• 호남수학학술지
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• 제37권3호
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• pp.299-315
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• 2015

In this paper, we study the first-order system least-squares (FOSLS) spectral method for parabolic partial differential equations. There were lots of least-squares approaches to solve elliptic partial differential equations using finite element approximation. Also, some approaches using spectral methods have been studied in recent. In order to solve the parabolic partial differential equations in parallel, we consider a parallel numerical method based on a hybrid method of the frequency-domain method and first-order system least-squares method. First, we transform the parabolic problem in the space-time domain to the elliptic problems in the space-frequency domain. Second, we solve each elliptic problem in parallel for some frequencies using the first-order system least-squares method. And then we take the discrete inverse Fourier transforms in order to obtain the approximate solution in the space-time domain. We will introduce such a hybrid method and then present a numerical experiment.

• 응용통계연구
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• 제21권2호
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• pp.275-290
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• 2008

마이크로어레이 유전자 발현 자료는 대용량이며 또한 관측 과정이 복잡하여 결측치가 빈번하게 발생된다. 본 논문에서는 관측 시점 간에 상관성을 갖는 시간경로 유전자 발현 자료에 대한 결측치 추정을 위하여 순차적 부분최소제곱(sequential partial least squares: SPLS) 회귀적합 방법을 제안한다. 이는 순차적 기법과 부분최소제곱(partial least squares: PLS) 회귀적합 방법을 결합시킨 것이다. 세 가지의 이스트(yeast) 시간경로 자료들에 대한 몇 가지 모의실험을 통하여 제안된 결측치 추정방법의 유용성을 평가한다.

• Journal of the Korean Data and Information Science Society
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• 제25권5호
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• pp.1151-1160
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• 2014

In DNA microarray studies, the number of genes far exceeds the number of samples and the gene expression measures are highly correlated. Partial least squares regression (PLSR) is one of the popular methods for dimensional reduction and known to be useful for the classifications of microarray data by several studies. In this study, we suggest a modified version of the partial least squares regression to analyze gene expression data with survival information. The method is designed as a new gene selection method using PLSR with an iterative procedure of imputing censored survival time. Mean square error of prediction criterion is used to determine the dimension of the model. To visualize the data, plot for variables superimposed with samples are used. The method is applied to two microarray data sets, both containing survival time. The results show that the proposed method works well for interpreting gene expression microarray data.

• 대한인간공학회지
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• 제20권1호
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• pp.45-62
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• 2001

This study suggests a genetic algorithm-based partial least squares (GA-based PLS) method to select the design variables for building a usability model. The GA-based PLS uses a genetic algorithm to minimize the root-mean-squared error of a partial least square regression model. A multiple linear regression method is applied to build a usability model that contains the variables seleded by the GA-based PLS. The performance of the usability model turned out to be generally better than that of the previous usability models using other variable selection methods such as expert rating, principal component analysis, cluster analysis, and partial least squares. Furthermore, the model performance was drastically improved by supplementing the category type variables selected by the GA-based PLS in the usability model. It is recommended that the GA-based PLS be applied to the variable selection for developing a usability model.

• Journal of the Korean Data and Information Science Society
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• 제22권5호
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• pp.931-940
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• 2011

분류분석은 학습표본으로부터 분류규칙을 도출한 후 새로운 표본에 적용하여 특정 범주로 분류하는 방법이다. 데이터의 복잡성에 따라 다양한 분류분석 방법이 개발되어 왔지만, 데이터 차원이 높고 변수간 상관성이 높은 경우 정확하게 분류하는 것은 쉽지 않다. 본 연구에서는 데이터차원이 상대적으로 높고 변수간 상관성이 높을 때 강건한 분류방법을 제안하고자 한다. 부분최소자승법은 연속형데이터에 사용되는 기법으로서 고차원이면서 독립변수간 상관성이 높을 때 예측력이 높은 통계기법으로 알려져 있는 다변량 분석기법이다. 벌점 부분최소자승법을 이용한 분류방법을 실제데이터와 시뮬레이션을 적용하여 성능을 비교하고자 한다.

• Bulletin of the Korean Chemical Society
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• 제27권6호
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• pp.863-868
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• 2006

The partial least squares (PLS-1) calibration model based on spectrophotometric measurement, for the simultaneous determination of sulfite and sulfide is described. This method is based on the difference between the rate of the reaction of sulfide and sulfite with Malachite Green in pH 7.0 buffer solution and at 25 ${^{\circ}C}$. The absorption kinetic profiles of the solutions were monitored by measuring the decrease in the absorbance of Malachite Green at 617 nm in the time range 10-180 s after initiation of the reactions with 2 s intervals. The experimental calibration matrix for partial least squares (PLS-1) calibration was designed with 24 samples. The cross-validation method was used for selecting the number of factors. The results showed that simultaneous determination could be performed in the range 0.030-1.5 and 0.030-1.2 $\mu$g m$L ^{-1}$ for sulfite and sulfide, respectively. The proposed method was successfully applied to simultaneous determination of sulfite and sulfide in water samples and whole human blood.

• Journal of the Korean Data and Information Science Society
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• 제18권2호
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• pp.327-344
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• 2007

다중공선성의 데이터에 사용되는 대표적인 편향회귀방법은 능형회귀(RR), 주성분회귀(PCR), 부분최소제곱회귀(PLS) 등이다. 이 회귀방법들은 계수베거 추정량의 놈(norm)이 모두 보통 최소제곱회귀(OLS)의 추정량의 놈보다 작아진다는 의미에서 축소회귀라 부른다. 새로운 회귀방법으로 RR과 PCR을 결합한 능형주성분회귀(RPCR)가 있고 RR과 PLS를 결합한 능형부분최소제곱회귀(RPLS)가 있으며 이들도 또한 축소회귀이다. 이들 추정량은 X'X의 고유벡터들의 선형결합으로 나타낼 수 있고 따라서 각 고유방향에서 OLS에 비해 얼마나 축소되는지를 연구할 수 있다. 본 논문에서는 먼저 이들 추정량을 일반적인 축소인자의 식으로 나타내고 이를 이용하여 MSE의 일반식을 구하였으며 PLS 추정량의 MSE 식도 구하였다. 그리고 RPLS의 축소인자 식을 두 가지 다른 형태로 유도하였다. RPLS의 경우도 이 축소인자 식을 MSE의 일반식에 대입하면 MSE 식이 바로 얻어진다. 그러나 PLS나 RPLS의 축소인자는 y의 복잡한 비선형이 되어 결정적이 아니므로 이들 추정량의 MSE는 근사적인 식이라 할 수 있다. 따라서 PLS나 RPLS를 평가하기 위해 이 MSE를 사용하는 것은 제한적이며, 경험적인 방법으로 이들 회귀의 수행성을 평가하는 것이 필요하다. 다중공선성의 대표적인 데이터인 근적외선 분광 데이터를 이용하여 이 유도된 회귀의 축소인자 값이 인자수에 따라 어떻게 변화하는지와 전체적인 축소 비율도 살펴보았다. 이들의 축소 형태를 잘 이해하면 회귀방법들의 예측력과 안정성을 파악하는데 많은 도움이 되리라 판단된다.

• 제어로봇시스템학회논문지
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• 제9권2호
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• pp.159-167
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• 2003

This study suggests the hybrid fault diagnosis method of signed digraph (SDG) and partial least squares (PLS). SDG offers a simple and graphical representation for the causal relationships between process variables. The proposed method is based on SDG to utilize the advantage that the model building needs less information than other methods and can be performed automatically. PLS model is built on local cause-effect relationships of each variable in SDG. In addition to the current values of cause variables, the past values of cause and effect variables are inputted to PLS model to represent the Process armies. The measured value and predicted one by dynamic PLS are compared to diagnose the fault. The diagnosis example of CSTR shows the proposed method improves diagnosis resolution and facilitates diagnosis of masked multiple-fault.

• Communications for Statistical Applications and Methods
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• 제30권1호
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• pp.65-73
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• 2023

Contemporary biomedical data often involve an ill-posed problem owing to small sample size and large number of multi-collinear variables. Partial least squares (PLS) method could be a plausible alternative to an ill-conditioned ordinary least squares. However, in the case of a PLS model that includes a random-effect, how to deal with a random-effect or mixed effects remains a widely open question worth further investigation. In the present study, we propose a modified multivariate PLS method implementing mixed-effect model (PLSM). The advantage of PLSM is its versatility in handling serial longitudinal data or its ability for taking a randomeffect into account. We conduct simulations to investigate statistical properties of PLSM, and showcase its real clinical application to predict treatment outcome of esthetic surgical procedures of human faces. The proposed PLSM seemed to be particularly beneficial 1) when random-effect is conspicuous; 2) the number of predictors is relatively large compared to the sample size; 3) the multicollinearity is weak or moderate; and/or 4) the random error is considerable.

• Journal of the Korean Data and Information Science Society
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• 제18권1호
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• pp.51-61
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• 2007

Ridge regression (RR), principal component regression (PCR) and partial least squares regression (PLS) are among popular regression methods for collinear data. While RR adds a small quantity called ridge constant to the diagonal of X'X to stabilize the matrix inversion and regression coefficients, PCR and PLS use latent variables derived from original variables to circumvent the collinearity problem. One problem of PCR and PLS is that they are very sensitive to overfitting. A new regression method is presented by combining RR and PCR and PLS, respectively, in a unified manner. It is intended to provide better predictive ability and improved stability for regression models. A real-world data from NIR spectroscopy is used to investigate the performance of the newly developed regression method.