• Honam Mathematical Journal
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• v.37 no.3
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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.

• The Korean Journal of Applied Statistics
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• v.21 no.2
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• pp.275-290
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• 2008

The size of microarray gene expression data is very big and its observation process is also very complex. Thus missing values are frequently occurred. In this paper we propose the sequential partial least squares(SPLS) regression fitting method to estimate missing values for time course gene expression data that has correlations among observations over time points. The SPLS method is to combine the sequential technique with the partial least squares(PLS) regression fitting method. The usefulness of method proposed is evaluated through some simulation study for three yeast time course data.

• Journal of the Korean Data and Information Science Society
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• v.25 no.5
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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.

• Journal of the Ergonomics Society of Korea
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• v.20 no.1
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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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• v.22 no.5
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• pp.931-940
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• 2011

Classification is to generate a rule of classifying objects into several categories based on the learning sample. Good classification model should classify new objects with low misclassification error. Many types of classification methods have been developed including logistic regression, discriminant analysis and tree. This paper presents a new classification method using penalized partial least squares. Penalized partial least squares can make the model more robust and remedy multicollinearity problem. This paper compares the proposed method with logistic regression and PCA based discriminant analysis by some real and artificial data. It is concluded that the new method has better power as compared with other methods.

• Bulletin of the Korean Chemical Society
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• v.27 no.6
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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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• v.18 no.2
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• pp.327-344
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• 2007

Ridge partial least squares regression (RPLS) is a regression method which can be obtained by combining ridge regression and partial least squares regression and is intended to provide better predictive ability and less sensitive to overfitting. In this paper, explicit expressions for the shrinkage factor of RPLS are developed. The structure of the shrinkage factor is explored and compared with those of other biased regression methods, such as ridge regression, principal component regression, ridge principal component regression, and partial least squares regression using a near infrared data set.

• Journal of Institute of Control, Robotics and Systems
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• v.9 no.2
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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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• v.30 no.1
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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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• v.18 no.1
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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.