• Title, Summary, Keyword: partial least squares

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A Study on Process Optimization Using Partial Least Squares Response Surface Function (편최소제곱 반응표면함수를 이용한 공정 최적화에 관한 연구)

  • Park, Sung-Hyun;Choi, Um-Moon;Park, Chang-Soon
    • Journal of the Korean Society for Quality Management
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    • v.27 no.2
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    • pp.237-250
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    • 1999
  • Response surface analysis has been a popular tool conducted by engineers in many processes. In this paper, response surface function, named partial least squares response surface function is proposed. Partial least squares response surface function is a function of partial least squares components and the response surface modeling is used in either a first-order or a second-order model. Also, this approach will have the engineers be able to do the response surface modeling and the process optimization even when the number of experimental runs is less than the number of model parameters. This idea is applied to the nondesign data and an application of partial least squares response surface function to the process optimization is considered.

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Prediction of Flash Point of Binary Systems by Using Multivariate Statistical Analysis (다변량 통계 분석법을 이용한 2성분계 혼합물의 인화점 예측)

  • Lee, Bom-Sock;Kim, S.Y.;Chung, C.B.;Choi, S.H.
    • Journal of the Korean Institute of Gas
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    • v.10 no.4
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    • pp.29-33
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    • 2006
  • Estimation of process safety is important in the chemical process design. Prediction for flash points of flammable substances used in chemical processes is the one of the methods for estimating process safety. Flash point is the property used to examine the potential for the fire and explosion hazards of flammable substances. In this paper, multivariate statistical analysis methods(partial least squares(PLS) quadratic partial least squares(QPLS)) using experimental data is suggested for predicting flash points of flammable substances of binary systems. The prediction results are compared with the values calculated by laws of Raoult and Van Laar equation.

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LEAST-SQUARES SPECTRAL COLLOCATION PARALLEL METHODS FOR PARABOLIC PROBLEMS

  • SEO, JEONG-KWEON;SHIN, BYEONG-CHUN
    • 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.

Missing Values Estimation for Time Course Gene Expression Data Using the Sequential Partial Least Squares Regression Fitting (순차적 부분최소제곱 회귀적합에 의한 시간경로 유전자 발현 자료의 결측치 추정)

  • Kim, Kyung-Sook;Oh, Mi-Ra;Baek, Jang-Sun;Son, Young-Sook
    • 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.

Unified Non-iterative Algorithm for Principal Component Regression, Partial Least Squares and Ordinary Least Squares

  • Kim, Jong-Duk
    • Journal of the Korean Data and Information Science Society
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    • v.14 no.2
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    • pp.355-366
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    • 2003
  • A unified procedure for principal component regression (PCR), partial least squares (PLS) and ordinary least squares (OLS) is proposed. The process gives solutions for PCR, PLS and OLS in a unified and non-iterative way. This enables us to see the interrelationships among the three regression coefficient vectors, and it is seen that the so-called E-matrix in the solution expression plays the key role in differentiating the methods. In addition to setting out the procedure, the paper also supplies a robust numerical algorithm for its implementation, which is used to show how the procedure performs on a real world data set.

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A modified partial least squares regression for the analysis of gene expression data with survival information

  • Lee, So-Yoon;Huh, Myung-Hoe;Park, Mira
    • 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.

Shrinkage Structure of Ridge Partial Least Squares Regression

  • Kim, Jong-Duk
    • 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.

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A Method for Screening Product Design Variables for Building A Usability Model : Genetic Algorithm Approach (사용편의성 모델수립을 위한 제품 설계 변수의 선별방법 : 유전자 알고리즘 접근방법)

  • Yang, Hui-Cheol;Han, Seong-Ho
    • 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.

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Simultaneous Kinetic Spectrophotometric Determination of Sulfite and Sulfide Using Partial Least Squares (PLS) Regression

  • Afkhami, Abbas;Sarlak, Nahid;Zarei, Ali Reza;Madrakian, Tayyebeh
    • 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.