data sets and compare results of those two methods.

• 응용통계연구
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• 제23권5호
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• pp.967-975
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• 2010

데이터마이닝 분야에서의 회귀모형에는 연관성이 높은 설명변수들이 포함되어 다중공선성을 유발하는 경우가 많은데, 다중공선성이 야기하는 문제를 해결하기 위하여 주성분회귀분석을 적용할 수 있다. 이 분석에서는 적절한 주성분을 선정하는 과정이 핵심인데, 기존의 선정방법들은 다중공선성을 잘 해결하지 못하거나 모형의 적합성을 저하시킨다는 지적을 받고 있다. 따라서 본 논문에서는 다중공선성 문제와 적합성 저하 현상을 동시에 해결할 수 있는 새로운 선정방법을 제안하였다. 다중공선성에 의해 최소제곱추정량의 분산이 팽창되는 문제를 주성분회귀에 의해 해결할 수 있지만, 주성분의 일부를 선정함에 따라 발생하는 편의도 동시에 통제해야 한다. 따라서 주성분회귀추정량의 평균제곱오차를 최소가 되게 하는 상태지수를 측정하고, 이 값에 영향을 미치는 주요 요인들을 컨조인트분석에 의해 파악하여 주성분 선정기준 모형을 구축하였다. 선정기준의 상한과 하한을 설정하고, 상태지수가 상한을 초과하면 해당 주성분을 제외시키고, 하한에 미달하면 해당 주성분을 포함시킨다. 그리고 상한과 하한 사이의 상태지수에 대응하는 주성분들에 대해서는 일반화선형검정을 순차적으로 적용하여 주성분을 선정하는 방법이다.

• 한국작물학회지
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• 제50권1호
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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.

• 대한인간공학회지
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• 제10권2호
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• pp.31-42
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• 1991

To understand the shape of the neck in a view of garment planning, principal component analysis has been appliedto the measurement of the neck. The neck surface development and the cross sections of the neck have been observed. The materials consist of the body mearsurements, the neck surface developments and the cross sec- tions of the necks of a total of 108 korean woman students. The difference between the right side and the left side of the neck has not been reconginiged. But the differenece among the height of the front neck point, that of the side neck point and that of the back neck point has been recognized. 2. The initial 41 items have been found having variety and duplication. So two criteria have been made to solve those problems and the selection of 34 items have been made by each criterion. 3. 43 and 34 items have been compared by means of accumulative ratios of contribution and of clearness within the meaning of principal component. As a result, 34 measurement items have been further anylysis. 4. As a result of principal component analysis on the 34 items, the four principal components have been found obtaines and inter-preted. The four principal components are 1) the thick of the neck, 2) the front neck-line on the waist basic pattern, basic pattern, 3) the shape of the neck surface development, and 4) the back neck-line on the waist basic pattern. 5. According to the graphic informations concerning these principal components, the meaning of these four principal components has been grasped on the visual. As a result, there is a large individual difference in the shape of neck.

• 생명과학회지
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• 제13권3호
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• pp.343-348
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• 2003

육종재료를 얻기 위하여 부산·경남지역에서 수집된 재래종 옥수수 49 계통을 선발하여 본 실험을 실시하였다. 본 시료는 주성분분석을 이용하여 재래종 옥수수를 해석하고 계통분류를 실시하였던 바 다음과 같은 결과를 얻었다. 7 개의 형질을 이용하여 실시한 주성분분석에서는 제 4주성분까지를 가지고 전체 변동의 86.3%를 설명할 수 있었고, 제 2 주성분까지는 전체 변동의 67.4%를 설명할 수 있었다. 주성분에 대한 형질들의 기여율은 형질에 따라 달랐고 상위 주성분에서 켰으며 하위 주성분에서 작았다. 주성분과 형질과의 상관계수는 주성분의 생물학적 의의와 주성분에 대응한 식물체의 형을 명확히 하였는데 제 1 주성분은 식물체의 크기 및 생장기간에 관련된 주성분이었고, 제2주성분은 이삭수와 분얼수에 관련된 주성분이었다. 제 3주성분과 제 4 주성분에서는 형질간에는 유의성이 인정되지 않았다.

• 대한수의학회지
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• 제53권1호
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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.